AUSTRALIAN DEFENCE THE UNIVERSITY OF FORCE ACADEMY NEW SOUTH WALES

UNIVERSITY COLLEGE UNIVERSITY OF NEW SOUTH WALES AUSTRALIAN DEFENCE FORCE ACADEMY SCHOOL OF ENGINEERING AND INFORMATION TECHNOLOGY

Range and endurance modeling of a multi- engine aircraft with one engine inoperative (OEI)

THESIS

Ye Naung Kyaw Kyaw

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Supervisors: Dr Rikard Heslehurst, Dr Michael Harrap

26 November 2014

A thesis submitted for fulfillment of the requirements for the Degree of Master of Engineering in Aerospace (Research)

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ABSTRACT When one of the engines on a multi-engine aircraft stops working the one engine inoperative (OEI) condition exists. This causes several negative effects to a number of performance variables in addition to the loss of engine thrust. The range and endurance of an aircraft are directly related to the quantity of the fuel available and the fuel consumption rate.

This thesis was conducted to investigate range and endurance performance of a twin- engine jet aircraft of the Boeing 737 class, with One Engine Inoperative (OEI). The aims of the thesis also include analysis on All Engine Operating (AEO) performance including range and endurance performance, and turning flight performance. The modelling was mainly based on methods available in Jan Roskam textbooks and USAF DATCOM.

The model used Thrust and Specific Fuel Consumption data presented in Jenkinson, L.R., Simpkin, P., and Rhodes, D., “Civil Jet Aircraft Design,” and detailed aircraft geometry properties given in Jane’s All the World Aircraft as well as materials made available in references.

Required control surface deflections (ailerons and rudder) to maintain a moment balance in a given flight condition were determined. The increment in total drag (trim drag) on the aircraft due to these control surface deflections as well as the drag from wind milling inoperative engine were then added to the steady state drag. The total drag in One Engine Inoperative (OEI) condition was calculated to be increased by 30% at optimum range speed at 12,000 ft.

The range and endurance were calculated using the Breguet Range and Endurance equations and then compared with numerical integration methods to verify the reliability of the equations. It was observed that sensitivity of weights in determining range performance was not significant with numerical integration methods yielding favourable results.

It was found that the range performance with one engine inoperative (OEI) is approximately 2 to 5% superior while the endurance performance is about 11 to 14% superior to those with all engine operative (AEO) condition at flight levels where single engine flight is possible. The maximum one engine inoperative (OEI) altitude capability for the aircraft was estimated to be 12,000 feet. Speed reduction of about 15-20% of optimum range and endurance speeds with AEO is required to achieve optimum range and endurance performance in OEI condition for the aircraft.

Validation of the results predicted for AEO and OEI conditions for the aircraft with performance data in Boeing 737-300 flight planning manual revealed that difference fell within 11% for both conditions for range.

Finally, a further investigation into asymmetric thrust was conducted: turning performance (left turn vs. right turn) in a level coordinated flight condition with right OEI was analysed with turning on operative engine side (left turn with right OEI) proving a better option.

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DISCLAIMER

This thesis is an account of research undertaken by the author while being enrolled as a postgraduate student in fulfillment of the requirements for the degree of Master of Engineering in Aerospace at the University of New South Wales @ ADFA. Views expressed in this thesis are based on research and/or analysis conducted by the author during the candidature and do not represent the views of the University.

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ACKNOWLEDGEMENTS

It has been a long and winding journey over the past 3 years to arrive at the completion of this research project. First of all, I would like to thank my supervisor, Dr Rik Heslehurst, for generously dedicating his time to provide supervision, direction, inspiration and guidance as well as for leaving a comfortable space for my own ideas and creativity. His encouragement throughout the year has motivated me to finish this thesis to schedule and to the specifications that were initially planned. I would also like to thank Dr Michael Harrap, my co-supervisor for his valuable suggestions and feedback on my thesis even though he has retired from his position with the University since a while ago.

I can never thank enough my parents back home in Burma, Capt. Kyaw Kyaw Oo Zin and Dr. Khin Mar Cho, and my sister, Dr. Khine Cho Kyaw for their relentless support in the pursuit of my life goals. My special thanks also go to my beloved wife, May Cho Chit Htwe, for her kind care, patient love, and constant motivation even from thousand “nautical” miles away helped me through the hardest time throughout the year.

A special mention also goes to the academic staff on my annual review board, which provided constructive suggestions and comments on my progress throughout the candidature. I thank staff from the Academy Library for their thorough help on any assistance required with finding literature and texts necessary for the research. I would like to express my gratitude to all who have made the completion of this Thesis possible in any way. Thank you all.

