Representation of Indigenous Cultures Essay

Since the European settlement of Australia, the Indigenous people have been represented in a myriad of ways. The Rabbits (1998), an allegorical picture book by John Marsden (writer) and Shaun Tan (illustrator) and Rabbit Proof Fence (2002), a film directed by Phillip Noyce, are just two examples of this. Techniques such as music, changing camera angles and symbolism are utilised in Rabbit Proof Fence to represent the Aboriginal people as strong-willed and spiritual and in The Rabbits, exaggeration, different colour themes and perspective are used to portray the Aborigines as technologically inferior and overwhelmed against the Europeans. In both texts, the Indigenous people are represented as oppressed by the Europeans. The Rabbit Proof Fence uses techniques such as slow motion close-ups, quick transition camera shots and intense music to show the strong-willed nature of the Aboriginals, which are be used in the scene where the three girls are taken by constable Riggs. Just before constable Riggs, we already hear the music building up the tension with some soft, yet ominous music and as they see the car, there is a slight silence before the intense music slams suddenly to support and symbolise the chaos and confusion of this part of the scene. This brief respite in music and the slow motion close-up shots of the horrified expressions on the faces of all of them emphasises the chaos that was about to happen when constable Riggs chases and captures the girls. Even after the girls were obstructed by the car and constable Riggs was taking the girls one by one, they continued to resist, especially Molly, who screamed and kicked the door shut as Riggs attempted to shove her inside the back seat. The quick transition camera shots that accompany this section of the scene from one character to another, exemplifies the franticness of it. During this scene, we clearly see the considerable amount will of resistance the Aborigines have because of the fact that, although they were powerless against the Europeans, they resisted to the bitter end. On the other hand, in The Rabbits, the Aboriginals (the Numbats) are represented as technologically inferior by the use of techniques such as: colour schemes, exaggeration and vanishing points. Colour schemes in this book are used effectively to emphasise the Indigenous population’s simplicity in life as the Aboriginal colour schemes consist of hues that blend well and warmly with its surroundings so the general overview of the texture of the painting in smooth. However, when analysing the Europeans (the Rabbits’) settlement in panels such as four and five, the colours are very sharp and more suited to the use of creating hard edges, which has been done as seen from the geometric construction of the objects within these two panels. In the tenth panel, the exaggeration of the wheat collectors is used to show the Europeans’ superior knowledge in machinery, in not only size, but also the quantity of objects that are attached like the taps. In the eighth panel, another representation of the Aboriginal’s inferiority in equipment is portrayed in the bottom right hand corner by an absolute domination in manpower and weapons. This is also epitomized by the vanishing point in that particular frame, which basically shows the reader that the army of soldiers is close to infinite. The spirituality of the Aboriginal people towards their land is portrayed in Rabbit Proof Fence by using symbolism, music and camera shifts, when Molly and Daisy on the verge of losing hope in the desert. In this scene, the very slow, lamenting music gives an audio representation of the two girls’ fatigue and hopelessness, using small accents to do so at every step. When the girls do collapse onto the ground, Molly sees an eagle soaring in the sky above them. This eagle, as explained by Molly’s mother in opening scene, was a symbol of protection and safety in Aboriginal culture. The appearance of this eagle in their time of need emphasises how the Aboriginals are truly bonded, psychologically and physically, to their land and culture. In this scene, the camera shifts back and forth between their elders back at Jigalong and the girls in the desert. This constant transition conveys the relationship between the girls (protected by the eagle) and the elders praying in an Aboriginal dialect for the girl’s safety. With these few examples, we can see how the Indigenous people have a special bond with their land through their cultural religion, which, in return, assists them when it is needed. Powerlessness of the Numbats (Aboriginals) against the Rabbits (Europeans) in The Rabbits is shown through the use of words within the mise en scene. Within this picture book, Marsden contributes to the meaning of the story to the readers through very short, but powerful sentences such as: â€Å"Sometimes we had fights/But there were too many rabbits/We lost the fights. † The way these sentences are structured so that it places emphasise the appropriate scenario that is occurring in each panel. With Shaun Tan, he conveys the powerless nature of the Indigenous by placing the Europeans in the foreground and the Aboriginal’s away from the focal point. For example, in panel eleven, the rabbits (Europeans) arjplaced in the foreground of the scene, holding up the words, â€Å"and they stole our children† and the tiny numbats (Aboriginals) are off into the far distance, holding up their hands in a fruitless gesture whilst their children are being taken away from them. This representation of the numbats in the background shows how the Europeans have gained most of the control in their land, causing a massive imbalance in power. The Rabbits and Rabbit Proof Fence provide audiences with different representations of the Indigenous culture by presenting various ideas by using visual and literary techniques to support them with: music, changing camera angles, exaggeration and perspective being a few that were discussed.

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.

