Literature Naturalism in Huck Finn Research Paper

Man versus Nature In the story â€Å"The adventure of Huckleberry Finn† by Mark Twain, many of the characters were facing some tough choices which were to either do what society believed in or do what they believed is right. Among the people that was mostly dominated by such choices, Huck Finn was the most critical character to always have to make these choices. In many occasions, he found himself on the spot to satisfy society but denied to do so because he does not care of what society think of him. Referring to the story can better help discussing the concept of man v. ociety that is so prevalent in Huckleberry Finn. The concept of man versus society that is so prevalent in Huckleberry Finn can be seen in many aspects. Huckleberry Finn in a way faces many aspects of society, which gives him the struggle of choosing his own individuality over society. In the beginning of the novel, Huck practically raises himself and relies on his instincts to guide him through his life on E arth. In the world as Huckleberry Finn views it, society has corrupted the notion of justice and morality  to fit the needs of its people in the nation at a particular period of time.In the very beginning of the novel † the Adventure of Huckleberry Finn† Huck plainly states that he did not wish to conform to society. Huckleberry Finn states that â€Å" the widow Douglas she took me for her son , and allowed she would sivilize me; but it was rough living in the house all the time, considering how dismal regular and descent the widow was in all her ways; and so when I couldn't stand it no longer, I lit out. I got into my old rags, and my sugar-hogshead again and was free and satisfied†( Mark Twain 102).Huck did not really want to live that civilize life miss Watson was trying to get him to lived. she would constantly give him direct orders like † don't put your feet up there Huckleberry† and † don't scrunch up like that , Huckleberry -set up stra ight † (102). she tried tirelessly to get Huck to be the way society expect him to be. it just wasn't working. After realizing this component of Huck’s personality, we can further identify the development of Huck as an individual that is outside of societies liking.We find next in the book that Huck’s own instincts tend to hold him in a higher moral standard than those of society. We first see this in the novel with Huckleberry’s decision to help free Jim, a known slave, is an example of one such occurrence. Huckleberry Finn recognizes Jim as a human being, but is actually fighting the beliefs bestowed upon him by society that believes slaves should not be free. However, it is even more important to realize though that Huckleberry’s decision creates the conflict between society and him.But, what Huckleberry Finn does not realize is that his decision defines his personal justice, the righteousness, and even the heroism of his own self that is develop ing. when Jim was captured, he decided that he will do the right thing by sending miss Watson a letter to tell her where her nigger was. He sat and think of all the bad thing that he had done and he mentioned how society think of helping a slave to escape was sin. Despite all of that thinking, his words were † All right, then, I'll go to hell† (239). Most of the time, society set the rules of how people suppose to live their live.In the face of the majority, you will be considered as immoral, out of order, miss-behave if one fail to follow those clear paths that been set. after reading this story, it is clear for one to see that he/she can distinguish his/herself from society. We can follow our own path just like Huck, and do what we think is right even if it hurt society. 01 November 2012Works Cited Twain, Mark. â€Å"The Adventure of Huckleberry Finn. † Vol. 2. The Norton Anthology. Ed. Nina Baym. Shorter seventh edition ed. New York: Norton & Company, 1884. Print.

Flight Control Systems

Flight Control Systems W. -H. Chen Department of Aeronautical and Automotive Engineering Loughborough University 2 Flight Control Systems by W. -H. Chen, AAE, Loughborough Contents 1 Introduction 1. 1 Overview of the Flight Envelope 1. 2 Flight control systems . . . . . . 1. 3 Modern Control . . . . . . . . . . 1. 4 Introduction to the course . . . . 1. 4. 1 Content . . . . . . . . . . 1. 4. 2 Tutorials and coursework 1. 4. 3 Assessment . . . . . . . . 1. 4. 4 Lecture plan . . . . . . . 1. 4. 5 References . . . . . . . . . 7 7 8 8 9 9 10 10 10 11 13 13 16 16 17 17 18 19 19 20 20 20 20 20 24 25 25 25 25 26 27 27 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Longitudinal response to the control 2. 1 Longitudinal dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 2. 2 State space description . . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 1 State variables . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 2 General state space model . . . . . . . . . . . . . . . . . . . 2. 3 Longitudinal state space model . . . . . . . . . . . . . . . . . . . . 2. 3. 1 Numerical example . . . . . . . . . . . . . . . . . . . . . . . 2. 3. 2 The choice of state variables . . . . . . . . . . . . . . . . . . 2. 4 Aircraft dynamic behaviour simulation using state space models . 2. 4. 1 Aircraft response without control . . . . . . . . . . . . . . . 2. 4. 2 Aircraft response to controls . . . . . . . . . . . . . . . . . 2. 4. 3 Aircraft response under both initial conditions and controls 2. 5 Longitudinal response to the elevator . . . . . . . . . . . . . . . . 2. 6 Transfer of state space models into transfer functions . . . . . . . . 2. 6. 1 From a transfer function to a state space model . . . . . . . 2. 7 Block diagram representation of state space models . . . . . . . . . 2. 8 Static stability and dynamic modes . . . . . . . . . . . . . . . . . . 2. 8. 1 Aircraft stability . . . . . . . . . . . . . . . . . . . . . . . . 2. 8. 2 Stability with FCS augmentation . . . . . . . . . . . . . . . 2. 8. 3 Dynamic modes . . . . . . . . . . . . . . . . . . . . . . . . . 2. 9 Reduced models of longitudinal dynamics . . . . . . . . . . . . . . 2. 9. Phugoid approximation . . . . . . . . . . . . . . . . . . . . 2. 9. 2 Short period approximation . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Lateral response to the controls 3. 1 Lateral state space models . . . . . . . . . . . . 3. 2 Transient response to aileron and rudder . . . . 3. 2. 1 Numerical example . . . . . . . . . . . . 3 . 2. 2 Lateral response and transfer functions 3. 3 Reduced order models . . . . . . . . . . . . . . 3. 3. 1 Roll subsidence . . . . . . . . . . . . . . 3. 3. Spiral mode approximation . . . . . . . 3. 3. 3 Dutch roll . . . . . . . . . . . . . . . . . 3. 3. 4 Three degrees of freedom approximation 3. 3. 5 Re-formulation of the lateral dynamics . CONTENTS 31 31 33 33 33 35 38 38 39 39 40 43 43 46 46 46 46 48 49 49 55 55 55 58 58 60 60 61 62 65 66 66 67 68 68 68 69 69 69 70 70 71 71 73 73 73 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Stability Augmentation Systems 4. 1 State space design techniques . . . . . . . . . . . 4. 2 Longitudinal stability augmentation systems . . . 4. 2. 1 The choice of feedback variables . . . . 4. 2. 2 SAS for short period dynamics . . . . . . 4. 3 Lateral stability augmentation systems . . . . . . 4. 3. 1 Yaw rate feedback for rudder control . . . 4. 3. 2 Roll feedback for aileron control . . . . . 4. 3. 3 Integration of lateral directional feedback 5 Autopilots 5. 1 Pitch holding autopilot . . . . . . . . . . . . . . . . . . . . . . . 5. 1. 1 phugoid suppress . . . . . . . . . . . . . . . . . . . . . . 5. 1. 2 Eliminate the steady error with integration . . . . . . . 5. 1. 3 Improve transient performance with pitch rate feedback 5. 2 Height holding autopilot . . . . . . . . . . . . . . . . . . . . . . 5. . 1 An intuitive height holding autopilot . . . . . . . . . . . 5. 2. 2 Improved height holding systems . . . . . . . . . . . . . 5. 3 Actuator dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 6 Handling Qualities 6. 1 Handing qualities for aircraft . . . . . . . . . . . . 6. 2 Pilot-in-loop dynamics . . . . . . . . . . . . . . . . 6. 2. 1 Pilot as a controller . . . . . . . . . . . . . 6. 2. 2 Frequency response of a dynamic system . . 6. 2. 3 Pilot-in-loop . . . . . . . . . . . . . . . . . 6. 3 Flying qualities requirements . . . . . . . . . . . . 6. 4 Aircraft role . . . . . . . . . . . . . . . . . . . . . . 6. . 1 Aircraft classi? cation . . . . . . . . . . . . . 6. 4. 2 Flight phase . . . . . . . . . . . . . . . . . . 6. 4. 3 Levels of ? ying qualities . . . . . . . . . . . 6. 5 Pilot opinion rating . . . . . . . . . . . . . . . . . . 6. 6 Longitudinal ? ying qualities requirements . . . . . 6. 6. 1 Short perio d pitching oscillation . . . . . . 6. 6. 2 Phugoid . . . . . . . . . . . . . . . . . . . . 6. 6. 3 Flying qualities requirements on the s-plane 6. 7 Lateral-directional ? ying qualities requirements . . 6. 7. 1 Roll subsidence mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONTENTS 6. 7. 2 6. 7. 3 6. 7. 4 5 Spiral mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Dutch roll mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Lateral-directional mode in s-plane . . . . . . . . . . . . . . . . . 75 77 . . . . . . . . . . . control derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 79 79 79 79 79 7 Fly-by-Wire ? ight control 8 Appendices 8. Boeing 747-100 data . . . . . . . . . . . 