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CONTENTS ABSTRACT ...... i DISCLAIMER ...... iii ACKNOWLEDGEMENTS ...... iv CONTENTS ...... v LIST OF FIGURES ...... x LIST OF TABLES ...... xiii CHAPTER 1: INTRODUCTION ...... 1 1.1 Background ...... 1 1.2 Origin of the Research ...... 2 1.3 Objectives of the Research ...... 2 1.4 Scope of the Thesis ...... 4 1.5 Assumptions and Limitations ...... 4 1.6 Thesis Structure ...... 5 1.7 Summary ...... 6 CHAPTER 2: LITERATURE REVIEW ...... 7 2.1 Introduction ...... 7 2.2 Aerodynamics ...... 7 2.2.1 Compressibility Effect ...... 8 2.2.2 Mach number ...... 8 2.2.3 Airfoils, Wings and Lift ...... 8 2.2.4 Aspect Ratio ...... 9 2.2.5 Lift for Wing-Body Interactions ...... 10 2.2.6 Drag ...... 10 2.2.7 Aerodynamic Force Coefficients ...... 11 2.3 Propulsion Systems ...... 11 2.3.1 Specific Fuel Consumption (SFC) ...... 14 2.3.2 Effects of Velocity and Altitude on Specific Fuel Consumption (SFC) ... 14 2.4 Equations of Motion ...... 14 2.4.1 The Four Forces ...... 14 2.4.2 Modelling the Equations of Motion ...... 15 2.4.3 Reference Frames ...... 15 2.5 Flight Dynamics and Control ...... 17

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2.5.1 Roll, Pitch and Yaw ...... 17 2.5.2 Control Surfaces ...... 18 2.6 Range and Endurance ...... 19 2.6.1 Range and Endurance - Constant AoA – Constant Mach ...... 19 2.6.2 Range and Endurance - Constant AoA – Constant Altitude ...... 19 2.6.3 Range and Endurance - Constant Altitude – Constant Mach ...... 19 2.7 One Engine Inoperative (OEI) Condition ...... 19 2.7.1 Thrust Asymmetry Effect ...... 20 2.7.2 Spillage Drag ...... 20 2.7.3 Trim Drag ...... 21 2.7.4 Range and Endurance Performance with One Engine Inoperative (OEI) . 21 2.8 Relevant Literature ...... 22 2.9 Summary ...... 25 CHAPTER 3: AIRCRAFT MODEL USED IN RESEARCH: B737-300 ...... 26 3.1 Introduction ...... 26 3.2 Brief History ...... 26 3.2.1 Wings ...... 27 3.2.2 Fuselage...... 28 3.2.3 Engine ...... 29 3.2.4 Control Surfaces ...... 29 3.2.5 High Lift Devices ...... 30 3.3 Aircraft Schematics ...... 30 3.4 Aircraft Details ...... 31 3.4.1 Powerplant Details ...... 31 3.4.2 Wing Geometry ...... 32 3.4.3 Horizontal Tail Geometry ...... 32 3.4.4 Vertical Tail Geometry ...... 33 3.4.5 Fuselage Details ...... 33 3.4.6 Weights ...... 33 3.4.7 Performance Details ...... 33 3.5 Estimation of Parameters ...... 33 3.5.1 Drag Polar Estimation ...... 34 3.5.2 Trim Drag Estimation ...... 34

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3.5.3 Estimation of Stability and Control Derivatives ...... 35 3.6 Summary ...... 36 CHAPTER 4: ALL ENGINE OPERATIVE FLIGHT ANALYSIS...... 37 4.1 Introduction ...... 37 4.2 Objectives ...... 37 4.3 Scope ...... 37 4.4 Thrust Model ...... 38 4.5 Specific Fuel Consumption Model ...... 39 4.6 Drag Polar ...... 41 4.7 Equations of Flight Equilibrium ...... 42 4.7.1 Stability and Control Derivatives ...... 43 4.8 Straight and Level Performance ...... 43 4.8.1 Variation of Minimum and Maximum Speeds with Altitude ...... 44 4.9 Range and Endurance Performance...... 46 4.9.1 Range and Endurance – All Engine Operative – Constant Altitude- Constant Speed ...... 46 4.9.2 Trim Angle of Attack and Elevator Deflections ...... 49 4.10 Limitations ...... 51 4.11 Summary ...... 51 CHAPTER 5: ONE ENGINE INOPERATIVE FLIGHT MODELLING ...... 53 5.1 Introduction ...... 53 5.2 Objectives ...... 53 5.3 Assumptions ...... 53 5.4 Lateral Stability and Control with One Engine Inoperative ...... 55 5.4.1 Lateral Equations of Flight Equilibrium ...... 56 5.4.2 Wind Milling Drag due to Inoperative Engine and Yawing Moment ...... 56 5.4.3 Yaw and Rudder Control ...... 57 5.4.4 Roll and Aileron Control ...... 59 5.4.5 Minimum Control Speed with One Engine Inoperative ...... 59 5.4.6 Trim Drag ...... 61 5.5 OEI Flight Analysis ...... 63 5.6 Range and Endurance with OEI ...... 68 5.6.1 Range and Endurance with OEI – Constant Speed and Constant Altitude 68 vii | P a g e