My Learning Experience Essay

How is it precisely, that people learn things? As you know, when being taught something it is presented through our five senses. Studies indicate that when it comes to the succession of entirely grasping the concept of something, how that information is presented is a governing factor. Furthermore, when you apply this concept to everyday life it is apparent that college educators should present information in a way that is best suitable to the content rather than the student. On my spare time, I like to disassemble and reassemble whatever computer devices I may have in my possession. About a week ago, I discovered that it is possible to get a custom colored added to your Apple iphone. Yesterday, I decided that I was going to learn how to disassemble my iphone. So naturally, when my custom purple parts came in the mail, I decided it was time to go to work. I approached the tasks by using what is known as the â€Å"Scientific Method. † This method is a form of learning style and includes the preliminary steps such as: visual research, recording data, formulating a plan and finally, executing your hypothesis on a test subject. Learning how to do this task is not easy, because I did not have a physical teacher and I was inexperienced with the mechanical design of the Apple iphone. I followed a visual tutorial that I found on Youtube on the disassembly of my specific phone. I watched the video once before determining that if I followed the guide in complete synchronization, that I would be able to apply the proper parts and make the phone look better than before. Which was a custom purple front and back-plate that I ordered online. Next, I put the video on widescreen and tried my best to mimic the guide as he move through the tutorial. I managed to completely disassemble my phone to the smallest of its components due to the effects of the visual interpretation I stored in my head from watching the video. Surprisingly, looking at the phone in pieces made way more sense than looking at it as a whole because you could see how every little piece adds up to its functional design. In my hands on experience, I learned how many things worked on the device without having read a manual. Furthermore, when I began to reassemble my iphone, I felt so confident in my ability that I closed out the tutorial that I reassembled without any help. Furthermore, when I was taking the iphone apart it took me about an hour to fully disassemble it but when I put it back together it took half of the time. This was made possible because of the video of the virtual instructor that I found on Youtube using the â€Å"Scientific Method†. I memorized every piece of the iphone because I had a vivid picture of the tutorial in my mind. This just goes to show how the use of a learning style is a governing factor of whether something is fully learned or not. The articles â€Å" Ask The Cognitive Scientist† and â€Å" The Myth of Learning Styles†, by Daniel T.  Willingham are informational collaborations on the study of cognitive science and its relation to how the human mind learns. On the other hand, the article â€Å"Learning Styles Fact and Fiction† by Derek Bruff slightly differs from the arguments posed by Willingham’s articles. The article â€Å" Ask the Cognitive Scientist†, analyzes whether visual, auditory, and kinesthetic learners actually need to be learned though visual, auditory, and kinesthetic instruction. Indicated studies suggest that to learn new material effectively depends on the modality of the content. In other words, it is how new knowledge is introduced to a person that affects whether that material will be able to effectively be learned. In fact, some topics may call for more than one modality to be used. Furthermore, the article â€Å"The Myths on Learning Styles† questions the accuracy of learning styles by illustrating four different theories on learning styles. In summation, the article illustrates that a certain number of factors that vary from person to person and are known to affect learning styles. These factors include ability, background knowledge, interest, and intelligence. The authors argue that the belief in learning styles continue to persevere because learning styles have become common knowledge or a widespread acceptance. In addition, most of the general theories on learning styles are true. However, people need to take into account the differences in learner ability. Overall, the author focuses on the belief that students have different many factors involved when it comes to learning but there are no difference their learning styles. On the other hand, the article â€Å"Learning Styles Fact and Fiction† by Derek Bruff argues that the analysis of the learning styles illustrated by the other two articles may be true, but they area not precise. Furthermore, pinpointing a student’s learning style through test does not have an affect on how well they will learn through various other activities. According to the article, there are precisely three main important factors about modalities drawn from cognitive science. These three factors include are that visual thinking tools help everyone, using the best modality or modalities for the content, and that people learn new material best when they encounter numerous times in numerous different ways. Overall, the incorporated studies illustrate the concept that how information is presented to a person effects how effectively a person learns that information. My experience further displays how the use of an effective learning style as a means of approach when dealing with a task I’m not experienced in is a tremendous contribution to whether information presented to a person is fully understood or not.