8. 2 De? nitions of Aerodynamic stability and 8. 3 Root Locus . . . . . . . . . . . . . . . . 8. 4 Frequency response . . . . . . . . . . . . appendices 6 CONTENTS Chapter 1 Introduction 1. 1 Overview of the Flight Envelope †¢ Flight planing †¢ Aircraft checking †¢ Taxi †¢ Take-o? – Rotate, â€Å"select† an attitude – Clean up (gear, ? aps, etc) – Emergencies (engine failure, ? re, etc) †¢ Climb – Speed control – Procedure (manual, autopilot) †¢ Mission Tasks – Cruise – Combat (air to air) – Strike (air to earth) – General handling (stalling, spinning, aerobatics) – Formation ? ing (Navigation, procedure etc) – Emergencies – Con? guration (weapons, tanks, fuel load) †¢ Recovery – Descent – Instrument approach – Landing – Overshoot 7 8 CHAPTER 1. INTRODUCTION Stick – Linkage 6 Trim ? -? Servo Actuator – Aircraft dynam ics Figure 1. 1: Manual pilot control aircraft – Formation – Procedures – Emergencies †¢ Taxi Longitudinal and lateral dynamics thus Flight control systems are involved in Take o? , Climb, Mission tasks and Recovery. †¢ Di? erent aircraft (aircraft class) †¢ Di? erent ? ight phase Manual– handling qualities/? ight qualities Improve the handling qualities of airplane; Autopilot 1. 2Flight control systems Objectives †¢ To improve the handling qualities †¢ To release the operation burden of pilots partly or fully †¢ To increase the performance of aircraft or missiles Types of Flight Control Systems (FCS) 1. Open-loop control 2. Stability augmentation systems 3. Autopilot 4. Integrated Navigation systems and Autopilots (? ight management systems) 1. 3 Modern Control †¢ Classic control– transfer function – frequency domain †¢ Limitation of classic design method: single input, single output (SISO), only conc ern the output behaviour, linear systems (saturation) †¢ System description in state space form. 1. 4.INTRODUCTION TO THE COURSE 9 Stick Trim – Aircraft dynamics – + ? + -Linkage – ? – ? – Servo Actuator 6 6  Stability Aug. Systems  Sensor  ? Figure 1. 2: Stability Augmentation Systems Reference Command + -? Autopilot – 6 6 + -? 6 – SAS – Actuators – Aircraft dynamics – Sensor  6  Navigation Systems ? ? Figure 1. 3: Autopilot con? guration †¢ Describe aircraft or other dynamics systems in a set of ? rst order di? erential equations. Expressed in a matrix form †¢ State space analysis and design techniques– very powerful technique for control systems †¢ Matrix manipulation knowledge required 1. 4 1. 4. 1 Introduction to the courseContent This course will cover †¢ state space analysis and design techniques for aircraft †¢ simple ? ight control systems including stability aug mentation systems, and simple autopilots †¢ handling qualities 10 CHAPTER 1. INTRODUCTION Flight Management 6 Systems/Autopilot 6 + -? 6 – SAS – Actuators – Aircraft dynamics – Sensor  6 Navigation Systems ? ? Figure 1. 4: Autopilot con? guration †¢ Fly-By-Wire (FBW) 1. 4. 2 Tutorials and coursework †¢ Tutorials will start from Week 3 †¢ One tutorial section in each week †¢ One coursework based on MATLAB/Simulink simulation, must be handed in before 4:00 PM Thursday, Week 11 1. 4. 3Assessment †¢ Coursework: 20%; †¢ Examination: 2 hours; attempt 3 from 5 questions; 80% of the ? nal mark. 1. 4. 4 Lecture plan †¢ Overall ? ight envelope †¢ Flight control systems †¢ Modern control design methodology †¢ The introduction of the course– structure, assessment, exercises, references 1. Introduction 2. Response to the controls (a) State space analysis (b) Longitudinal response to elevator and throttle (c) Transient response to aileron and rudder 3. Aircraft stability augmentation systems 1. 4. INTRODUCTION TO THE COURSE (a) Performance evaluation †¢ †¢ †¢ †¢ stability Time domain requirements Frequency domain speci? ations Robustness 11 (b) Longitudinal Stability Augmentation Systems †¢ Choice of the feedback variables †¢ Root locus and gain determination †¢ Phugoid suppress (c) Lateral stability augmentation systems †¢ Roll feedback for aileron control †¢ Yaw rate feedback for rudder control 4. Simple autopilot design †¢ Augmented longitudinal dynamics †¢ Height hold systems 5. Handling Qualities (a) Time delay systems (b) Pilot-in-loop dynamics (c) Handling qualities (d) Frequency domain analysis (e) Pilot induced oscillation 6. Flight Control system implementation Fly-by-wire technique 1. 4. 5 References 1. Flight Dynamics Principles.M. V. Cook. 1997. Arnold. Chaps. 4,5,6,7,10,11 2. Automatic Flight Control Systems. D. McL ean. 1990. Prentice Hall International Ltd. Chaps. 2, 3,6,9. 3. Introduction to Avionics Systems. Second edition. R. P. G. Collinson. 2003. Kluwer Academic Publishers. Chap. 4 12 CHAPTER 1. INTRODUCTION Chapter 2 Longitudinal response to the control 2. 1 Longitudinal dynamics From Flight Dynamics course, we know that the linearised longitudinal dynamics can be written as mu ? ? ? X ? X ? X ? X u? w? ? w + (mWe ? )q + mg? cos ? e ? u ? w ? ?w ? q ? Z ? Z ? Z ? Z ? u + (m ? )w ? ? w ? (mUe + )q + mg? sin ? e ? u ? w ? ?w ? q ?M ? M ? M ? M u? w? ? w + Iy q ? ? q ? ?u ? w ? ?w ? q = = = ? X ? t ? Z ? t ? M ? t (2. 1) (2. 2) (2. 3) The physical meanings of the variables are de? ned as u: Perturbation about steady state velocity Ue w: Perturbation on steady state normal velocity We q: Pitch rate ? : Pitch angle Under the assumption that the aeroplane is in level straight ? ight and the reference axes are wind or stability axes, we have ? e = We = 0 (2. 4) The main controls in longitudina l dynamics are the elevator angle and the engine trust. The small perturbation terms in the right side of the above equations can be expressed as ? X ? t ?Z ? t ? M ? t where 13 = = = ? X ? X ? e + ? e ?Z ? Z ? e + ? e ?M ? M ? e + ? e (2. 5) (2. 6) (2. 7) 14 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL ? e : the elevator de? ection (Note ? is used in Appendix 1) ? : engine thrust perturbation Substituting the above expression into the longitudinal symmetric motion yields ? X ? X ? X ? X u? w? ? w? q + mg? ?u ? w ? ?w ? q ? Z ? Z ? Z ? Z ? u + (m ? )w ? ? w ? (mUe + )q ? u ? w ? ?w ? q ? M ? M ? M ? M u? w? ? w + Iy q ? ? q ? ?u ? w ? ?w ? q mu ? ? = = = ? X ? X ? e + ? e ?Z ? Z ? e + ? e ?M ? M ? ?e + e (2. 8) (2. 9) (2. 10)After adding the relationship ? ? = q, (2. 11) Eqs. (2. 8)- (2. 11) can be put in a more concise vector and matrix format. The longitudinal dynamics can be written as ? m ? 0 ? ? 0 0 ? ?X ? w ? ?Z m ? ?w ? ? ? M ? w ? 0 0 0 Iy 0 u ? 0 0 w ? ? 0 q ? ? 1 ? ? ? = ? ? ? ? ? ? ? ? ? ?X ? u ? Z ? u ? M ? u ? X ? w ? Z ? w ? M ? w ? Z ? q ? X ? q + mUe ?M ? q 0 0 ?X e ? Z e ? M e 0 ?X ?Z ?M ? ? ? ? 1 ?mg u 0 w 0 q ? 0 ? ? ?+ ? ?e ? (2. 12) 0 Put all variables in the longitudinal dynamics in a vector form as ? ? u ? w ? ? X=? ? q ? ? and let m ? ?X ? w ? ? 0 m ? ?Z ? ?w ? = ? 0 ? ?M ? w ? 0 ? ?X ? X ? = ? ? ? B ? = ? ? ? u ? Z ? u ? M ? u ? w ? Z ? w ? M ? w ? Z ? q (2. 13) ? M 0 0 Iy 0 ?X ? q ? 0 0 ? ? 0 ? 1 (2. 14) ? ?mg 0 ? ? 0 ? 0 A + mUe ?M ? q (2. 15) 0 0 ?X e ? Z e ? M e 0 ?X ?Z ?M ? ? ? ? 1 (2. 16) 0 U= ?e ? (2. 17) 2. 1. LONGITUDINAL DYNAMICS Equation (2. 12) becomes 15 ? MX = A X + B U (2. 18) It is custom to convert the above set of equations into a set of ? rst order di? erential equations by multiplying both sides of the above equation by the inverse of the matrix M , i. e. , M ? 1 . Eq. (2. 18) becomes ? ? ? ? ? ? u ? xu xw xq x? x? e x? u ? w ? ? zu zw zq z? ? ? w ? ? z? z? ? ? e ? ? ? =? ? ? ? ( 2. 19) ? q ? ? mu mw mq m? ? ? q ? + ? m? e m? ? ? ? ? ? 0 0 1 0 0 0 ? Let xu ? zu A = M ? 1 A = ? ? mu 0 ? ? xw zw mw 0 xq zq mq 1 ? x? z? ? ? m? ? 0 (2. 20) and x? e ? z? e B = M ? 1 B = ? ? m ? e 0 ? x? z? ? ? m? ? 0 (2. 21) It can be written in a concise format ? X = AX + BU (2. 22) Eq. (2. 22) with (2. 20) and (2. 21) is referred as the state space model of the linearised longitudinal dynamics of aircraft. Appendix 1 gives the relationship between the new stability and control derivatives in the matrix A and B, i. e. xu , so on, with the dimensional and non-dimensional derivatives, where ?X ? Xu = ? u (2. 23) denotes dimensional derivative and Xu its corresponding non-dimensional derivative. These relationships are derived based on the Cramer’s rule and hold for general body axes. In the case when the derivatives are referred to wind axes, as in this course, the following simpli? cations should be made Ue = Vo , We = 0, sin ? e = 0, cos ? e = 1 (2. 24) The description of the longitudinal dynamics in the matrix-vector format as in (2. 19) can be extended to represent all general dynamic systems. Consider a system with order n, i. e. , the system can be described by n order di? rential equation (as it will be explained later, this is the same as the highest order of the denominator polynomial in the transfer function is n). In the representation (2. 22), A ? Rn? n is the system matrix ; B ? Rn? m is the input matrix ; X ? Rn is the state vector or state variables and U ? Rm the input or input vector. The equation (2. 22) is called state equation. For the stability augmentation system, only the in? uence of the variation of the elevator angle, i. e. the primary aerodynamic control surface, is concerned. The above equations of motion can be simpli? ed. The state space representation remains the 6 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL same format as in eq. (2. 