5.6.2 Range and Endurance –Constant Lift (AoA) and Constant Speed ...... 71 5.6.3 Range and Endurance – Constant Altitude and Constant Lift (AoA) ...... 72 5.6.4 Range and Endurance performance comparison AEO and OEI ...... 73 5.6.5 Weight Sensitivity on Range and Endurance ...... 73 5.7 Validation of Results ...... 80 5.7.1 Range Validation ...... 81 5.7.2 Endurance Validation ...... 81 5.7.3 AEO Range and Endurance Validation Discussion ...... 82 5.7.4 OEI Range and Endurance Validation Discussion...... 84 5.8 Summary ...... 87 CHAPTER 6: LATERAL CONTROL AND MANEOUVERABILITY WITH ONE ENGINE INOPERATIVE ...... 88 6.1 Introduction ...... 88 6.2 Objectives ...... 88 6.3 Lateral Control and Maneuverability ...... 88 6.4 Turning Performance ...... 89 6.4.1 Flight equilibrium during turning flight ...... 90 6.4.2 Load factor and bank angle ...... 90 6.4.3 Radius of turn ...... 93 6.4.4 Minimum Turn Radius ...... 94 6.4.5 Sustained Rate of turn ...... 96 6.5 Lateral flight equilibrium with OEI ...... 98 6.5.1 Yawing moment with One Engine Inoperative ...... 99 6.5.2 Effect of bank angle ...... 101 6.5.3 Minimum control speed when banked with OEI ...... 103 6.6 Level coordinated turn with One Engine Inoperative ...... 109 6.6.1 Change in control surfaces required for sustained level coordinated turn 109 6.6.2 Observations ...... 112 6.7 Summary ...... 114 CHAPTER7: CONCLUSIONS AND RECOMMENDATIONS ...... 115 7.1 Conclusion ...... 115 7.2 Summary of Findings/ Results ...... 115 7.3 Possible Future Directions for Research ...... 117 viii | P a g e

7.4 Final Comment ...... 118 REFERENCES ...... 119 Appendix A: Estimation of Drag Polar Parameters ...... 122 Zero Lift Drag ...... 122 Zero-lift drag coefficient due to fuselage ...... 122 Zero-lift drag due to Wing, Horizontal Tail and Vertical tail ...... 122 Zero-lift drag coefficient due to High Lift Devices ...... 123 Zero-lift drag coefficient due to Nacelle...... 124 Miscellaneous contribution to Zero-lift drag coefficient ...... 124 Correction factor ...... 125 Appendix B: Stability and Control derivatives estimation ...... 126 Estimation of stability derivatives ...... 126 Variation of Drag Coefficient with Angle of Attack ...... 126 Variation of Lift Coefficient with Angle of Attack: Lift Curve Slope ...... 126 Variation of Pitching Moment Coefficient with Angle of Attack ...... 128 Estimation of Longitudinal Control Derivatives ...... 128 Variation of Lift Coefficient with Stabilizer Incidence ...... 128 Variation of Pitching Moment Coefficient with Stabilizer Deflection ...... 128 Variation of Lift Coefficient with Elevator Deflection ...... 129 Variation of Pitching Moment Coefficient with Elevator Deflection ...... 130 Estimation of Lateral Stability Derivatives ...... 130 Variation of Side Force Coefficient with Sideslip Angle ...... 130 Variation of Rolling Moment Coefficient with Sideslip Angle ...... 131 Variation of Yawing Moment Coefficient with Sideslip Angle ...... 132 Estimation of Lateral Control Derivatives ...... 133 Variation of Sideforce Coefficient with Aileron Deflection ...... 133 Variation of Rolling Moment Coefficient with Aileron Deflection ...... 133 Variation of Yawing Moment Coefficient with Aileron Deflection ...... 134 Appendix C: Thrust Model Derivation ...... 135 Appendix D: Thrust Specific Fuel Consumption Model Derivation ...... 138 Appendix E: Boeing 737-300 Flight Planning and Performance Manual Data ...... 141

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LIST OF FIGURES Figure 1: Aerodynamic forces acting on an airfoil [3] ...... 8 Figure 2: Flight regimes and Mach numbers [5] ...... 8 Figure 3: Breakdown of drag build-up for a typical transport aircraft [6] ...... 11 Figure 4: Aircraft propulsion systems [12] ...... 12 Figure 5: A Turbofan Engine (Honda’s HF120) [13] ...... 13 Figure 6: Four forces of flight [12] ...... 15 Figure 7: Body fixed and earth fixed axis systems [18]...... 16 Figure 8: Stability axis system (non zero side slip) [18] ...... 17 Figure 9: Roll, pitch and yaw motion of an aircraft [19] ...... 18 Figure 10: Control surfaces of Airbus A320 [20] ...... 18 Figure 11: High drag characteristics of the Airbus A320-200 and Boeing 737-800[6].. 21 Figure 12: Airfoil sections used in Boeing 737-300 aircraft wings [36] ...... 27 Figure 13: Design Features of the Boeing 737-300 [38] ...... 29 Figure 14: Front view of Boeing 737-300[39] ...... 30 Figure 15: Side view of Boeing 737-300 [39] ...... 31 Figure 16: Plan view of Boeing 737-300 [39] ...... 31 Figure 17: Thrust available for different Mach number at various altitudes (2x Engine) ...... 40 Figure 18: SFC for different Mach No at different altitudes (2x Engine) ...... 40 Figure 19: Estimated drag polar for the B737-300 for different configurations ...... 42 Figure 20: Control surfaces sign conventions ...... 43 Figure 21: Thrust available (cruise) Vs Drag at 10,000 ft (AEO) ...... 44 Figure 22: Variation of minimum and maximum speeds with altitude (AEO) ...... 45 Figure 23: Range vs. Speed at different altitudes with AEO (at MTOW) ...... 47 Figure 24: Endurance vs. Speed at different altitudes with AEO (at MTOW) ...... 48 Figure 25: Trim angle of attack vs. speed at different altitudes ...... 50 Figure 26: Trim elevator deflection vs. speed at different altitudes ...... 50 Figure 27: Forces associated with OEI (Right Engine Out) [41] ...... 55 Figure 28: Force and moment the aircraft is subject to with OEI and side slip [41] ...... 57 Figure 29: Maximum sideslip Vs speeds at different altitudes (Right Engine Inoperative at low altitudes) ...... 58 Figure 30: Rudder deflections required for zero side slip at different speeds at different altitudes ...... 58 Figure 31: Aileron deflections (for zero rolling moment) Vs speed at different altitudes at max side slip ...... 59 Figure 32: Minimum Control Speed at different altitudes with max rudder deflection of 15 deg ...... 60 Figure 33: Profile Drag Increment: Plain Flaps [47] ...... 62 Figure 34: Trim Drag with OEI over a range of speeds at different altitudes ...... 62 Figure 35: Aileron (constant) and rudder deflection for zero side slip at different speeds at different altitudes with OEI ...... 64