R.V. Martin (Anthony Edward (2001) ECWA Crim 2245; Q.B1 Case (Critic) Essay

R.V. Martin (Anthony Edward (2001) ECWA Crim 2245; Q.B1 Case (Critic) - Essay Example The jury could convict the defendant if self-defence evidence presented by the defendant raised doubts or the fact that Mr, Martin had used excessive force. The manslaughter charge that Mr. Martin faced would mean the defendant is believed to have used excessive force then the sentence would not be a life imprisonment. Then this would mean that the jury did not believe the defendants defence of having acted on self-defence. The facts that led to, the sentencing of Mr. Martin is knowledge that Mr. Martin used his firearm, yet he knew he was entitled to possessing it. The jury strongly believe that the although it is true that the two men who broke into Mr. Martins house intended to commit a burglary, Mr. martin was entitled to use reasonable force yet he used excessive force when he shot the 16 year old dead and left the other seriously injured. According to the jury Mr. Martin did not act reasonably in both of the cases. The judge in passing the sentence took into consideration the f rustration that Mr, Martin felt at the event of the Burglary as well as the medical report presented by his doctor. The court put into account the situation threat Mr. Martin faced, but it also pointed out that a dangerous weapon was not to be used in the manner that Mr. Martin used during the night of the Burglary. According to Almandras, she points out that the law states clearly that a householder may be liable in civil law or criminal law or in both if he is found to have used unwarranted force in opposition to a burglar or trespasser resulting to the death of the intruder or injury. Matters raised during Mr. Martin’s case suggest that any householder who kills or injuries a burglar will have a complete defence. The defendant is acquitted if he used was reasonable force and this must prove to be in defence of himself or another in the prevention of a crime (2011. p.1). The principal issue raised by conservatives is the measure of reasonable force, which they argue, should be proven, and the householders would not face prosecution unless their action is proven grossly disproportionate. However, democrats support the view that the current law was reliable and did not require a change. In the case, of Mr. Martin Almandras observes that the accused Mr. Martin had experienced several break ins. Mr. Martin had already expressed his dissatisfaction with the police response. On the night of the burglary, Mr. Martin shot onto the two burglars with an unlicensed gun. During his appeal, Mr. Martin presented fresh psychiatric evidence showing that, he was suffering from a long personal disorder. However, the court still ruled that the Mr. Martins state of mind was irrelevant to the purpose of self-defence. The psychiatric evide

Qualitative proposal research regarding ARE DOCTORS SUPPORTIVE OR Thesis

Qualitative proposal research regarding ARE DOCTORS SUPPORTIVE OR OBSTICLES IN QUALITY IMPROVMENT PROGRAM - Thesis Example Physicians often view CQI as a threat to professional autonomy (McLaughlin & Kaluzny, 1990) and are skeptical that a management technique can improve patient outcomes. Structural barriers, including inadequate training (Shortell et al., 1995), longstanding social norms (Mittman, Tonesk, & Jacobson, 1992), and the fact that many physicians are independent providers (Chan & Ho, 1997), can also impede physician involvement in CQI and other changes in health care. Physician involvement in CQI becomes critical as quality improvement initiatives turn from administrative functions (e.g., streamlining outpatient registration) to clinical functions (e.g., increasing adherence to clinical practice guidelines). Unfortunately, traditional approaches to physician behavior change are unlikely to increase physician involvement in CQI. A meta-analysis of 102 studies examining the efficacy of continuing medical education strategies found that our most heavily used interventions, educational materials and conferences, tend to have little impact on physician behavior or patient outcomes in health care (Davis, Thomson, Oxman, & Haynes, 1995). There is growing recognition that the success of interventions may depend in part on individual readiness to change (Armstrong, Reyburn, & Jones, 1996; Cantillon & Jones, 1999; Davis et al., 1995). The transtheoretical model (TTM, also known as the stage model), one of the leading approaches to health behavior change, offers a promising approach to behavior change among health care professionals. The model systematically integrates the following four theoretical concepts central to change: The TTM understands change as progress, over time, through a series of stages: precontemplation, contemplation, preparation, action, and maintenance. Nearly 20 years of research on a variety of health behaviors have identified processes of change that work best in each stage to facilitate progress. This research can serve as a

Wgs Essay Example | Topics and Well Written Essays - 500 words

Wgs - Essay Example AWDF also mobilizes human, material and financial resources in order to foster gender parity in Africa, and to promote the rights of African women. AWDF believes that helping women organizations acquire enough skills, adequate livelihoods, information and the chance to actualize transformatory decisions gives rise to all-inclusive, dynamic and healthy communities (See: http://www.awdf.org/our-work/about). The problems that AWDF seeks to address are oppression of women’s rights, minimal political participation, conflicts, HIV/AIDS prevalence, economic disempowerment of women, and the absence of health and reproductive rights of women. AWDF sees these problems as social challenges as stark manifestation of the position of powerlessness into which patriarchal African societies relegated the womenfolk. In this light, AWDF describes these issues as thematic areas (goals). The failure to democratize has exacerbated women’s problems. Undemocratic governments lack stable mechanisms for the peaceful transfer of power from one regime to another. Political violence readily erupts after elections in Africa, with women suffering the heaviest casualty. Likewise, these governments, because of the absence of checks and balances, suffer a lot of excesses from the executive wing; with corruption, ineptitude and inequitable distribution of resources being prevalent. Women suffer the most in these governments due to the absence of affirmative action (See: http://www.fawe.org/). AWDF identifies itself explicitly as feminist. Nominally, the second initial of the acronym AWDF standing for ‘women’. Secondly, the aim of the organization underscores the restriction of its services to women, since AWDF asserts that its chief intent is funding African women’s organizations. Thirdly, AWDF staff comprises women only. Some of its leaders are Professor Bene Madunagu (Nigeria), Prudence Mabele (South Africa), Dr. Rose Mensah Kutin