22) with the same matrix A and state variables but with a di? erent B and input U as given below ? ? x ? e ? z ? B = M ? 1 B = ? ?e ? (2. 25) ? m? e ? 0 and U = ? e (2. 26) Remark: It should be noticed that in di? erent textbooks, di? erent notations are used. For the state space representation of longitudinal dynamics, sometime widetilded derivatives are used as follows ? ? 1 ? X 1 ? X ? ? 1 ? X ? ? 0 ? g u ? u m ? u m ? w m e 1 ? Z 1 ? Z 1 ? Z ? w ? ? 0 ? ? w ? ? m e ? ?+? ? ? ? = ? m ? u m ? w Ue ? ? e (2. 27) ? q ? Mu ? Mw Mq 0 ? ? q ? ? M? e ? ? ? ? 0 0 1 0 0 where Mu = Mw = 1 ? M 1 ? Z 1 ? M + ? Iyy ? u m ? u Iyy ? w ? 1 ? M 1 ? Z 1 ? M + ? Iyy ? w m ? w Iyy ? w ? 1 ? M 1 ? M + Ue ? Iyy ? q Iyy ? w ? (2. 28) (2. 29) (2. 30) (2. 31) Mq = M? e = 1 ? M 1 ? Z 1 ? M + ? Iyy e m e Iyy ? w ? The widetilded derivatives and the other derivatives in the matrices are the same as the expression of the small letter derivatives under certain assumptions, i. e. using stability axis. 2. 2 2. 2. 1 State space description State variables A minimum set of variables which, when known at time t0 , together with the input, are su? ient to describe the behaviours of the system at any time t > t0 . State variables may have no any physical meanings and may be not measurable. For the longitudinal dynamic of aircraft, there are four state variables, i. e, ? ? u ? w ? ? X=? (2. 32) ? q ? ? and one input or control variable, the elevator de? ection, U = ? e (2. 33) 2. 3. LONGITUDINAL STATE SPACE MODEL Thus n=4 m=1 17 (2. 34) The system matrix and input matrix of the longitudinal dynamics are given by ? ? xu xw xq x? ? z zw zq z? ? ? A = M ? 1 A = ? u (2. 35) ? mu mw mq m? ? 0 0 1 0 and ? x? e ? z ? B = M ? 1 B = ? ?e ? ? m ? e ? 0 ? (2. 36) respectively. . 2. 2 General state space model w Ue When the angle of attack ? is of concern, it can be written as ? = which can be put into a general form as y = CX where y=? = and C= 0 1/Ue 0 0 (2. 40) Eq. (2. 38) is called Output equation; y the output variable and C the output matrix. For more general case where there are more than one output and has a direct path from input to output variable, the output equation can be written as Y = CX + DU (2. 41) w Ue (2. 38) (2. 39) (2. 37) where Y ? Rr ,C ? Rr? n and D ? Rr? m . For motion of aerospace vehicles including aircraft and missiles, there is no direct path between input and output.In this course only the case D = 0 is considered if not explicitly pointed out. Eq. (2. 22) and (2. 38) (or (2. 41)) together represent the state space description of a dynamic system, which is opposite to the transfer function representation of a dynamic system studied in Control Engineering course. 2. 3 Longitudinal state space model When the behaviours of all the state variables are concerned, all those variables can be chosen as output variables. In addition, there are other response quantities of interest including the ? ight path angle ? , the angle of attack ? and the normal acceleration az (nz ).Putting all variables together, the output vector can be written a s 18 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL ? ? ? ? ? Y =? ? ? ? ? Invoking the relationships ? = ? ? ? ? ? ? ? ? ? ? u w q ? ? ? az w Ue (2. 42) (2. 43) w Ue (2. 44) the ? ight path angle ? = = and the normal acceleration az (nz ) az = = = ?Z/m = ? (Zu u + Zw w + Zq q + Zw w + Z? e ? e )/m ? ? ? (w ? qUe ) ? ?zu u ? zw w ? zq q ? z? e ? e + Ue zq (2. 45) where the second equality substituting the expression matrix is given by ? ? ? u 1 ? w ? ? 0 ? ? ? ? q ? ? 0 ? ? ? Y =? ? ? =? 0 ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? 0 az ? zu ollows from (2. 9) and the last equality is obtained by of w in its concise derivative format. Hence the output ? 0 1 0 0 1/Ue ? 1/Ue ? zw 0 0 1 0 0 0 ? zq + Ue 0 0 0 1 0 1 0 ? ? ? ? ? ? ? ? ? ? u ? ? ? w ? ? +? q ? ? ? ? ? 0 0 0 0 0 0 ? z? e ? ? ? ? ? ? ? e ? ? ? ? (2. 46) There is a direct path between the output and input! The state space model of longitudinal dynamics consists of (2. 22) and (2. 46). 2. 3. 1 Numerical example Boeing 747 jet transpor t at ? ight condition cruising in horizontal ? ight at approximately 40,000 ft at Mach number 0. 8. Relevant data are given in Table 2. 1 and 2. 2.Using tables in Appendix 1, the concise small derivatives can be calculated and then the system matrix and input matrix can be derived as ? ? ? 0. 006868 0. 01395 0 ? 32. 2 ? ?0. 09055 ? ?0. 3151 774 0 ? A=? (2. 47) ? 0. 0001187 ? 0. 001026 ? 0. 4285 ? 0 0 0 1 0 ? ? ? 0. 000187 ? ?17. 85 ? ? B=? (2. 48) ? ?1. 158 ? 0 Similarly the parameters matrices in output equation (2. 46) can be determined. It should be noticed that English unit(s) is used in this example. 2. 4. AIRCRAFT DYNAMIC BEHAVIOUR SIMULATION USING STATE SPACE MODELS19 Table 2. 1: Boeing 747 transport data 636,636lb (2. 83176 ? 106 N) 5500 ft2 (511. m2 ) 27. 31 ft (8. 324 m) 195. 7 ft (59. 64 m) 0. 183 ? 108 slug ft2 (0. 247 ? 108 kg m2 ) 0. 331 ? 108 slug ft2 (0. 449 ? 108 kg m2 ) 0. 497 ? 108 slug ft2 (0. 673 ? 108 kg m2 ) -0. 156 ? 107 slug ft2 (-0. 212 ? 107 kg m2 ) 774 ft /s (235. 9m/s) 0 5. 909 ? 10? 4 slug/ft3 (0. 3045 kg/m3 ) 0. 654 0. 0430 W S c ? b Ix Iy Iz Izx Ue ? 0 ? CL0 CD Table 2. 2: Dimensional Derivatives– B747 jet X(lb) Z(lb) M(ft. lb) u(f t/s) ? 1. 358 ? 102 ? 1. 778 ? 103 3. 581 ? 103 w(f t/s) 2. 758 ? 102 ? 6. 188 ? 103 ? 3. 515 ? 104 q(rad/sec) 0 ? 1. 017 ? 105 ? 1. 122 ? 107 2 w(f t/s ) ? 0 1. 308 ? 102 -3. 826 ? 103 5 ? e (rad) -3. 17 ? 3. 551 ? 10 ? 3. 839 ? 107 2. 3. 2 The choice of state variables The state space representation of a dynamic system is not unique, which depends on the choice of state variables. For engineering application, state variables, in general, are chosen based on physical meanings, measurement, or easy to design and analysis. For the longitudinal dynamics, in additional to a set of the state variables in Eq. (2. 32), another widely used choice (in American) is ? u ? ? ? ? X=? ? q ? ? ? (2. 49) Certainly, when the logitudinal dynamics of the aircraft are represented in terms of the above state variab les, di? rent A, B and C are resulted (see Tutorial 1). 2. 4 Aircraft dynamic behaviour simulation using state space models State space model developed above provides a very powerful tool in investigate dynamic behavious of an aircraft under various condition. The idea of using state pace models for predicting aircraft dynamic behavious or numerical simulation can be explained by 20 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL the following expression X(t + ? t) = X(t) + dX(? ) ? |? =t ? t = X(t) + X(t)? t d? (2. 50) ? where X(t) is current state, ? t is step size and X(t) is the derivative calculated by the state space equation. . 4. 1 Aircraft response without control ? X = AX X(0) = X0 (2. 51) 2. 4. 2 Aircraft response to controls ? X = AX + BU ; X(0) = 0 (2. 52) where U is the pilot command 2. 4. 3 Aircraft response under both initial conditions and controls ? X = AX + BU ; X(0) = X0 (2. 53) 2. 5 Longitudinal response to the elevator After the longitudinal dynamics are descri bed by the state space model, the time histories of all the variables of interests can be calculated. For example, the time responses of the forward velocity u, normal velocity w (angle of attack) and ? ight path angle ? under the step movement of the levator are displayed in Fig 2. 1–2. 5 Discussion: If the reason for moving the elevator is to establish a new steady state ? ight condition, then this control action can hardly be viewed as successful. The long lightly damped oscillation has seriously interfered with it. A good operation performance cannot be achieved by simply changing the angle of elevator. Clearly, longitudinal control, whether by a human pilot or automatic pilot, demands a more sophisticated control activity than open-loop strategy. 2. 6 Transfer of state space models into transfer functions Taking Laplace transform on both sides of Eq. (2. 2) under the zero initial assumption yields sX(s) = Y (s) = where X(s) = L{X(t)}. AX(s) + BU (s) CX(s) (2. 54) (2. 55) 2. 6. TRANSFER OF STATE SPACE MODELS INTO TRANSFER FUNCTIONS21 Step response to elevator: Velocity 90 80 70 60 Velocity(fps) 50 40 30 20 10 0 0 1 2 3 4 5 Time(s) 6 7 8 9 10 Figure 2. 1: Longitudinal response to the elevator Step response to evelator: angle of attack 0 ?0. 005 ?0. 01 Angle of attack(rad) ?0. 015 ?0. 02 ?0. 025 ?0. 03 0 1 2 3 4 5 Time(s) 6 7 8 9 10 22 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Step respnse to elevator: Flight path angle 0. 1 0. 08 0. 06 0. 04 Flight path angle (rad) 0. 02 0 0. 02 ?0. 04 ?0. 06 ?0. 08 ?0. 1 0 1 2 3 4 5 Time(s) 6 7 8 9 10 Figure 2. 2: Longitudinal response to the elevator Step Response to elevator: long term 90 80 70 60 Velocity (fps) 50 40 30 20 10 0 0 100 200 300 Time (s) 400 500 600 Figure 2. 3: Longitudinal response to the elevator 2. 6. TRANSFER OF STATE SPACE MODELS INTO TRANSFER FUNCTIONS23 Step response to elevator: long term 0 ?0. 005 ?0. 01 Angle of attack (rad) ?0. 015 ?0. 02 ?0. 025 ?0. 03 0 100 200 300 Time (s) 400 50 0 600 Figure 2. 4: Longitudinal response to the elevator Step response to elevator: long term 0. 1 0. 08 0. 06 0. 04 Flight path angle (rad) 0. 02 0 ?0. 2 ?0. 04 ?0. 06 ?0. 08 ?0. 1 0 100 200 300 Time (s) 400 500 600 Figure 2. 