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Figure 36: Bank angle for zero side slip at different speeds at different altitudes with OEI ...... 64 Figure 37: Thrust Available Vs Drag over a range of speed at 20,000 ft ...... 66 Figure 38: Thrust Available Vs Drag over a range of speed at 10,000 ft ...... 66 Figure 39: Thrust Available Vs Drag over a range of speed at 5,000 ft ...... 67 Figure 40: Thrust Available Vs Drag over a range of speed at S.L ...... 67 Figure 41: Range Vs Speed at different altitudes (OEI) (constant speed – constant altitude) ...... 68 Figure 42: Endurances Speed at different altitudes (OEI) (constant speed – constant altitude) ...... 69 Figure 43: Thrust available Vs Drag curve with OEI at 12,000 ft ...... 70 Figure 44: Typical passenger aircraft flight profile [18] ...... 74 Figure 45: Plot of specific range vs. speed at 10,000 ft using 5 weight steps (AEO) ..... 76 Figure 46: Plot of specific endurance vs. speed at 10,000 ft using 5 weight steps (AEO) ...... 76 Figure 47: Specific range vs. weights at 10,000 ft (at Max Range Mach No) (AEO) .... 77 Figure 48: Specific endurance vs. weights at 10,000 ft (at Max Range Mach No) (AEO) ...... 77 Figure 49: Plot of specific range vs. speed at 10,000 ft using 5 weight steps (OEI) ...... 79 Figure 50: Plot of specific endurance vs. speed at 10,000 ft using 5 weight steps (OEI) ...... 79 Figure 51: Specific range vs. weights at 10,000 ft (at Max Range Mach No) (OEI) ..... 80 Figure 52: Specific endurance vs. weights at 10,000 ft (at Max Range Mach No) (OEI) ...... 80 Figure 53: AEO Endurance estimation from Long Range Cruise En-route Fuel and Time [47] ...... 82 Figure 54: AEO Range Comparison Plot ...... 83 Figure 55: AEO Specific Range Vs Speed Plot ...... 84 Figure 56: AEO Specific Endurance Vs Speed Plot ...... 84 Figure 57: OEI Range Comparison Plot ...... 85 Figure 58: OEI Specific Range Vs Speed Plot...... 86 Figure 59: OEI Specific Endurance Vs Speed Plot ...... 86 Figure 60: Force components and geometry in level coordinated turning flight [1] ...... 90 Figure 61: Load factor variation with respect to speed at different altitudes (AEO) (MTOW) ...... 93 Figure 62: Turn Radius with respect to speed at different Altitudes (AEO) (MTOW) .. 94 Figure 63: Turn radius with respect to speed at different altitudes (AEO) (MTOW) (Zoomed) ...... 95 Figure 64: Sustained turn rate Vs speed at different altitudes (AEO) (MTOW) ...... 96 Figure 65: Load Factor vs speed at different altitudes (OEI) (MTOW) ...... 97 Figure 66: Sustained turn radius vs speed at different altitudes (OEI) (MTOW) ...... 98 Figure 67: Sustained turn rate vs speed at different altitudes (OEI) (MTOW) ...... 98