Demand-side and Supply-side Policies on Economic Growth Case Study

Demand-side and Supply-side Policies on Economic Growth - Case Study Example These policies are either expansionary (catalyze spending in a recessionary economy) or contractionary (reduce spending in an inflationary economy). Also, supply side policies are those policies employed by the government to increase the country’s productivity hence shifting the aggregate curve outwards. They also are designed to affect an economy’s ability to produce goods and services. They increase the country’s aggregate productivity over time and improve the potential of the economy to produce. These policies are always expansionary with an aim increasing an economy’s production capacity which translates into increased living standards (Sloman, 2006). Demand side policies are further broken down to fiscal and monetary policies. Fiscal policies are those policies that are aimed at bringing changes in the government spending or taxes collected while monetary policies aim at bringing changes to the money supply engineered by the central bank. Expansionar y policies are then defined as those policies designed to stimulate economic growth through changes in real Gross Domestic Product (GDP) and the potential output of the economy (Economics Online, 2013). The policies are characterized and implemented in the demand side by any of the four categories of expenditure i.e. consumption expenditure, investment expenditure, government expenditure, or net export expenditure that constitutes the Gross Domestic Product (GDP). On the supply side, the expansionary policies are designed to add flavor to the capacity of production of the economy through labor policies (education, immigration, retirement), capital accumulation, research and development (seeking technological improvements), or promotion of resource availability. Monetary policies lower rates of interest that accompany an increase in money supply hence affecting investment expenditure. A monetary policy would increase the amount of local currency available in the exchange market which will then weaken the rates of exchange with other currencies. Also, the lower rates of interest will make the economy unattractive to investors when compared to other economies which will lead to a capital overflow resulting in the sale of domestic assets and the currency in the exchange market resulting in an ultimate weak currency. A weaker currency makes exports relatively cheaper to foreign buyers hence will stimulate the demand for the local goods while at the same time imports will be more expensive to domestic buyers leading to a reduced demand for imported goods (Pettinger, 2011). This will result in an increase in Net Export expenditure. In times of large deficits in the budget, fiscal policies tend to be missing from the policy maker’s ideologies. These policies are easy to legislate as they are politically popular and supported. Monetary expansionary policies are ineffective and unpredictable compared monetary contractionary (Sloman, 2006). In a case where the wea k economic growth or high level of unemployment worries the Federal Reserve, the policy will react by increasing bank reserves by open market purchase (where the central bank buys or sells government bonds on the open market to manipulate the short term interest rate and supply of base money in an economy) prompting banks to convert their reserves into loans to their customers.  

Ethical behavior in business Essay Example | Topics and Well Written Essays - 500 words

Ethical behavior in business - Essay Example This incident is a serious matter that should not be treated lightly. To clean up the mess the company has to invest millions of dollars, but the damage caused by the spillage hurt the ecosystem and killed thousands of animals. Big Dirty Oil faces an ethical dilemma in regard to how the firm should approach the problem. This essay includes the view and perspective of three stakeholders: CEO, local fisherman, and the shareholders of the company. The CEO of a company is the person that has the most power within an organization. When a firm faces any controversial situations the CEO must act as the spokesman of the organization. The oil spillage that occurred off the coast of British Columbia and Alaska was a major crisis that had to be attended to immediately. The CEO of the company must find a balance between doing the right thing and maximizing shareholders’ wealth. Maximizing shareholders’ wealth is the goal of all publicly traded companies. In light of the sensitive situation the CEO should have reacted in a different manner. The current position of the CEO is that the incident was a tragedy and he offered two million dollars to aid in the clean up. The proposal of the CEO was outrageous due to the fact that it could cost hundreds of millions of dollars to properly clean up the area. The CEO acted in an unethical manner. Instead of facing up to the problem he dismissed the protests against the company by ca lling the protesters â€Å"the outpourings of Greenies and other fanatics.† The reality was that the company had polluted thousands of square meters of water and killed thousands of fish and wildlife in the region. These creatures no longer had a habitat to live. The stance taken by the CEO was wrong. He cared more about the quarterly profits of the company than about the well being of thousands of animals and hundreds of fishermen that depended on fishing in the region everyday to support their families. The fishermen in

National and International Perspectives on Health (Mental Health Essay

National and International Perspectives on Health (Mental Health Nursing) - Essay Example The symptoms are sometimes responsible for major psychological and social problems especial at work and in relationships. If the disorder is left unattended, it may lead to serious mental conditions that may result into the death of victims. In the U.K for instance, the country has properly established intervention mechanisms that ensure children and other people suffering from this disorder are diagnosed and treated effectively. On the other hand, Sri Lanka has had to battle with this order for a very long time.This has been brought about by the country’s inferior structures and response to these problems and others related to it. Many children that have suffered this condition in Sri Lanka have ended up with serious mental problems compared to the United Kingdom and other countries where there are clearly defined systems and structures to address the problem. This paper examines the prevalence of PTSD and the impacts it has had to children in Sri Lanka and the United Kingdom. It compares how intervention mechanisms have been adopted in the two countries, including the future of mental health nursing as far as PTSD is concerned in the United Kingdom Sri Lanka has been on the path of recovery after having endured a 30 year period of armed conflict that has affected not only the economy of the country, but also has caused serious Post Traumatic Stress Disorders in children and other people in its population (Abeyasinghe 2012, 376). It is estimated that over 100, 000 of the country’s army were involved in various types of direct and indirect combat. The experiences during that time were hostile and pathetic; they included screams from all over, handling decomposing bodies of people among others. The trauma from the war is said to have led to serious psychological problems among the children and adults at large. The Sri Lankan government has responded to the increasing