5: Longitudinal response to the elevator 24 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Y (s) = C[sI ? A]? 1 BU (s) Hence the transfer function of the state space representation is given by G(s) = C[sI ? A]? 1 B = C(Adjoint(sI ? A))B det(sI ? A) (2. 56) (2. 57) Example 1: A short period motion of a aircraft is described by ? ? q ? = ? 0. 334 ? 2. 52 1. 0 ? 0. 387 ? q + ? 0. 027 ? 2. 6 ? e (2. 58) where ? e denotes the elevator de? ection. The transfer function from the elevator de? ection to the angle of attack is determined as follows: ? (s) ? 0. 27s ? 2. 6 = 2 ? e (s) s + 0. 721s + 2. 65 (2. 59) # The longitudinal dynamics of aircraft is a single-input and multi-output system with one input ? e and several outputs, u, w, q, ? , ? , az . Using the techniq ue in Section (2. 6), the transfer functions between each output variable and the input elevator can be derived. The notation u(s) Gue = (2. 60) ? ?e (s) is used in this course to denote the transfer function from input ? e to output u. For the longitudinal dynamics of Boeing 747-100, if the output of interest is the forward velocity, the transfer function can be determined using formula (2. 56) as u(s) ? e (s) ? 0. 00188s3 ? 0. 2491s2 + 24. 68s + 11. 6 s4 + 0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 0041959 (2. 61) Gue ? = = Similarly, all other transfer functions can be derived. For a system with low order like the second order system in Example 1, the derivation of the corresponding transfer function from its state space model can be completed manually. For complicated systems with high order, it can be done by computer software like MATLAB. It can be found that although the transfer functions from the elevator to di? erent outputs are di? erent but they have the same denominat or, i. e. s4 + 0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 041959 for Beoing 747-100. Only the numerators are di? erent. This is because all the denominators of the transfer functions are determined by det(sI ? A). 2. 6. 1 From a transfer function to a state space model The number of the state variable is equal to the order of the transfer function, i. e. , the order of the denominator of the transfer function. By choosing di? erent state variables, for the same transfer function, di? erent state space models are given. 2. 7. BLOCK DIAGRAM REPRESENTATION OF STATE SPACE MODELS 25 2. 7 Block diagram representation of state space models 2. 8 2. 8. 1 Static stability and dynamic modesAircraft stability Consider aircraft equations of motion represented as ? X = AX + BU (2. 62) The stability analysis of the original aircraft dynamics concerns if there is no any control e? ort,whether the uncontrolled motion is stable. It is also referred as openloop stability in general control engineeri ng. The aircraft stability is determined by the eigenvalues of the system matrix A. For a matrix A, its eigenvalues can be determined by the polynomial det(? I ? A) = 0 (2. 63) Eigenvalues of a state space model are equal to the roots of the characteristic equation of its corresponding transfer function.An aircraft is stable if all eigenvalues of its system matrix have negative real part. It is unstable if one or more eigenvalues of the system matrix has positive real part. Example for a second order system Example 1 revisited 2. 8. 2 Stability with FCS augmentation When a ? ight control system is installed on an aircraft. The command applied on the control surface is not purely generated by a pilot any more; it consists of both the pilot command and the control signal generated by the ? ight control system. It can be written as ? U = KX + U (2. 64) ? where K is the state feedback gain matrix and U is the reference signal or pilot command.The stability of an aircraft under ? ight co ntrol systems is refereed as closed-loop stability. 26 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Then the closed-loop system under the control law is given by ? ? X = (A + BK)X + B U (2. 65) Stability is also determined by the eigenvalues of the system matrix of the system (2. 65), i. e. , A + BK. Sometimes only part of the state variables are available, which are true for most of ? ight control systems, and only these measurable variables are fed back, i. e. output feedback control. It can be written as ? ? U = KY + U = KCX + B U where K is the output feedback gain matrix.Substituting the control U into the state equation yields ? ? X = (A + BKC)X + B U (2. 67) (2. 66) Then the closed-loop stability is determined by the eigenvalues of the matrix A+BKC. Boeing Example (cont. ) Open-loop stability: ? 0. 3719 + 0. 8875i ? 0. 3719 ? 0. 8875i eig(A) = ? 0. 0033 + 0. 0672i ? 0. 0033 ? 0. 0672i (2. 68) Hence the longitudinal dynamics are stable. The same conclusion can be drawn from the the transfer function approach. Since the stability of an open loop system is determined by its poles from denominator of its transfer function, i. e. , s4 +0. 750468s3 + 0. 935494s2 + 0. 0094630s + 0. 041959=0. Its roots are given by s1,2 = ? 0. 3719  ± 0. 8875i s3,4 = ? 0. 0033  ± 0. 0672i (2. 69) (This example veri? es that the eigenvalues of the system matrix are the same as the roots of its characteristic equation! ) 2. 8. 3 Dynamic modes Not only stability but also the dynamic modes of an aircraft can be extracted from the stat space model, more speci? cally from the system matrix A. Essentially, the determinant of the matrix A is the same as the characteristic equation. Since there are two pairs of complex roots, the denominator can be written in the typical second order system’s format as 2 2 (s2 + 2? ? p s + ? p )(s2 + 2? s ? s s + ? s ) (2. 70) (2. 71) (2. 72) where ? p = 0. 0489 for Phugoid mode and ? s = 0. 3865 for the short period mode. ?s = 0. 9623 ? p = 0. 0673 2. 9. REDUCED MODELS OF LONGITUDINAL DYNAMICS B 747 Phugoid mode 1. 5 27 1 93. 4s 0. 5 Perturbation 0 ? 0. 5 ? 1 0 300 600 Time (s) Figure 2. 6: Phugoid mode of Beoing 747-100 The ? rst second order dynamics correspond to Phugoid mode. This is an oscillad d tion with period T = 1/? p = 1/(0. 0672/2? ) = 93. 4 second where ? p is the damped frequency of the Phugoid mode. The damping ratio for Phugoid mode is very small, i. e. , ? p = 0. 489. As shown in Figure 2. 6, Phugoid mode for Boeing 747-100 at this ? ight condition is a slow and poor damped oscillation. It takes a long time to die away. The second mode in the characteristic equation corresponds to the short period mode in aircraft longitudinal dynamics. As shown in Fig. 2. 7, this is a well damped response with fast period about T = 7. 08 sec. (Note the di? erent time scales in Phugoid and short period response). It dies away very quickly and only has the in? uence at the beginning of the response. 2. 9 Reduced mode ls of longitudinal dynamics Based on the above example, we can ? d Phugoid mode and short period mode have di? erent time scales. Actually all the aircraft have the similar response behaviour as Boeing 747. This makes it is possible to simplify the longitudinal dynamics under certain conditions. As a result, this will simplify following analysis and design. 2. 9. 1 Phugoid approximation The Phugoid mode can be obtained by simplifying the full 4th order longitudinal dynamics. Assumptions: †¢ w and q respond to disturbances in time scale associated with the short period 28 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Beoing 747 Short period mode From: U(1) 0. 7 0. 6 0. 5 0. 4Perturbation To: Y(1) 0. 3 0. 2 0. 1 0 ?0. 1 ?0. 2 0 5 10 15 Time (sec. ) Figure 2. 7: Short Period mode of Beoing 747-100 mode; it is reasonable to assume that q is quasi-steady in the longer time scale associated with Phugoid mode; q=0; ? †¢ Mq , Mw , Zq , Zw are neglected since both q and w are rel atively small. ? ? ? Then from the table in Appendix 1, we can ? nd the expression of the small concise derivatives under these assumptions. The longitudinal model reduces to ? ? ? Xu Xw ? ? X? e ? 0 ? g u ? u m m m Zw ? w ? ? Zu Ue 0 ? ? w ? ? Z? e ? m m ? ? ? =? M ? + ? M ? ?e (2. 73) ? m ? ? 0 ? ? u Mw 0 0 ? q ? ? ? e ? Iyy Iyy Iyy ? ? ? 0 0 1 0 0 This is not a standard state space model. However using the similar idea in Section 2. 6, by taking Laplace transform on the both sides of the equation under the assumption that X0 = 0, the transfer function from the control surface to any chosen output variable can be derived. The characteristic equation (the denominator polynomial of a transfer function) is given by ? (s) = As2 + Bs + C where A = ? Ue Mw Ue B = gMu + (Xu Mw ? Mu Xw ) m g C = (Zu Mw ? Mu Zw ) m (2. 75) (2. 76) (2. 77) (2. 74) 2. 9. REDUCED MODELS OF LONGITUDINAL DYNAMICS 29 This corresponds to the ? st mode (Phugoid mode) in the full longitudinal model. After substit uting data for Beoing 747 in the formula, the damping ratio and the natural frequency are given by ? = 0. 068, ? n = 0. 0712 (2. 78) which are slightly di? erent from the true values, ? p = 0. 049, ? p = 0. 0673, obtained from the full 4th longitudinal dynamic model. 2. 9. 2 Short period approximation In a short period after actuation of the elevator, the speed is substantially constant while the airplane pitches relatively rapidly. Assumptions: †¢ u=0 †¢ Zw (compared with m) and Zq (compared with mUe ) are neglected since they ? are relatively small. w ? q ? Zw m mw Ue mq w q + Z ? e m m ? e ?e (2. 79) The characteristic equation is given by s2 ? ( Zw 1 1 Mq Zw + (Mq + Mw Ue ))s ? (Ue Mw ? )=0 ? m Iyy Iyy m (2. 