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Figure 68: Thrust moment, and yawing moment the aircraft is subject to at different speeds at different altitudes (negative bank angle of 5 deg, zero sideslip, max aileron) ...... 100 Figure 69: Thrust moment, yawing moment and rolling moment the aircraft is subject to at different speeds at different altitudes (positive bank angle 5 deg, zero side slip, max aileron) ...... 101 Figure 70: Bank angle effect on yawing moment developed at different altitudes with OEI (Right Engine Inoperative with Left bank turn at max gross weight) ...... 102 Figure 71: Bank angle effect on yawing moment developed at different altitudes with OEI (Right Engine Inoperative with right bank at max gross weight) ...... 102 Figure 72: Minimum control speeds and corresponding control surface deflections (-30 deg bank) ...... 105 Figure 73: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (-30 deg bank)...... 106 Figure 74: Minimum control speeds and corresponding control surface deflections (-60 deg bank) ...... 106 Figure 75: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (-60 deg bank)...... 107 Figure 76: Minimum control speeds and corresponding control surface deflections (30 deg bank) ...... 107 Figure 77: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (30 deg bank) ...... 108 Figure 78: Minimum control speeds and corresponding control surface deflections (60 deg bank) ...... 108 Figure 79: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (60 deg bank) ...... 109 Figure 80: Change in control surface deflections required for a level coordinated turn with AEO ...... 111 Figure 81: Change in control surface deflections required for a level coordinated turn with OEI ...... 112 Figure 82: Bypass ratio 6.5 Max Cruise Thrust [44] ...... 135 Figure 83: Thrust data curve fit ...... 136 Figure 84: Curve fit for A, B and C coefficients for thrust model ...... 137 Figure 85: Bypass ratio 6.5 SFC Data [44] ...... 138 Figure 86: SFC curve fit ...... 139 Figure 87: Curve fit of A, B, C coefficients Vs Mach No for SFC model ...... 140 Figure 88: CFM56 Turbofan Engine specifications [14] ...... 141 Figure 89: Long Range Cruise Enroute Fuel and Time (37000 ft to 29000 ft) Boeing 737-300 Flight Planning and Performance Manual [47] ...... 151 Figure 90: Long Range Cruise Enroute Fuel and Time (28000 ft- 10000 ft) Boeing 737- 300 Flight Planning and Performance Manual [47] ...... 152 Figure 91: Long Range Cruise Diversion Fuel and Time Boeing 737-300 Flight Planning and Performance Manual [47] ...... 153

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LIST OF TABLES Table 1: Details of powerplant used in Boeing 737-300 [40] ...... 32 Table 2: Details of wing design used in Boeing 737-300 [35] ...... 32 Table 3: Details of horizontal tail of Boeing 737-300 [35] ...... 32 Table 4: Details of vertical tail of Boeing 737-300 [35] ...... 33 Table 5: Fuselage details of Boeing 737-300 [35] ...... 33 Table 6: Boeing 737-300 weights [35] ...... 33 Table 7: Performance details of Boeing 737-300 [36] ...... 33 Table 8: Stability and control derivatives and their dependent variables [28] ...... 36

Table 9: CDo and K values for take-off, landing and clean configurations ...... 41 Table 10: Estimated longitudinal derivatives required for analysis ...... 43 Table 11: Thrust Available Vs Drag at various altitudes (AEO) ...... 46 Table 12: Optimum range and endurance at different altitudes with corresponding speeds (AEO at MTOW) ...... 49 Table 13: Minimum Control Speed and Stalling Speed (cruise clean configuration) at different altitudes with OEI ...... 61 Table 14: Vstall, Vmca, Vmin, Vmax with OEI at different altitudes...... 65 Table 15: Best range and endurance with corresponding speeds at each Altitude ...... 70 Table 16: Range and Endurance comparison for AEO and OEI at different altitudes ... 73 Table 17: Weight sensitivity on Range with AEO at 10,000 ft ...... 75 Table 18: Weight sensitivity on Endurance with AEO at 10,000 ft...... 75 Table 19: Weight sensitivity on Range with OEI at 10,000 ft ...... 78 Table 20: Weight sensitivity on Endurance with OEI at 10,000 ft ...... 78 Table 21: Range and Endurance comparison (Flight planning manual data vs Thesis) (AEO) ...... 83 Table 22: Range and Endurance comparison (Flight planning manual data vs Thesis) (OEI) ...... 85 Table 23: Summary of turning performance of B737-300 at 10,000 feet with AEO ..... 97 Table 24: Summary of Stall and minimum control speed with corresponding control surface deflections at various flight conditions ...... 105 Table 25: Trim control deflections and change in control surface deflections required for 20 degree bank ...... 112 Table 26: Summary of OEI and AEO results...... 117

Table 27: ΔCLmax estimation for different type of flaps [41]...... 124 Table 28: Bypass ratio 6.5 Max Cruise Thrust in table form ...... 135 Table 29: A, B and C coefficients Vs density ratio for thrust model ...... 137 Table 30: SFC Data in table form ...... 138 Table 31: A, B and C coefficients Vs Mach No in table form ...... 140 Table 32: International Standard Atmosphere[14] ...... 142 Table 33: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (37000 ft to 32000 ft)[47] ...... 143

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Table 34: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (31000 ft to 26000 ft)[47] ...... 144 Table 35: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (25000 ft to 20000 ft)[47] ...... 145 Table 36: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (13000 ft to 8000 ft)[47] ...... 146 Table 37: Long Range Cruise Table (One Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual (19000 ft to 14000 ft)[47] ...... 147 Table 38: Long Range Cruise Table (One Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual (13000 ft to 6000 ft)[47] ...... 148 Table 39: Long Range Cruise Altitude Capability (Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual[47] ...... 149 Table 40: Long Range Cruise Table (Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual[47] ...... 150

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1 CHAPTER 1: INTRODUCTION “To invent an airplane is nothing. To build one is something. But to fly is everything.” Otto Lilienthal

“Come to the edge. We might fall. Come to the edge. It's too high! COME TO THE EDGE! And they came, and he pushed, and they flew.”

— Christopher Logue

This thesis concerns the range and endurance modelling of a multi-engine aircraft of Boeing 737 class with one engine inoperative (OEI). This chapter of the thesis introduces the research project it is based on and presents background information concerning the project.