Position of the Music Industry Prior to Introduction of Internet Essay Example for Free

Position of the Music Industry Prior to Introduction of Internet Essay In the music industry prior to the introduction of internet marketing there were different roles being played by different actors of the market. The usual way a product is prepared for market is to contract the artists. The artists who were the content providers record materials which are either their own or provided to them by other writers. This is clearly depicted in the figure below. Traditional Value Chain in the Music Industry Source: John B. Meisel and Timothy S. Sullivan The recordings will be done on the basis of the contracts entered into with the recording companies. Hence the power and control over the supply of the product remained with the record company. The recording company thus would be regarded as the holder of the major item of value in the supply chain being the exclusive rights over the recorded artists’ content. (Hardaker and Graham, 2001) Most of the part of the distribution is in the hands of the record companies and they also retain the rights to select the suppliers. The distribution and supplier selection is based on the record companies’ perception about the quality of the recording and the music, past reputation of the suppliers and the contract price for the recording. In return for the content in the form of recording, the artist is compensated by the provision of promotions for the recording and its merchandising in connection with the sales there of and the distribution of the content as a saleable commodity – CD for example. It was usual in the traditional music industry that the major record companies have their own distribution channels and businesses. Hence it would become necessary for a retailer to source his music products from different sources. Sometimes the retailer may have to place orders with major record companies and up to 20 other firms from the independent sector. The new releases of music albums or other sales of the record companies are usually handled by the wholesalers. If the retailer would like to follow the wholesaler route then he might have to order through only one wholesaler. The main wholesalers also offer another service called ‘rack jobbing’ which is a different method of supply being adopted by them. The function of a rack jobber includes the supply of complete package that contains records and other promotional and display materials. It is also the duty of the wholesaler to keep a regular stock usually on a sale or exchange basis. Just as the advancement in the telecommunication had its effect on all the other sectors from airline reservations to banking and related financial services the music recording industry has also been severely impacted both positively and negatively observes Eric de Fontenay. In fact the impact of internet on the music industry is much more profound than on any other industries. Despite the fact that the entertainment related products and services have taken their own time to develop and take advantage of the improvements in digital technology over the decades, during the intervening period the overall structure of the industry has remained dormant. The reasons for the industry to remain without major changes can be traced to the following reasons: 1. The cost of creation of content has always remained higher and this prohibited any new entrants in to the industry. 2. The structure of content ownership and rights of licensing system remained unaltered thereby keeping the structure of the industry in tact. 3. There has been a continuous necessity for the presence of a distribution network almost everywhere in the world irrespective of the geographical barriers. This has restricted the existing firms to make any changes in the structure. There was no possibility of new firms entering the market in view of the high capital intensive nature. 4. Similarly there had always been a constant scarcity for the distribution networks which also prevented any new forms of distribution or change in the structure of the distribution networks. (Eric de Fontenay) The internet has affected the music industry in so many ways. It has made the industry incur additional costs in completely restructuring itself. Further the internet has reduced the entry barriers. This was possible by a considerable increase in the number of downstream outlets having varied nature. At the same time the internet has provided the actors in the upstream end to enjoy greater control over the aspects of content ownership, production and distribution. This has created a distinct fear in the record labels that they cannot eliminate the possibility of getting bypassed by both the markets in the downstream and upstream. This impact has created the following reaction on the part of the traditional industry actors. They tried to impose the existing rules and procedures to the new medium so that they could exercise the same leverage and control over the market. The process by which they attempted to do it involves a twin aspects strategic approach. At one end they used legal channels to restrict the availability and use of the new technology in the Industry. On the other end they adopted new technologies to tackle the potential legal threats that would affect the control derived by them from the traditional systems. This strategy backfired and left them high and dry in the market while new information technology players like AOL, Microsoft, E Music and MP3 took advantage of the stalemate. They reacted aggressively by building their infrastructure and systems for the online marketing and distribution of music. They also involved themselves in the retailing of music over internet. The distribution of revenues in the music industry involves the portion of the performer. As per the contract terms the performer is to be paid a portion of the revenue each time there is a sale of the record. Before the money is paid to the performer the revenue is to be apportioned towards the expenses incurred by the company for marketing and distribution. This gives an opportunity for the artists to earn considerable amounts from the sale of products. For gaining maximum revenue the artists should control the publishing rights to their songs or they have the capacity to negotiate contracts with terms that are favourable to the artists. In the case of revenue distribution Internet has its impact on the industry in the following respects.