80) Using the data for B747-100, the result obtained is s2 + 0. 741s + 0. 9281 = 0 with roots s1,2 = ? 0. 371  ± 0. 889i The corresponding damping ratio and natural frequency are ? = 0. 385 wn = 0. 963 (2. 83) (2. 82) (2. 81) which are seen to be almost same as t hose obtained from the full longitudinal dynamics. Actually the short period approximation is very good for a wide range of vehicle characteristics and ? ight conditions. Tutorial 1 1. Using the small concise derivatives, ? d the state equations of longitudinal dynamics of an aircraft with state variables ? ? u ? ? ? ? X=? (2. 84) ? q ? ? 30 CHAPTER 2. LONGITUDINAL RESPONSE TO THE CONTROL Normal acceleration at the pilot seat is a very important quantity, de? ned as the normal acceleration response to an elevator measured at the pilot seat, i. e. aZx = w ? Ue q ? lx q ? ? (2. 85) where lx is the distance from c. g. to the pilot seat. When the outputs of interest are pitch angle ? and the normal acceleration at the pilot seat, ? nd the output equations and identify all the associated parameter matrices and dimension of variables (state, input and output). . The motion of a mass is governed by m? (t) = f (t) x (2. 86) where m is mass, f (t) the force acting on the mass and x(t) the di splacement. When the velocity x(t) and the velocity plus the position x(t) + x(t) are chosen ? ? as state variables, and the position is chosen as output variable, ? nd the state space model of the above mass system. Determine the transfer function from the state space model and compare it with the transfer function directly derived from the dynamic model in Eq. (2. 86). 3. Find the transfer function from elevator de? ection ? e to pitch rate q in Example 1.Determine the natural frequency and damping ratio of the short period dynamics. Is it possible to ? nd these information from a state space model directly, instead of using the transfer function approach? 4. Suppose that the control strategy ? ?e = ? + 0. 1q + ? e (2. 87) ? is used for the aircraft in Example 1 where ? e is the command for elevator de? ection from the pilot. Determine stability of the short period dynamics under the above control law using both state space method and Routh stability criterion in Control Engineeri ng (When Routh stability criterion is applied, you can study the stability using the transfer function from ? to q or that from ? e to ? (why? )). Compare and discuss the results achieved. Chapter 3 Lateral response to the controls 3. 1 Lateral state space models mv ? ?Y v ? ( ? Y + mWe )p ? ?v ? p ? mUe )r ? mg? cos ? e ? mg? sin ? e ? L ? L ? L ? v + Ix p ? ? p ? Ixz r ? ? r ? v ? p ? r ? N ? N ? N v ? Ixz p ? ? p + Iz r ? ? r ? ?v ? p ? r = = = ? Y ? A + A ? L ? A + A ? N ? A + A ? Y ? R R ? L ? R R ? N ? R R (3. 1) (3. 2) (3. 3) Referred to body axes, the small perturbed lateral dynamics are described by ? ( ? Y ? r where the physical meanings of the variables are de? ed as v: Lateral velocity perturbation p: Roll rate perturbation r: Yaw rate perturbation ? : Roll angle perturbation ? : Yaw angle perturbation ? A : Aileron angle (note that it is denoted by ? in Appendix 1) ? R : Rudder angle (note that it is denoted by ? in Appendix 1) Together with the relationships ? ?= p and ? ? = r, (3. 4) (3. 5) the lateral dynamics can be described by ? ve equations, (3. 1)-(3. 5). Treating them in the same way as in the longitudinal dynamics and after introducing the concise notation as in Appendix 1, these ? ve equations can be represented as ? ? ? ? ? ? v ? p ? r ? ? ? ? ? ? yv lv nv 0 0 yp lp np 1 0 yr lr nr 0 1 y? 0 0 0 0 y? 0 0 0 0 v p r ? ? ? ? y? A l? A n ? A 0 0 y? R l? R n ? R 0 0 ? ? ? ? ? ? ? A ? R (3. 6) ? ? ? ? ?=? ? ? ? ? ? ? ? ? ?+? ? ? ? ? 31 32 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS When the derivatives are referred to airplane wind axes, ? e = 0 (3. 7) from Appendix 1, it can be seen that y? = 0. Thus all the elements of the ? fth column in the system matrix are zero. This implies that ? has no in? uence on all other variables. To simplify analysis, in most of the cases, the following fourth order model is used ? ? ? ? ? v ? v y? A y? R yv yp yr y? ? p ? ? lv lp lr 0 ? ? p ? ? l? A l? R ? ?A ? ? ? ? ? ? =? (3. 8) ? r ? ? n v n p n r 0 ? ? r ? + ? n ? A n ? R ? ? R ? ? ? 0 1 0 0 0 0 ? (It should be noticed that the number of the states is still ? ve and this is just for the purpose of simplifying analysis). Obviously the above equation can also be put in the general state space equation ? X = AX + BU with the state variables ? v ? p ? ? X=? ? r ? , ? ?A ? R yp lp np 1 yr lr nr 0 ? (3. 9) (3. 10) the input/control variables U= the system matrix yv ? lv A=? ? nv 0 and the input matrix ? ? , ? y? 0 ? ? 0 ? (3. 11) (3. 12) y ? A ? l? A B=? ? n ? A 0 ? y? R l? R ? ? n ? R ? 0 (3. 13) For the lateral dynamics, another widely used choice of the state variables (American system) is to replace the lateral velocity v by the sideslip angle ? and keep all others. Remember that v (3. 14) Ue The relationships between these two representations are easy to identify. In some textbooks, primed derivatives, for example, Lp , Nr , so on, are used for state space representation of the lateral dynamics. The primed derivatives ar e the same as the concise small letter derivatives used in above and in Appendix 1.For stability augmentation systems, di? erent from the state space model of the longitudinal dynamics where only one input elevator is considered, there are two inputs in the lateral dynamic model, i. e. the aileron and rudder. 3. 2. TRANSIENT RESPONSE TO AILERON AND RUDDER Table 3. 1: Dimensional Derivatives– B747 jet Y(lb) L(ft. lb) N(ft. lb) v(ft/s) ? 1. 103 ? 103 ? 6. 885 ? 104 4. 790 ? 104 p(rad/s) 0 ? 7. 934 ? 106 ? 9. 809 ? 105 r(rad/sec) 0 7. 302 ? 106 ? 6. 590 ? 106 ? A (rad) 0 ? 2. 829 ? 103 7. 396 ? 101 ? R (rad) 1. 115 ? 105 2. 262 ? 103 ? 9. 607 ? 103 33 3. 2 3. 2. 1 Transient response to aileron and rudderNumerical example Consider the lateral dynamics of Boeing 747 under the same ? ight condition as in Section 2. 3. 1. The lateral aerodynamic derivatives are listed in Table 3. 1. Using the expression in Appendix 1, all the parameters in the state space model can be calculated, gi ven by ? ? ? 0. 0558 0. 0 ? 774 32. 2 ? ?0. 003865 ? 0. 4342 0. 4136 0 ? ? A=? (3. 15) ? 0. 001086 ? 0. 006112 ? 0. 1458 0 ? 0 1 0 0 and 0. 0 ? ?0. 1431 B=? ? 0. 003741 0. 0 ? ? 5. 642 0. 1144 ? ? ? 0. 4859 ? 0. 0 (3. 16) Stability Issue ? 0. 0330 + 0. 9465i ? 0. 0330 ? 0. 9465i eig(A) = ? 0. 5625 ? 0. 0073 (3. 17)All the eigenvalues have negative real part hence the lateral dynamics of the Boeing 747 jet transport is stable. 3. 2. 2 Lateral response and transfer functions ? v p ? ?+B r ? ? State space model of lateral dynamics ? ? ? v ? ? p ? ? ? ? ? = A? ? r ? ? ? ? ? ?A ? R (3. 18) This is a typical Multi-Input Multi-Output (MIMO) system. For an MIMO system like the lateral dynamics, similar to the longitudinal dynamics, its corresponding transfer function can be derived using the same technique introduced in Chapter 2. However, in this case the corresponding Laplace transform of the state space model, 34 CHAPTER 3.LATERAL RESPONSE TO THE CONTROLS G(s) ? Rr? m is a complex functi on matrix which is referred as a transfer function matrix where m is the number of the input variables and r is the number of the output variables. The ijth element in the transfer function matrix de? nes the transfer function between the ith output and jth input, that is, Gyij (s) = u yi (s) . uj (s) (3. 19) For example, GpA (s) denotes the transfer function from the aileron, ? A , to the roll ? rate, p. Its corresponding transfer function matrix is given by ? ? ? ? v G? A (s) GvR (s) v(s) ? ? p(s) ? ? Gp (s) Gp (s) ? ?A (s) ? R ? ? ? ? ?A (3. 20) ? r(s) ? ? Gr (s) Gr (s) ? ?R (s) ? A ? R ? p ? (s) G? A (s) G? R hi(s) With the data of Boeing 747 lateral dynamics, these transfer functions can be found as ? 2. 896s2 ? 6. 542s ? 0. 6209 GvA (s) = 4 fps/rad (3. 21) ? s + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 ? 0. 1431s3 ? 0. 02727s2 ? 0. 1101s rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 22) 0. 003741s3 + 0. 002708s2 + 0. 0001394s ? 0. 004534 GrA (s) = rad/s/rad, deg/s/deg ? s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 23) ? 0. 1431s2 ? 0. 02727s ? 0. 1101 ? rad/rad, or deg/deg (3. 24) G? A (s) = 4 s + 0. 6344s3 + 0. 9375s2 + 0. 097s + 0. 003658 and GpA (s) = ? GvR (s) = ? 5. 642s3 + 379. 4s2 + 167. 5s ? 5. 917 fps/rad s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 25) GpR (s) = ? 0. 1144s3 ? 0. 1991s2 ? 1. 365s rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 26) ? 0. 4859s3 ? 0. 2321s2 ? 0. 008994s ? 0. 05632 rad/s/rad, or deg/s/deg s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 (3. 27) 0. 1144s2 ? 0. 1991s ? 1. 365 rad/rad, or deg/deg (3. 28) s4 + 0. 6344s3 + 0. 9375s2 + 0. 5097s + 0. 003658 GrR (s) = ? G? R (s) = ? The denominator polynomial of the transfer functions can be factorised as (s + 0. 613)(s + 0. 007274)(s2 + 0. 06578s + 0. 896) (3. 29) 3. 3. REDUCED ORDER MODELS 35 It has one large real root, -0. 5613, one small real root, -0. 0073 (very close to origin) and a pair of complex roots (-0. 0330 + 0. 9465i, -0. 0330 – 0. 