1.1 Background In modern aviation, the widespread application of multi-engine aircraft has resulted in marked improvement of flight safety as well as operational efficiency. However, at the same time, the probability of having an engine failure in multi-engine operations has increased consequently.

In twin engine aircraft, asymmetric thrust (due to failure of one engine) caused by asymmetric lift causes the aircraft to yaw which needs to be corrected by application of rudder. This rudder deflection induces adverse roll towards the opposite direction as one wing produces more lift than the other when the yaw is countered. This needs to be balanced with aileron deflection. An elevator deflection is also needed for pitching up and down trim. These control inputs contribute towards the increased total drag of the aircraft as trim drag which needs to be overcome with remaining thrust available.

The range and endurance of an aircraft are directly dependent on fuel availability and fuel consumption rate. The weight of the aircraft changes continuously as the fuel is burnt as flight progresses. The aircraft’s attitude, altitude and speed determine the fuel consumption rate. Flying slower than the normal cruise speeds could have adverse

1 | P a g e effects on fuel consumption as engines do not operate at the optimal throttle setting, causing higher consumption. A compromise must be reached between range, speed and weight to obtain the desired range and endurance performance.

1.2 Origin of the Research There has been a large volume of work directed towards analysis of effects of an engine failure in a multi-engine airplane, with focus more on emergency scenarios in commercial flights as required by stipulations mandated by civil aviation authorities. This research intends to look into using One Engine Operative (OEI) flight profile for mission requirements as opposed to emergency.

In reality, there are situations where an aircraft is required to fly without all engine operating (AEO) such as in long endurance missions in a P-3 Orion. In a four engine aircraft such as P-3, asymmetric flight is not a concern for (OEI) operations because asymmetric thrust can be balanced by remaining engines; the left outboard engine of P- 3, which has no generator is often shutdown, so is the right outboard engine occasionally, for loiter operations.

The P-8 Poseidon is a military derivative of the Boeing 737-800 next generation variant with twin engines which provides long range maritime reconnaissance capabilities. It is intended to replace the P-3 Orion in operations such as maritime surveillance and search and rescue mission. The Boeing 737-300 aircraft is used throughout this research and results achieved through analysis can be considered representative of the P-8.

1.3 Objectives of the Research In this research project, an operational possibility rather than emergency requirement is investigated in terms of optimum range and endurance with one engine inoperative (OEI) condition in a multi-engine aircraft for application in operations such as patrol and surveillance flights. Such operations require efficient engine operations at low altitudes and speeds.

The main aim of the research is to determine the optimal speed and flight attitude of One Engine Inoperative (OEI) operations of a multi-engine aircraft at varying altitudes which would result in the maximum range and endurance through theoretical and computational approach.

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In order to achieve the research goal, sets of linearized mathematical equations for longitudinal and lateral motions of an aircraft are derived in stability reference system. The drag polar and stability and control derivatives are then estimated for a B737-300 aircraft for sub-sonic flight conditions based on USAF Stability and Control DATCOM. Additional trim drag resulted from control surface deflections in balancing the flight equilibrium in (OEI) condition are investigated. This increase in drag compared to aerodynamically clean configuration alters the performance of the aircraft.

A set of assumptions are necessary to simplify the equations. Iterative matrix methods are used to solve the equations simultaneously with the aid of Matlab functions.

The range and endurance of the aircraft in (OEI) are then estimated for a range of speeds at various altitudes with different flight attitudes by applying Breguet’s equations. Three possible critical flight profiles: constant altitude - constant angle of attack flight, constant speed - constant angle of attack flight, and constant speed - constant altitude flight are considered.

The other objective of the research is to look at turning performance of the aircraft with OEI to see whether turning away from inoperative engine or operative engine performs better.

The major aims of this thesis can be summarized as follows:  Determine thrust and specific fuel consumption model for the Boeing 737-300 aircraft  Estimate aerodynamic properties (lift, drag, and weights) and drag polar for the aircraft for subsonic AEO as well as OEI conditions.  Investigate range and endurance performance of the aircraft with AEO.  Analyse thrust asymmetry, and additional drag developed due to control surface deflections to balance the flight equilibrium and wind milling inoperative engine.  Estimate range and endurance performance of the aircraft with OEI. This includes comparison of range and endurance performance between AEO and

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OEI condition to see if range and endurance performance can be improved with OEI under normal operating flight conditions.  Analyse turning performance of the aircraft with OEI and determine a more favourable direction of turning with OEI.  Perform sensitivity analysis on effect of weights on range and endurance performance of the aircraft.  Validate modeled data.

1.4 Scope of the Thesis The objectives of this thesis are outlined through different stages as discussed further in relevant chapters. The research started with project planning stage followed by readings on back ground and relevant literature. The research was then carried out over 2 years in stages to achieve the objectives outlined in each chapter.

1.5 Assumptions and Limitations There are a number of significant assumptions made and limitations encountered in this thesis due to limited availability of some of the data of the Boeing 737-300 aircraft used in the research. The noteworthy assumptions and limitations are as listed below. Other parameters required for modelling engine performance, aircraft performance analysis, and estimating stability and control derivatives are obtained from a combination of published materials, measured geometric data, and commonly accepted and estimated data.  For aircraft performance analysis (both AEO and OEI), only the subsonic flight condition is considered using Boeing 737-300 whose known cruise Mach No is 0.75, to determine optimum flight altitude and attitude for best range and endurance performance.  Only aerodynamically clean cruise flight is assumed in determining range and endurance performance of the aircraft in both AEO and OEI situations.  In performing analysis for OEI condition, the inoperative engine is assumed to be the starboard side engine (engine no 2) of the aircraft. It is also assumed that the inoperative engine is allowed to windmill.  Analysis assumes ideal standard atmospheric conditions at altitudes selected and neglects factors such as wind effects.