Concepts in Nursing Research Methods

Concepts in Nursing Research Methods Critique criteria The criteria used for this critique were derived from relevant nursing literature (Feninstein Horwitz, 1997; Cormack, 2000; Khan et al, 2003). About a dozen criteria were specified: design, sample, inclusion/exclusion criteria, time frame of study, data collection, reliability validity, and data analysis. Study Design Catlette (2005) used a qualitative design. While this approach has its merits, principally a greater degree of realism and richer data, it has a number of significant drawbacks (Coolican, 1994). Observations are typically unreliable. In other words, if the same nurses were interviewed on several different occasions, about workplace violence, using the same open-ended interview protocol, their responses may vary somewhat. Various biases creep in, often caused by situational factors (e.g. open-ended questions, a very violent week followed by a particularly calm week), or personal considerations (e.g. memory deficits). Furthermore there is low internal validity. This means that it is difficult to establish with any certainty the relationship between variables, due to the lack of statistical analysis (which can estimate the probability that results occurred by chance). For example, Catlettes interview data suggests a link between workplace violence and feelings of vulnerability amongst n urses. However, the extent to which the former variable causes the latter cannot be reliably established in a qualitative study. Winstanley and Whittington (2004) enjoy the precision of a quantitative design. While internal validity is high, the level of realism is questionable. Participants were ‘forced’ to respond to predetermined questions (e.g. on physical assault) using a fixed response format (e.g. ‘Once’, ‘More than once’). Thus, the data obtained was heavily influenced by the kind of questions asked and the particular response format used. In the real world, health care staff may perceive the level of aggression in terms that don’t match the questionnaire format. For example, a nurse may perceive physical assaults as ‘sporadic’ or ‘once in a blue moon’. Since these categorisations weren’t available in the questionnaire, the study effectively lacks a certain degree of realism. In a qualitative desi gn, subjects describe the world as they see it, rather than via terms imposed by the researcher. Sample Ideally a sample should be randomly selected so that it is representative of the population from which it was drawn, in this case nurses or health care professionals. This allows findings from a single study to be generalised to the wider community. Catlette (2005) used a convenience sample, meaning it wasn’t representative of nurses in general. Granted there are considerable practical and logistic difficulties in trying to recruit a random sample of nurses. Their busy schedules and irregular shifts, for example, hamper proper scientific selection. It is also quite common for small convenience samples to be used in qualitative studies, since it is often impractical to conduct in-depth interviews with large groups. Nevertheless, Catlette’s findings, while relevant to the particular trauma centres involved, are unlikely to apply to nurses in general. This is a serious limitation, since Catlettes stated objectives suggest a general interest in the level of violence in hosp ital emergency departments, rather than the particular trauma units from which subjects were drawn. Winstanley and Whittington (2004) also appear to have a used a convenience sample: they simply invited health care staff working in a general hospital, and who had regular contact with patients, to participate. Although the target sample was quite large (a bigger sample improves representation), only a minority of staff actually completed and returned questionnaires. All in all, participants weren’t recruited randomly, therefore the findings cannot be generalised to the wider population of health care staff. Inclusion/Exclusion Criteria Both studies seemed to have clear inclusion/exclusion criteria. Catlette (2005) only recruited and interviewed nurses who were registered, worked in a level 1 trauma centre, and had experienced workplace violence. A clear definition of what constituted violence was developed, helping to minimise any ambiguities about eligibility. Winstanley and Whittington (2004) also specify inclusion criteria. Only health care staff that had regular and substantial contact with patients were invited to participate. What constituted ‘regular’ and ‘substantial’ contact was well defined (e.g. daily contact with patients). The advantage of having clear inclusion/exclusion criteria is that it helps the researcher recruit a homogenous sample. If the participants in a study are too diverse, this effectively introduces additional sources of error that may obscure interesting themes, or relationships between variables. Findings may be more difficult to interpret. However, a major d isadvantage of a homogenous sample is that it is invariably ‘ad-hoc’, that is special or unique, and hence unlikely to reflect the wider community. Nevertheless, it can be argued that sample homogeneity isn’t problematic if the wider community of interest exactly matches the inclusion/exclusion criteria. For example, Winstanley and Whittington’s (2004) study was about patient aggression towards health care staff. Thus, the population of interest was invariably going to be staff that had regular contact with patients. In this respect the sample selected corresponds with the population of interest. However, randomly selecting nurses from the designate population would have provided a representative sample that permits useful generalisations. Simply using volunteers, as Winstanley and Whittington did is unscientific. Time frame of study Winstanley and Whittington’s (2004) study was effectively a retrospective (i.e. cross-sectional) survey. This means that data was collected at one point in time, specifically an 8-week period. Retrospective designs are considered inferior to prospective (i.e. longitudinal) designs in which data is collected on two or more occasions, over several weeks, months, or even years (Coolican, 2004). This method allows tentative causal inferences to be made – if a variable measured at Time 1 predicts or correlates with a factor measured at Time 2, then there is a possibility