9465i). For most of the aircraft, the denominator polynomial of the lateral dynamics can be factorized as above, ie. , with two real roots and a pair of complex roots. That is, 2 (s + 1/Ts )(s + 1/Tr )(s2 + 2? d ? d s + ? d ) = 0 (3. 30) where Ts Tr is the spiral time constant (for spiral mode), Tr is the roll subsidence time constant (for roll subsidence), and ? d , ? are damping ratio and natural frequency of Dutch roll mode. For Boeing 747, from the eigenvalues or the roots, these parameters are calculated as: Spiral time constant Ts = 1/0. 007274 = 137(sec); (3. 31) Roll subsidence time constant Tr = 1/0. 5613 = 1. 78(sec) and Dutch roll natural frequency and damping ratio ? d = 0. 95(rad/sec), ? d = 0. 06578 = 0. 0347 2? d (3. 33) (3. 32) The basic ? ight condition is steady symmetric ? ight, in which all the lateral variables ? , p, r, ? are identically zero. Unlike the elevator, the lateral controls are not used individually to produce changes in steady state.That is because the steady state values of ? , p, r, ? that result from a constant ? A and ? R are not of interest as a useful ? ight condition. Successful movement in the lateral channel, in general, should be the combination of aileron and rudder. In view of this, the impulse response, rather than step response used in the lateral study, is employed in investigating the lateral response to the controls. This can be considered as an idealised situation that the control surface has a sudden move and then back to its normal position, or the recovering period of an airplane deviated from its steady ? ght state due to disturbances. The impulse lateral responses of Boeing 747 under unit aileron and rudder impulse action are shown in Figure 3. 1 and 3. 2 respectively. As seen in the response, the roll subsidence dies away very quickly and mainly has the in? uence at the beginning of the response. The spiral mode has a large time constant a nd takes quite long time to respond. The Dutch roll mode is quite poorly damped and the oscillation caused by the Dutch roll dominates the whole lateral response to the control surfaces. 3. 3 Reduced order models Although as shown in the above ? gures, there are di? rent modes in the lateral dynamics, these modes interact each other and have a strong coupling between them. In general, the approximation of these models is not as accuracy as that in the longitudinal dynamics. However to simplify analysis and design in Flight Control Systems, reduced order models are still useful in an initial stage. It is suggested that the full lateral dynamic model should be used to verify the design based on reduced order models. 36 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS Lateral response to impluse aileron deflection 0. 1 Lateral velocity (f/s) 0. 05 0 ? 0. 05 ? 0. 1 ? 0. 5 0 10 20 30 Time(s) 40 50 60 0. 05 Roll rate (deg/sec) 0 ? 0. 05 ? 0. 1 ? 0. 15 0 x 10 ?3 10 20 30 Time (s) 40 50 60 5 Yaw rate(deg/sec) 0 ? 5 ? 10 ? 15 0 10 20 30 Time (s) 40 50 60 0 Roll angle (deg) ? 0. 05 ? 0. 1 ? 0. 15 ? 0. 2 ? 0. 25 0 10 20 30 Time (s) 40 50 60 Figure 3. 1: Boeing 747-100 lateral response to aileron 3. 3. REDUCED ORDER MODELS 37 Lateral response to unit impluse rudder deflection 10 Lateral velocity (f/s) 5 0 ? 5 ? 10 0 10 20 30 Time (s) 40 50 60 2 Roll rate (deg) 1 0 ? 1 ? 2 0 10 20 30 Time (s) 40 50 60 0. 4 Yaw rate (deg) 0. 2 0 ? 0. 2 ? 0. 4 ? 0. 6 0 10 20 30 Time (s) 40 50 60 Roll angle (deg) 0 ? 1 ? 2 ? 3 ? 4 0 10 20 30 Time (s) 40 50 60 Figure 3. 2: Boeing 747-100 lateral response to Rudder 38 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS 3. 3. 1 Roll subsidence Provided that the perturbation is small, the roll subsidence mode is observed to involve almost pure rolling motion with little coupling into sideslip and yaw. A reduced order model of the lateral-directional dynamics retaining only roll subsidence mode follows by removing the side force and yaw moment equations to giv e p = lp p + l? A ? A + l? R ? R ? (3. 34) If only the in? uence from aileron de? ction is concerned and assume that ? R = 0, taking Laplace transform on Eq. (3. 34) obtains the transfer function p(s) l ? A kp = = ? A s ? lp s + 1/Tr where the gain kp = l? A and the time constant Tr = 1 Ix Iz ? Ixz =? lp Iz Lp + Ixz Np (3. 36) (3. 37) (3. 35) Since Ix Ixz and Iz Ixz , then equation (3. 37) can be further simpli? ed to give the classical approximation expression for the roll mode time constant Tr = ? Ix Lp (3. 38) For the Boeing 747, the roll subsidence estimated by the ? rst order roll subsidence approximation is 0. 183e + 8 Tr = ? = 2. 3sec. (3. 39) ? 7. 934e + 6 It is close to the real value, 1. sec, given by the full lateral model. 3. 3. 2 Spiral mode approximation As shown in the Boeing 747 lateral response to the control surface, the spiral mode is very slow to develop. It is usual to assume that the motion variables v, p, r are quasi-steady relative to the time scale of the mo de. Hence p = v = r = 0 and the ? ? ? lateral dynamics can be written as ? ? ? 0 yv ? 0 ? ? lv ? ? ? ? 0 ? = ? nv ? 0 ? yp lp np 1 yr lr nr 0 y? v 0 p 0 r 0 ? ? y? A ? ? l ? A ? +? ? ? n ? A 0 ? ? y ? R l? R ? ? n ? R ? 0 ?A ? R (3. 40) If only the spiral mode time constant is concerned, the unforced equation can be used.After solving the ? rst and third algebraic equations to yield v and r, Eq. (3. 40) reduces to lp nr ? l n l np ? lp n 0 p yv lr nv ? lr np + yp + yr lv nv ? lv nv y? v r r r (3. 41) ? = ? ? 1 0 3. 3. REDUCED ORDER MODELS 39 Since the terms involving in yv and yp are assumed to be insigni? cantly small compared to the term involving yr , the above expression for the spiral mode can be further simpli? ed as ? y? (lr nv ? lv nr ) ? = 0 ? + (3. 42) yr (lv np ? lp nv ) Therefore the time constant of the spiral mode can be estimated by Ts = yr (lv np ? lp nv ) y? (lr nv ? lv nr ) (3. 43)Using the aerodynamic derivatives of Boeing 747, the estimated spiral mode time c onstant is obtained as Ts = 105. 7(sec) (3. 44) 3. 3. 3 Dutch roll ? p=p=? =? =0 ? v ? r ? = yv nv yr nr v r + 0 n ? A y? R n ? R ? A ? R (3. 45) (3. 46) Assumptions: From the state space model (3. 46), the transfer functions from the aileron or rudder to the lateral velocity or roll rate can be derived. For Boeing 747, the relevant transfer functions are given by GvA (s) = ? GrA (s) = ? GvR (s) = ? GrR (s) = ? ?2. 8955 s2 + 0. 2013s + 0. 8477 0. 003741(s + 0. 05579) s2 + 0. 2013s + 0. 8477 s2 5. 642(s + 66. 8) + 0. 013s + 0. 8477 (3. 47) (3. 48) (3. 49) (3. 50) ?0. 4859(s + 0. 04319) s2 + 0. 2013s + 0. 8477 From this 2nd order reduced model, the damping ratio and natural frequency are estimated as 0. 1093 and 0. 92 rad/sec. 3. 3. 4 Three degrees of freedom approximation Assume that the following items are small and negligible: 1). The term due to gravity, g? 2). Rolling acceleration due to yaw rate, lr r 3). Yawing acceleration as a result of roll rate, np p Third order Dutch roll approximation is given by ? ? ? ? ? ? v ? yv yp yr v 0 y ? R ? p ? = ? lv lp 0 ? ? p ? + ? l? A l? R ? ? r ? nv 0 nr r n? A n?R ?A ? R (3. 51) 40 CHAPTER 3. LATERAL RESPONSE TO THE CONTROLS For Boeing 747, the corresponding transfer functions are obtained as GvA (s) = ? GpA (s) = ? GrA (s) = ? ?2. 8955(s + 0. 6681) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) ? 0. 1431(s2 + 0. 1905s + 0. 7691) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 0. 003741(s + 0. 6681)(s + 0. 05579) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 5. 642(s + 0. 4345)(s + 66. 8) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) 0. 1144(s ? 4. 432)(s + 2. 691) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) ? 0. 4859(s + 0. 4351)(s + 0. 04254) (s + 0. 4511)(s2 + 0. 1833s + 0. 8548) (3. 52) 3. 53) (3. 54) and GvR (s) = ? GpR (s) = ? GrR (s) = ? (3. 55) (3. 56) (3. 57) The poles corresponding to the Dutch roll mode are given by the roots of s2 + 0. 1833s + 0. 8548 = 0. Its damping ratio and natural frequency are 0. 0995 and 0. 921 rad/sec. Compared wit h the values given by the second order Dutch roll approximation, i. e. , 0. 1093 and 0. 92 rad/sec, they are a little bit closer to the true damping ratio ? d = 0. 0347 and the natural frequency ? d = 0. 95 (rad/sec) but the estimation of the damping ratio still has quite poor accuracy. 3. 3. 5 Re-formulation of the lateral dynamicsThe lateral dynamic model can be re-formulated to emphasise the structure of the reduced order model. ? ? v ? yv ? r ? ? nv ? ? ? ? ? p ? = ? lv ? ? 0 ? ? yr nr lr 0 yp np lp 1 g v 0 r 0 p 0 ? ? 0 ? ? n ? A ? +? ? ? l? A 0 ? ? y? R n ? R ? ? l? R ? 0 ? A ? R (3. 58) The system matrix A can be partitioned as A= Directional e? ects Directional/roll coupling e? ects Roll/directional coupling e? ects Lateral or roll e? ects (3. 59) Tutorial 2 1. Using the data of Boeing 747-100 at Case II, form the state space model of the lateral dynamics of the aircraft at this ? ight condition.When the sideslip angle and roll angle are of interest, ? nd the output equa tion. 2. Find the second order Dutch roll reduced model of this airplane. Derive the transfer function from the rudder to the yaw rate based on this reduced order model. 3. 3. REDUCED ORDER MODELS 41 3. Using MATLAB, assess the approximation of this reduced order model based on time response, and the damping ratio and natural frequency of the Dutch roll mode. 4. Based on the third order reduced model in (3. 51), ? nd the transfer function from the aileron to the roll rate under the assumption y? A = yp = 0.