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1.6 Thesis Structure The first chapter of the thesis introduces the background information to the research undertaken. In this chapter, the origin, objectives and scope of the thesis have been outlined. The assumptions and limitations assumed have also been discussed.

The second chapter presents a review of literature relevant to One Engine Inoperative (OEI) flight performance. It also discusses relevant aerodynamic principles, propulsion systems, equations of flight equilibrium, and methods of estimating range and endurance performance of the aircraft including the One Engine Inoperative flight condition. A review of similar studies performed in the context of One Engine Inoperative (OEI) flight and range and endurance estimation is also presented. The third chapter presents the overview of important design features of the aircraft used in the research, a Boeing 737-300. It also touches on stability and control derivatives required in analysis in the subsequent chapters. The variables that are function of the derivatives and the extent to which they have an impact on these are also discussed in this chapter.

The fourth chapter describes the performance analysis of the Boeing 737-300 aircraft with All Engine Operating (AEO). It presents drag polar estimation, and thrust and specific fuel consumption model estimation as well as for the aircraft. The analysis also focuses on straight and level performance with AEO. The range and endurance performance based on Breguet’s equations are also discussed analysing control surface deflections required to trim the aircraft.

The fifth chapter presents the One Engine Inoperative (OEI) performance analysis. It discusses the range and endurance performance of the aircraft using Breguet’s equations. A comparison between range and endurance performances with AEO and those with OEI is also presented in this chapter. It also covers a comparison between a direct numerical integration method using weight steps and Breguet’s equations on range and endurance performance.

The sixth chapter discusses the One Engine Inoperative (OEI) turning performance of the aircraft used in the research. It focuses on yawing moment the aircraft develops during turning with OEI and presents performance comparison between turning on inoperative engine and operative engine assuming a right engine failure. 5 | P a g e

The seventh and final chapter present conclusions from the research and recommendations for possible future research work.

1.7 Summary In this chapter an overview of the thesis research has been outlined and the background to the research has been introduced. The next chapter presents a review of pertinent literature and discussion of more in depth relevant background material

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2. CHAPTER 2: LITERATURE REVIEW 2.1 Introduction This chapter will look at relevant literature concerned with research presented in forthcoming chapters in this thesis. It discusses aerodynamics, various propulsion systems, equations of motion, flight dynamics and control, range and endurance performance and relevant literature surrounding the one engine inoperative (OEI) condition, and aerodynamic modelling and analysis. It intends to provide an overview of the theoretical foundation necessary for materials discussed in subsequent chapters of this thesis.

2.2 Aerodynamics An aircraft requires “a carefully designed synthesis of various aerodynamic components- the wings, fuselage, horizontal and vertical tail, and other appendages- which are working harmoniously with one another to produce the lift necessary to sustain the airplane in the air while creating the smallest possible amount of drag”[1]. When the surface area of the airplane is subject to airflow, pressure and sheer stress exert on the surface. The pressure acts locally perpendicular to the surface, and shear stress acts locally parallel to the surface Figure 1. The net aerodynamic force is the resultant aerodynamic force due to the pressure and shear stress distributions over the total exposed surface area.

In order to produce the airflow and hence the lift, the aircraft requires airspeed- it needs to propel through air at a certain speed. A consequence of this lift/speed requirement for flight is a retarding force called drag. The required force to overcome drag is called thrust and produced by power plants. These forces acting on the aircraft must be in equilibrium to maintain straight and level flight. The aerodynamic force acting on the aircraft depends on the velocity of the aircraft through air, the density of the ambient air, the size of the aircraft and the angle of attack: the angle between the relative wind and a reference line on the aircraft or wing.[2]

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Figure 1: Aerodynamic forces acting on an airfoil [3] 2.2.1 Compressibility Effect Since friction accounts for part of the aerodynamic force, ambient viscosity and compressibility of the medium through which the aircraft moves need to be taken into consideration. As an aircraft moves through the air, the air molecules near the aircraft surfaces are disturbed as they move around the aircraft. At a low speed, the density of the air remains constant whereas for high speeds, some of the energy of the aircraft goes into compressing the air, locally changing the density of the air. This alters the amount of resulting force on the aircraft. This compressibility effect becomes more pronounced as the speed increases. “When the speed approaches near and beyond the speed of sound, small and sharp disturbances in the flow are transmitted to other locations isentropically, generating a shock wave that affects the lift and drag of an aircraft”. [4]

2.2.2 Mach number The ratio of the speed of the aircraft to the speed of sound in the air is the indicator of the magnitude of the compressibility effects. This ratio is known as Mach number. The Mach number defines flight regimes in which compressibility effects vary as can be seen in Figure 2.