that former variable affected the latter, but not vice versa. Retrospective designs don’t allow for such inferences. Any correlations between variables are just that – correlations! There is no sequence that may help delineate possible causality. For example, in their introduction and statements of study aims, Winstanley and Whittington imply that particular professions (e.g. nurses, doctors) a nd hospital departments (e.g. medical, A E) may elicit different levels of physical aggression experienced by staff. Thus, profession/department seemed to be conceptualised as causal factors. However, although data analysis revealed relationships between these factors and physical aggression, there is no provision in the retrospective design to infer causality, since all the variables are measured simultaneously. A prospective method in which profession/department predicts experiences of physical assault several weeks subsequently would be more conclusive. Catlette (2005) doesn’t explicitly state the time frame for her study, albeit interviews typically take several days, weeks, or perhaps months to complete. Notions of prospective and retrospective designs are typically associated with quantitative studies, and rarely applied to qualitative research. This is because qualitative studies are often exploratory, merely seeking to identify interesting phenomena rather than estab lish causal relationships between variables. Nevertheless, interviewing participants on two or more separate occasions can be used to demonstrate the robustness and reliability of any themes observed. For example, if the same themes emerge during interviews conducted at two different points in time, this would suggest that the themes are significant rather than fleeting. Data Collection Catlette (2005) appears to have used semi-structured interviews for data collection (Coolican, 1994). By asking every interviewee pre-set but open-ended questions in a particular sequence, she avoided the inconsistency and sloppiness often associated with wholly unstructured (i.e. casual) interviews. It is possible the interviews were informal but guided, meaning that pre-set questions were asked, albeit in no particular order. Either way, a guided or semi-structured interview suffers from certain constraints. Asking specific questions, albeit open-minded ones, restricts the interviewers flexibility to ask follow-up questions depending on the interviewees response. Interviews are also heavily affected by interpersonal factors, such as lack of rapport, physical attraction, and psychological manipulation. Winstanley and Whittington (2004) collected data via a questionnaire. This method has a number of limitations. One is the typically low response rate. Of 1141 questionnaires posted ou t to participants, only 375 (33%) were returned, denoting a considerable waste of resources. Often the questionnaires returned represent an unusually keen sub-sample that may differ in key respects from the original target group. This means that the researcher has to devote time and resources establishing what these differences are, and how they might affect the results. Furthermore, because the final sample is smaller, statistical power is reduced, increasing the possibility of a type II error. Another limitation of questionnaires is the use of restricted (or ‘forced choice’) response format. For example, subjects in Winstanley and Whittingtons’ (2004) study were forced to choose from three options – ‘none’, ‘one’ or ‘more than one’. Thus, there is no room for participants to qualify their answers, for example by pointing out memory lapses (e.g. ‘I can’t remember’), or indicating ambiguous experie nces (e.g. ‘not sure’). All in all, these restrictions reduce the realism and richness of data collected. Interviewing subjects on the same issues, but using open-ended questions, will probably yield slight different outcomes to those reported by Winstanley and Whittington (2004). Another limitation is that the bulk of questionnaire communication is written. There is no provision to measure visual cues and gestures, which typically account for much of human communication, or even auditory cues. For example, a frown or grunt, may signify a particularly traumatising experiencing, which simply can’t be detected from questionnaire responses. Finally, questionnaires are often completed in the absence of the researcher (e.g. postal questionnaire), making it difficult to supervise the proceedings, or verify whether the subject is the same person who completed the questionnaire. Overall, these constraints negate the conclusiveness of Winstanley and Whittington’s ( 2004) findings. Data Analysis In line with standard procedure in qualitative research Catlette (2005) performed thematic analysis to identify recurring patterns in the data. Meaningful information was extracted from the interview transcripts, after which themes were identified using a coding system. Although a highly useful procedure, Braun and Clarke (2006) note that thematic analysis has certain disadvantages. One is the possible overlap between themes. Catlette identifies two themes – vulnerability and inadequate safety measures. Categories, and subcategories reported suggest considerable overlap between these dimensions (e.g. the sentiment ‘feeling unsafe’ may depict both feelings of vulnerability and an unsafe environment). Another weakness is the high correspondence between the data collection questions (i.e. interview guide) and themes identified. In other words, the themes reported merely reflect the questions asked during the interview (e.g. questions on safety, such as â€Å"How do you feel about the safety of your workplace?