Standard Deviation and Cumulative Frequency

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Beowulf Essay Example for Free

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Relevance of Earlier Warfare to Modern Warfare Essay Example for Free

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This similarity is more profound if you find yourself fighting for the same ideals, the same land and the same enemy. It is this similarity between the two that allows the current military professional to reassess himself in light of what is happening today. For example, according to Adam Hart – Davis (2007), the prime reason for the fall of Napoleon was that he invaded Russia, in the year 1812 (P. 179). The Russian Generals tactfully withdrew from territory destroying their own towns, farms, cultivation and infrastructure along the way. A month after defeating the Russians outside Moscow, Napoleon decided to retreat back to Paris out of concern of loss of control. However, his decision to do so in the winter proved fatal as the lack of shelter and infrastructure killed his troops physically and mentally. The Russians kept pursuit of the retreating forces and managed to kill scores of them. By the time Napoleon managed to get back home, all that was left of his army was a demoralized handful of men against an efficiently trained numerous force that had left Paris with him on the way to Russia earlier that year, contributing to his eventual fall in 1815. According to Gilbert (2004), a 130 years on, Hitler made the same mistake when he invaded Russia in 1941 just when the harsh winter started (P. 249). The Russians employed the same strategy and after defeating the Germans at the siege of Moscow and Stalingrad, they chased the retreating German forces back into Germany proper and were instrumental in the fall of Berlin and the end of the Nazi regime itself. Thus, had Hitler paid attention to the fault at which his predecessor had been, there was a great probability that he would not have met the end that he did in 1945. The second point of argument is that although how we conduct warfare these days has changed, the strategy or tactfulness has not. No matter what resources in weaponry and personnel that a general may have at his disposal, there is no denying that as far as tact is concerned, there is always a lot to learn. Consider Fredrick the Great who, in 1756, fearing a joint attack by major European powers including Russia, Sweden, and Hapsburg Austria etc launched a pre-emptive strike on its neighbors. According to The strategy was of immense benefit as he was able to destroy part of the hostile forces that allowed moral and tangible support when confronted by a full scale invasion. According to Adam Hart Davis (2007), the same strategy was followed by Israel in 1967 when on rumors of a joint Arab attack on her lands compelled her to make a pre emptive strike on Egypt, Syria and Jordan (P. 353). The result was that Israel doubled its land area in just six days by capturing the Sinai Peninsula, the West Bank and the Golan heights. Again, what mattered was not the advanced weaponry that Israel had but the line of thought that was mutual between Fredrick the Great in 1756 and the Israeli leadership of 1967. Another example is the use of landscape and climate by the Russian Tsar Alexander in 1812 against Napoleon and by the Russian leader Joseph Stalin in 1941 against Nazi Germany. This use of the climate is yet to be seen again but, according to Adam Hart – Davis (2007), the use of the terrain and the landscape by the Viet-Cong against American forces in Vietnam and the Afghan Guerrillas against Soviet troops in Afghanistan enforces my point that tact is something which can be learned from the great Generals of the past (P. 355, 373-4). The last reason to support my thesis is that the rules of engagement have not changed as weaponry or tools have improved and not changed completely. This calls for a more proactive approach as to how we address the issue at hand, namely, whether the current military professional stand to benefit from the study of the Great generals of the past. Consider an example. The Trojan War, as depicted by Homer in the Iliad and the Odyssey, could be the first example in warfare history of deception. Whereby the Trojan horse was meant to be a gift, it turned out to be a mechanism as to how the Athenian forces enter the city. Contrast this with reports that in the run up to the 2003 Second Gulf War. According to Sifry and Cerf (2007), American intelligence agencies planted false evidence to make Saddam Hussein believe that the coalition attack would come from Turkey and not from the Southern neighboring countries of Kuwait and Saudi Arabia (P. 114). This forced Saddam to place more battalions to defend the Northern front than would have been necessary. Thus, it can be argued that weaponry or tools, to a large extent have remained the same in nature but have changed in form. Guns have replaced swords but their use remains the same. Cannon guns have been replaced but their use remains the same. The Trojan horse has been replaced by false intelligence and thus the use remains the same. In the end, the point of contention is that if the tools at hand for the general have only changed in form and not in substance, there is every reason to believe that the current military professional stands to benefit a lot by studying his counterparts from centuries ago. Conclusion Thus, as can be seen, there is still a lot for the current military professional to learn from his predecessors. The reasons are that situations repeat themselves, tactfulness is an attribute that can be readily applied and does not wither with age and the use of the tools at the military disposal remains the same. It can be argued, thus, that the greatest armies of our time will not be those that have the most advanced weaponry but those with the best Generals who happen to know the history of those before them yet alike them. Adam Hart Davis (2007). History: The Definitive Visual Guide from the Dawn of Civilization to the Present Day. London: Dorling Kindersley. Gilbert, M. (2004). The Second World War: A complete History. London: Henry Holt and Co. Sifry, M. Cerf. C. (2007). Iraq War Reader: History, Documents, Opinions. . New york: Simon Schuster

History of Standards Of Beauty

History of Standards Of Beauty We live in a consumer culture and we are bombarded with advertising, retailing and entertainment industry. It is forcing us to buy and consume products, promising us happiness and self-transformation. Media is ever present in our lives. We look to the media to help us define, explain, and shape the world around us (Kellner, 2003). We make comparisons of ourselves, those close to us, and situations in our lives after seeing images in the media. And as a result, after these comparisons we are motivated to try to achieve new goals and expectations. In the contemporary world, messages about goods are all pervasive- advertising has increasingly filled up the spaces of our daily existenceà ¢Ã¢â€š ¬Ã‚ ¦ it is the air that we breathe as we live our daily lives (Jhally, 1990: 250). The important thing is that we cannot avoid comparisons of ourselves to the images which we are surrounded with from media and most of us will find ourselves inadequate when we do this (Kellner, 2003). How many times have we after seeing some beautiful woman in a magazine or on TV, thought: I want hair, lips, body, breasts or something else like she has?! Media is our most important information source. But I think we are not educated by it. We believe in everything that media serves us. This essay seeks to address so many women who feel they just dont measure up when it comes to their looks. Women who believe their thighs are too big, their breasts too small, their hair boring, their skin flawed, their body shaped funny, or their clothes outdated. We are surrounded with women who believe their life would improve if they could only lose 15 pounds; if they could afford contact lenses, that new perfume or anti-cellulite lotion; if they got a nose job, a face lift, a tummy tuck, etc, women who feel shame or unhappiness when they think about some part (or all) of their body. In other words, every day we see there is a great majority of women who feel this way. We all want to be beautiful. But I want to write about what lies behind that, behind that beauty myth. In this essay I will try to explore and to explain, how media plays a dominant role in influencing females perceptions of the world around them, as well as helping them to define their sense of self. I will try to examine the influences that media has on females feelings towards their place in society, sexuality, self-esteem and body image. I hope will give some answers to some questions. What media does in terms of imposing the beauty myth? How standards of beauty changed over time and yet beauty for women is still compulsory? What can we say about pressure on women as opposed to men when it comes to looks? How is beauty being sold to women and what the consequences of these issues are? I will try to show you who is getting the profit in this non-ending battle. In other words I will try to answer these questions that at one point we all should ask ourselves. STANDARDS OF BEAUTY THROUGHOUT THE PAST The cultural standard of beauty, when it comes to body shape, is always changing. Womens bodies is not what changed, it is the ideals (Kilbourne, 1995). Advertising, retailing and entertainment produce notions of beauty that change over time. These notions place pressure upon women who try to be in vogue (Wykes and Gunter, 2005). Between 1400 and 1700, a fat body shape was considered sexually appealing and fashionable (Attie and Brooks Gun, 1987). By the nineteenth century, the fat shape was replaced by voluptuous figure, centered at a generous breasts and hips and narrow waist (Fallon, 2005). The voluptuous shape for women persisted through the early part of the twentieth century, and eventually was replaced by the slender shape of the 1920s (Mazur, 1986). The curvaceous ideal continued through the 1940s and 1950s (Mazur, 1986). By the mid-1960s, however, fashions shifted once again towards the idealization of slender body shapes over curvaceous ness. Since then the only slight shi ft from extreme thinness as the feminine ideal was the muscularization of the still very thin body during the 1980s (Mazur, 1986). We are bombarded today with images of the perfect woman. She is usually a gorgeous blonde, although brunettes, redheads and exotic women of color are also shown. She is tall and skinny, weighing at least 20% less than an average woman weighs. She rarely looks older than 25, has no visible flaws on her skin, and her hair and clothes are always immaculate (Kilbourne, 1995). In other words, one perfect woman looks pretty much like the next. Like Kilbourne (1995) said in Slim Hopes it is likely that these women we see are not real. BEAUTY AND WOMEN The beauty myth tells a story: The quality called beauty objectively and universally exists. Women must want to embody it and men must want to possess women who embody it. This embodiment is an imperative for women and not for men, which situation is necessary and natural because it is biological, sexual, and evolutionary: Strong men battle for beautiful women, and beautiful women are more reproductively successful. Womens beauty must correlate to their fertility, and since this system is based on sexual selection, it is inevitable and changeless. None of this is trueà ¢Ã¢â€š ¬Ã‚ ¦ (Wolf, 1990: 12) In the near past as the new wave of feminism emerged women have broken trough many of the material and legal obstructions. And finally they got out of their houses and became emancipated. But then more strictly and heavily and cruelly images of female beauty have come to burden upon us (Wolf, 1990). And now we are in the middle of a strong reaction against feminism that uses images of female beauty as a political weapon against womens advancement and success. According to Wolf (1990) beauty is a money system. Like economy it is determined by politics. It is not about women at all, it is about institutional power. I will show you later where the money goes. It seems like we are a good way to make money. We are vulnerable when it is about our self-worth and self-esteem. The ideal of womens beauty contradicted womens freedom and power by moving the social limits to womens lives directly onto our faces and bodies ( Wolf, 1990). And the consequence is that we now ask the questions about our bodies, skin, hair, clothes etc, which women a generation ago asked about their place in society. After so many years fighting to get our rights to everything, we are now prisoners of our body. And beauty image presented in time is our tormentor. Once again we have to fight for our rights and freedom of choice. Throughout the years, there have been forces in culture that attempt to punish women who tray to succeed in their lives, in other words to get control over their lives and environment (Wolf, 1990). There is a strong cultural reaction against women that uses images of female beauty to keep women in their place. And we have to ask ourselves where men in that strong reaction against women are. MEN AND WOMEN Media pressures women to strive for the very thin look. For example, magazines for women celebrate the very thin look, but magazines for men do not do that. In fact, there are not so many that skinny women in mens magazines. Women have low self-esteem because they are surrounded with male idea of beauty that is linked with media representations. We all think that men want to possess the beautiful women we see every day in magazines or on TV. That is the thing that Wolf (1990) claims to be the beauty myth. We all have to strive for beauty because men want to possess women who have it. In other words women are being sold to themselves in order to achieve a self whom the men in the future might choose. But Loaded magazine said that women do not have the difficulty of living with the male idea of beauty shown on the catwalk. John Perry in Loaded magazine stated: No, men fancy models because they have beautiful faces, not because they look like theyve been fed under a door. Sleeping with a supermodel would be about as pleasurable as shagging a bicycle. The truth is it is women themselves who see these freaks as the epitome of perfection (2002: 79). We all think that men want to possess beautiful women like the ones shown on TV and in magazines. And the key point is that a womans sense of her body actually has not been hers but mans view of her body. Women see themselves trough mens eyes. But Berger (2005) notes that this is not an equal and opposite phenomenon. Men are pressured to be thin and well-toned too. But they can get away with imperfection as long as they have charm and humor (Gauntlett, 2002). Levels of skinniness are irrelevant. Almost all of the beautiful women in both womens and mens magazines are thin, not fat, and this must have an impact. Magazines impose us standard of beauty and women feel inadequate after seeing men longing for some perfect woman represented by media with flawless face, big breast, narrow waist, long legs, beautiful tan etc. Our culture teaches women they cant be happy unless they are beautiful, but I have to emphasize that it also teaches men they cant be happy unless they are rich and/or powerful (Wolf, 1990). But the difference is that rich and powerful men come in all shapes, sizes, and ages. Men can get away with every small imperfection. But when Julia Roberts was seen to have armpits at the premiere of Notting Hill in 1999, the worlds press went crazy with excitement over this (wholly natural)  ´outrage ´ (Gauntlett, 2002). So we have to face the fact that there is a difference between media representation of women and the one of men. We all are pressured because media does not just reflect our world but also shapes it. And it sells us all kind of