† are bound to produce safety-related responses, and hence themes). This suggests very limited analytic work was done to identify themes independent of the interview format. Another shortcoming of thematic analysis is failure to incorporate alternative or contradictive data in the results reported. Catlette offers little if any account of oddities in the data that don’t necessarily fit the two emerging themes. For example, the interviews revealed that violence wasn’t a concern during interactions with co-workers. Clearly this revelation is incompatible with the notion of vulnerability and lack of safety in the workplace. Yet, little is made of this inconsistency, making Catlettes’ rather ‘tidy’ themes appear rather suspicious. Few data sets in qualitative research are completely harmonious with no contradictions, so a study that fails to report these oddities is highly questionable. Winstanley and Wh ittington (2004) employed an inferential statistical test to analysis their data, consistent with the quantitative design of their study. Chi-square was used to test for significant trends in the frequency of physical assaults as a function of different health care professionals (e.g. nurses and doctors) and hospital departments (e.g. medical, surgical, A E). Chi-square was appropriate given that the data was categorical (i.e. in the form of frequencies). However, as a non-parametric test, chi-square lacks sensitivity. This combined with the limitations of frequency data (e.g. it fails to account for subtle degrees of variation between individual subjects or groups; for example, asking nurses if they’ve experienced aggression ‘once’ or ‘more than once’ fails to take into account any differences in the intensity and duration of these aggressive episodes), increases the risk of wrongly accepting the null-hypothesis. Reliability Validity A major methodological concern in scientific research is reliability and validity. Reliability refers to the consistency of observations, while validity depicts the authenticity of observations. Both issues are particularly pertinent in qualitative studies, due to the lack of structure, precision, and quantification. Catlette (2005) appears to have taken steps to enhance reliability/validity. She kept a journal throughout the duration of the study, in order to identify any biases that may corrupt the data. Interviews were conducted using a standard protocol, then the data was transcribed verbatim, and analysed using regular procedures. However, these measures may be inadequate. Coolican (1994) identifies several procedures for ensuring good reliability, none of which appears to have been used by Catlette: triangulation, analysis of negative cases, repetition of research cycle, and participant consultation. Triangulation involves verifying emerging themes using another data collection method other than open-ended interviews. For example a questionnaire measure of perceived workplace violence and safety strategies could have been administered or close-ended interviews conducted. Data from these alternative methods could then be compared with the original observations to gauge the degree of consistency in emerging themes. Analysis of negative cases involves scrutinising cases that don’t fit the emerging themes. Repetition of research cycle entails repeatedly reviewing assumptions and inferences, to further verify emerging themes. Finally participant consultation involves communicating with participants to see if observations from the study match their own experiences. None of these measures seem to have been applied in Catlette’s study, raising serious concerns about the stability and authenticity of her observations. Winstanley and Whittington’s’ (2004) study doesn’t appear to have fared much better. Although the numerical preci sion inherent in quantitative designs offers some degree of reliability and validity, this is by no means guaranteed, and has to be demonstrated empirically. They fail to report any Cronbach Alpha reliability coefficients for the questionnaire used. Thus, it is unclear if the items in this instrument were internally consistent. Test-retest reliability wasn’t reported either, again raising questions about the consistency of participants responses over time. A badly designed questionnaire (e.g. one with ambiguous statements, or grammatical errors) could easily confuse participants, leading to irregularities in their responses over time. No information on validity is provided either. Normally, validity could be demonstrated by correlating data from the questionnaire with data from another measure of experiences of aggression (a high correlation would indicate good validity), submitting the questionnaire to a team of judges to ascertain if the content addresses all forms of human aggression (e.g. indirect forms of aggression, such as spreading rumours or social exclusion don’t appear to have been assessed), and even performing factor analysis to establish construct validity (i.e. verify the dimensions of aggression assumed to be measured by items in the questionnaire). These inadequacies render the findings from Winstanley and Whittington’s (2004) study inconclusive. For example, the claim that aggression is â€Å"widespread† is questionable because not all forms of aggression were measured. Overall, both studies are fairly categorical in their conclusions. Winstanley and Whittington (2004) surmise that their data demonstrates the significant levels of aggression to which hospital staff are exposed. Catlette (2005) reaches a similar conclusion, emphasising the vulnerability and lack of safety perceived by nurses. However, both studies suffer from various analytic and methodological constraints. Perhaps the most serious of these is the apparent absence of reliability and validity measures that may reveal any volatility or misrepresentations in the data. These limitations mean that any conclusions have to be regarded as tentative, subject to further research. Bibliography Braun, V. Clarke, V. (2006) Using thematic analysis in psychology. Qualitative  Research in Psychology, 3, pp.77-101. Catlette, M. (2005) A descriptive study of the perceptions of workplace violence and  safety strategies of nurses working in Level I trauma centres. Journal of  Emergency Nursing, 31, 519-525. Coolican, H. (1994) Research Methods and Statistics in Psychology, London, Hodder   Stoughton. Cormack, D. (2000) The Research Process in Nursing: Fourth Edition. London:  Blackwell Science. Eastabrooks, C.A. (1998) Will evidence-based nursing practice make practice perfect.  Canadian Journal of Nursing Research. 30, pp.15-36. Feninstein, A. R., Horwitz, R. I. (1997) Problems in the evidence of evidence-based medicine. American Journal of Medicine 103, 529-535. Khan, K., Kunz, R., Kleijnen, J. Antes, G. (2003) Systematic Reviews to Support  Evidence-based Medicine: How to Review and Apply Findings of Healthcare  Research. Oxford: Royal Society of Medicine Press. Winstanley, S. Whittington, R. (2004) Aggression towards health care staff in a UK  general hospital: variation among professions and departments. Journal of  Clinical Nursing, 13, pp.3-10.