solutions to improve ourselves. SELLING BEAUTY We are all bombarded every day with messages from television shows, movies, advertisements, magazine articles that we need to look a certain way in order to be accepted (Kilbourne, 1995). For many of us, these images are neither realistic nor achievable. The result is that we feel bad about ourselves if we dont measure up. This gives a sense of insecurity among women, and this drives sales in the beauty industry. In Slim Hopes Kilbourne (1995) argues that some could say we cannot blame only advertisements, but they are the most persuasive aspect of media power to influence us culturally and individually. Girls are extremely desirable to advertisers because they are new consumers, are beginning to have significant disposable income, and are developing brand loyalty that might last a lifetime (Kilbourne, 1999: 259). Girls of all ages get the message that they must be flawlessly beautiful and thin. They get the message that with enough effort and self-sacrifice, they can achieve this ideal. And the result is that young girls from the early start to feel bad about them. Kilbourne (1999) argues that these images of perfect women that surround us would not influence us so much if we did not live in a culture that imposes us the belief that we can and should remake our bodies into perfect ones. These images play into the American belief of transformation and ever-new possibilities, no longer via hard work but via the purchase of the right products (Kilbourne, 1999: 260). Magazines represent a strong insistence that women of all ages must do their best, and that they must spend their money in order to look as beautiful as possible. Some of their content is the fashion and beauty material, which takes up many pages in the magazines. But womens magazines today construct women in a social way too. As Beetham and Boardman say, magazines not only address women as consumers but also as readers, as in search of entertainment or in need of instruction in various social roles ( 2005: 41). We can say that magazines for women took the task of defining what it meant to be a woman, or what it meant to be a particular kind of woman. Through advertising women are told clearly what women should be, and what particular product they could use/buy to help. Women are suggested an identity and told they are not good enough being natural. We can say that women are asked to buy themselves. As Berger puts it, the publicity image steals her love of herself as she is, and offe rs it back to her for the price of the product (2005: 43). A massive worldwide industry is eager to tell women that there are products for sale which can improve their looks. And we all buy them, dont we!? And the worst part is that identity is understood as something that could be reworked, improved upon, and even dramatically changed. There are so many magazines that promised every girl the chance to get a stylish and attractive look that fashion models and famous women have. Spending money on clothing, cosmetics, and accessories are presented as necessity if we want to construct a desirable self (Ouellette, 1999). How many times have we as we read some magazine or watch TV advertisement and thought I have to have that? We all have products in our homes that we bought because of some add on TV or magazine article that told us that it is the best product for our hair to be astonishing , for our face to be immaculate, our figure to be fit, our lips to be attractive etc. And the important thing is that it seems like women get the messages/promises from magazines full of articles telling us that if women use these product they will improve their looks and, theyll have it all-the perfect marriage, loving children, great sex, and a rewarding career. But actually there is no link between these things. I think that it does not mean that we will be happy in our life if we try to change our looks using some product. One of the most powerful disciplinary practices for women is that of dieting. By dieting women are disciplining their bodies to only consume a certain amount of food. By doing this women feel they are becoming more like the image of the perfect (properly feminine) woman. Media activist Jean Kilbourne concludes that, Women are sold to the diet industry by the magazines we read and the television programs we watch, almost all of which make us feel anxious about our weight (Kilbourne, 1995). Many women tend to over diet which leads to anorexia and women who dont diet are mocked by society or they feel guilty for not doing that. After filling up the women audience with images of super-thin models, television networks then proceed to show hours and hours of commercials on weight-loss, dieting and fitness programs (Kilbourne, 1995). We can se that this is a marketing strategy. Firstly, media makes us feel bad about ourselves by showing us stereotypes of beautiful women that we are not and then they offer us the best solution to improve ourselves, to change our looks into prefect commodities of beautiful women. Another disciplinary practice that is given by the media is that of skin care and make-up. A womans skin must be soft, hairless, and smooth and ideally it should not show any sign of wear, experience, age, or deep thought. Magazines can give you page upon page of makeup tips and skin care strategies that women should follow in order to conform to the universal feminine standard (Wykes and Gunter, 2005). Cosmetic products are being sold to women to achieve those attributes that makes a women desirable. An unwrinkled face, thighs without cellulite, and large breasts have become the metaphor for female success because reaching these female symbols needs a lot of sacrifice, hard work, and self-control ( Wykes and Gunter, 2005). But I have to mention one thing that could lead us women to a completely different era when it comes to beauty. Theres a very different approach from Dove with its revolutionary campaign for real beauty that has received enormous publicity by using women of all shapes and sizes wearing white bra and pants to advertise their products. The whole point is to make beauty more accessible, as accessible as it can be, explains Alessandro Manfredi, vice president of Dove. So by widening the definition of beauty, we believe that more women will gain the confidence, because they will see beauty is closer to them than the beauty of a supermodel that is so far, and people could give upà ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦We dont want women to give up, we want to tell them; beauty, its at your reach (Austen, 2006). Dove is launching a major initiative in order to encourage discussion and debate about the nature of beauty. The Campaign for Real Beauty asks women to give serious thought about beauty issues such as societys definition of it, the quest for perfection, the difference between beauty and physical attractiveness, and the way the media shapes our perceptions of beauty.  [1]  Dove has established the Dove Self-Esteem Fund to raise awareness of the connection between beauty and body-related self-esteem.The Dove Self-Esteem Fund in the US helps build self-confidence in girls ages 8-14. The Dove mission is to make women feel more beautiful every day by challenging todays stereotypical view of beauty and inspiring women to take great care of themselves.  [2]  But we have to face the fact that Dove, is the No. 1 personal wash brand nationwide. One in every three households uses a Dove product.  [3]  That includes bar cleansers, body washes, face care, anti-perspirants/ deodorants and hair care. Dove is available nationwide in food, drug and mass outlet stores. So we must ask ourselves, is it really about women or again some beauty industry is manipulating us and making money from our pockets?! BEAUTY AS PROFIT All this beauty selling leads us to the question: who benefits from this beauty market! Is it really about women or are we tricked by those who have the power? Media and beauty industry including diet, surgery and cosmetic industry is manipulating us by making us throw our money on reworking our looks. That leads me to one conclusion that it cannot be about women, for the ideal is not about women but about money. We should ask ourselves how much money we spend on the best thing that will make us desirable and beautiful. The cosmetic surgery industry in the United States takes $300 million every year, and is growing annually by 10 percent (Wolf, 1990). One reason why media is so influential is that advertising is 130 billion dollar a year industry. The average American watches 30 hours of TV a week and spends 110 hours a year reading magazines (Wolf, 1990). It is very unfortunate that the media influences society to the point that it defines the ideal woman. Advertising is a powerful force in our culture that informs us but does not educate us. Economics is also a significant factor in the development of the ideal image. There is a wealth of businesses that depend upon the American desire for thinness to survive (Wolf, 1990). Exercise and diet companies are an example. In order to create a market for their product, they attempt to make women feel inadequate about their own bodies through advertisement. According to Wolf, the diet industry has tripled its income in the past 10 years from a $10 billion industry to a $33.3 billion industry. When we compare some results with UK we can see that there is also a lot of profiting going on. The UK beauty industry takes  £8.9 billion a year by selling products to women. Magazines are financed by the beauty industry (Greer, 2002). They start with young girls and teach them how to use the right product and they establish loyalty that lasts a lifelong (Greer, 2002). We all probably have one cosmetic product that we use for so many years. Cosmetics for teenagers are relatively cheap but within a few years more cultured market will persuade the most rational woman to throw her money on the right product that promises to defend women from their own weakness So we can see that the economy depends on manipulating consumers to buy as much as possible. And we can link the beauty industry and mass media, it is as Wykes and Gunter say symbiotic relationship, because beauty industry depends on mass media and vice versa. It seems there is no limit in how one can be beautiful, or how much money can we spend in order to feel beautiful, completely disregarding our health. And the consequences are harmful or sometimes even devastating. CONSEQUENCES OF MEDIA REPRESENTATION Women learn to reconstruct themselves. It is second nature to disguise them, dress them and decorate themselves with a huge range of materials. Over the past 30 years they have gone further than ever before in this process. They can re-arrange some of the organic material that is their body-sometimes without any harm, sometimes with devastating consequences.(Wykes and Gunter, 2005:48) A research by the British Medical Association has shown that eating disorders have one of the highest mortality rates of all psychological illnesses, and that the level of skinniness enforced by fashion models is both unachievable and biologically inappropriate and gives a wrong picture of an ideal body to young women (Gauntlett, 2002). However, we cannot blame media influences to directly cause eating disorders. There are some others components that play an important role with these consequences. Report notes that eating disorders are caused by genetics, family history and cultural environment (Gauntlett, 2005). But for those who are psychologically and genetically predisposed to anxiety when it comes about body image, media plays an unhelpful role. The American research group Anorexia Nervosa and Related Eating Disorders, Inc. reports that one out of every four college-aged women uses unhealthy methods of dieting, including fasting, skipping meals, extreme workouts, laxative abuse, and self-induced vomiting.  [4]  The Canadian Fitness and Lifestyle Research Institute notes that girls even at age of nine are trying to control their weight. Research in the US gives similar results. In 2003, Teen magazine reported that 35 per cent of girls aged 6 to 12 are using at least one kind of dieting, and that 50 to 70 per cent girls of normal weight girls think they are overweight.  [5]   Cosmetic surgeons are making a lot of money with women doing cosmetic surgeries for every imperfection that we can imagine (Wolf, 1990). Women get the message that normal, round womens bodies are too fat; that soft womens flesh is really cellulite; that women with small breasts arent sexy; that women who dont have the perfect face arent attractive; that a women over 30 who in their faces have sings of their ageing are ugly. No wonder women are thinking about or doing cosmetic surgeries in order to be beautiful. In conclusion, what is the result of this sought for perfection? One out of every 4 college girls has an eating disorder. A psychological study in 1995 found that 3 minutes spent looking at models in a fashion magazine caused 70% of women to feel depressed, guilty and shameful. 50% of American women are dieting and 75% of normal weight women think they are too fat (Wolf, 1990). All these arguments lead us to one conclusion: to view ones body from the outside, that is, to put center onto physical attractiveness, sex appeal, measurements, weight, face characteristics has many harmful effects- feelings of shame, anxiety, depression, low self-esteem, development of eating disorder. CONCLUSION The traditional definition of beauty, based only on physical appearance, is powerfully communicated through the mass media and has been assimilated through popular culture. It is this ideal that many women measure themselves against and aspire to attain. According to the narrow-minded society we live in, there just doesnt seem to be a limit on how beautiful one can become.Well, someone has given us a definition of beauty that is superior to our mind. Can we hope for a day when mind in body will be a notion of beauty? I hope I have showed that by media presentation of an ideal difficult to achieve and maintain, the cosmetic and diet product industries are assured of growth and profits. I hope I have proved that in our society media has created an environment so image obsessed that those with power( and by those I mean beauty industry and media) have caused emerging of a generation of women so self conscious about their body image, that it is affecting their health. However, women around the world would like to see media change in way it represents beauty. We have to face the fact that wearing makeup, losing weight, having surgeries, dressing up etc, will not change who we are. Our identity is what makes us unique. We should not want anymore to look like someone else. There is nothing wrong in doing things that makes a woman feel good about her as long as we have a choice of doing that because of ourselves not because someone told us it is proper thing to do for a woman in order to be beautiful. So I have to emphasis that I in this essay I did not try to attack wearing make up, having surgeries, working out, dieting etc, as long as we do not feel shame, guilt or anxiety when we dont do these practices. We have to speak out for ourselves. It is wrong to use our looks as our voices. It is not the look that should do the talking. Beauty shouldnt be our weapon for success in life, but also it shouldnt be media and beauty industry weapon against women themselves. Media is always going to be present in our lives, but we have to realize that not everything we are exposed to by the media is real. So what can we do? We can take their power. We can reject political manipulation. Like Wolf (1990) said, we should turn away from them, and look directly at one another. We should look for the beauty in female subculture; try to find music, films, biographies, plays that illustrate women in three dimensions. And perhaps then we will unveil the beauty myth and find the truth about beauty.