Figure 2: Flight regimes and Mach numbers [5] 2.2.3 Airfoils, Wings and Lift An airplane is built with its wings, horizontal, and vertical stabilizers in airfoil-shaped cross sections. In olden days, the aircraft industry relied primarily on a series of airfoils empirically designed and tested by government agencies such as the Royal Aircraft Establishment (RAE) in Britain and the National Advisory Committee for Aeronautics (NACA) in the United States. This enabled the aircraft designers to choose from families of “standard airfoils” from the research work of these organizations. Many of

8 | P a g e the NACA standard airfoils can be seen used in the aircraft worldwide still flying today. In today’s computer world, most aircraft manufactures rely on aerodynamic computer programs to custom make the shape of the airfoil section for the wings to be used in the modern aircraft designs.[1]

Studies of airfoils are based on the properties of the airfoil with infinite span and hence airfoil data are sometimes labeled as infinite-wing data. The lifting surfaces of the aircraft such as wings, horizontal and vertical stabilizers of the aircraft are designed with airfoil shapes. The wings which have finite wing span produce strong vortices at the wing tips which trail downstream and induce changes in the velocity and pressure fields around the wing. The downward component of the velocity over the span of the wing induced by the vortices from both wing tips modifies the relative local wind. It means that the effective angle of attack is smaller than a geometric angle of attack. Hence, the aerodynamic force in finite wings is smaller than that of airfoils.[1]

In selecting an airfoil for the aircraft lifting surfaces, it is important to consider factors such as lift to drag ratio (performance at a certain lift value such as engine-out climb performance), thickness (increased thickness means weight reduction), thickness distribution (for favourable span loading/or high fuel carrying capability), and stall characteristics into account.[6, 7]

2.2.4 Aspect Ratio Aspect ratio is a measure of the aerodynamic performance of a wing. It is essentially the ratio of the square of a wing’s span to the area of the wing planform, (the projected area of the wing). [1] As the aspect ratio is decreased, the magnitude of lift decreases for a given angle of attack.

General aviation aircraft such as the PA-28 Cherokee has an aspect ratio of 5.6 whereas the Bombardier Dash 8 has 12.8 and Boeing 747 has 7. Concorde has AR=1.55. The aspect ratio of most subsonic aircraft falls between 6 and 9”.[1]

The selection of aspect ratio is generally made based on the design requirements such as structural strength of the wings, aircraft maneuverability, lift to drag ratio, practicality and the size of the airfields. The common types of aspect ratios most of the wings of the

9 | P a g e aircraft have usually fall under one of these categories: high aspect ratio straight wings, low aspect ratio straight wings, swept wings and delta wings.

2.2.5 Lift for Wing-Body Interactions As mentioned previously, lift is produced when air flows over the surfaces of the aircraft due to the movement of it through the air. Lift is produced by the fuselage of an airplane as well as the main wings, horizontal and vertical wings However, when the wing is mated to the fuselage, the flow over the wing is modified by the wing body interaction and the lift produced is not the simple addition of that produced by wing and that by fuselage.

“For subsonic speeds, the lift of the wing body combination can be treated as simply the lift on the complete wing by itself, including that portion of the wing that is masked by the fuselage”. [8]

2.2.6 Drag While it is important for an aircraft to produce enough lift to cancel out the weight to stay straight and level, the production of lift comes with inevitable penalty known as drag. The focus in design of aircraft has always been to produce the required lift as efficiently as possible, that is, with as little drag as possible. In other words, the aircraft designers always look for the best lift to drag ratio in designing an aircraft as it is an indicator of aerodynamic efficiency. The lift to drag ratio of a typical jet transport aircraft in cruise configuration is 15.8. In comparison, a typical fighter aircraft has a ratio of 12 in subsonic cruise condition and a ratio of 1.7 in supersonic cruise condition. The lower lift to drag ratio for the fighter aircraft can be attributed to the occurrence of wave drag due to compressibility as their roles require these aircraft to fly in transonic and supersonic conditions. [6]

2.2.6.1 Pressure Drag and Friction Drag The two types of drag are pressure drag and friction drag. In the subsonic flight regime, induced drag which is a by-product of wings producing lift and parasite drag (all drag which is not dependent on the production of lift) dominate. Parasite drag is the drag associated with skin friction and pressure drag due to flow separation, integrated over the complete airplane surface. It also consists of interference drag which is an additional pressure drag resulted from mutual interaction of the flow fields around each component

10 | P a g e of the airplane. [9] A breakdown of drag build up for a typical transport aircraft can be seen in Figure 3.

Figure 3: Breakdown of drag build-up for a typical transport aircraft [6] Drag depends on the air density (altitude), airspeed, wing surface area and the coefficient of drag (which depends on the aircraft’s angle of attack (AoA). The induced drag increases with AoA whereas the parasite drag increases with increase in airspeed.

When the speed approaches the transonic region, the drag rises due to the presence of shock waves which is the pressure drag. The shock waves become the dominant feature of the flow field around the airplane at supersonic speeds. [9]

2.2.7 Aerodynamic Force Coefficients In airplane dynamics analysis, the aerodynamic forces and moments are expressed in non-dimensionalised coefficients for the sake of simplification. It divides out the effect of size by using dimensionless parameters according to Buckingham’s Pi Theorem. [10, 11] It allows much more efficient experiments in airplane dynamic analysis. For instance, the coefficients of a scaled model of a Boeing 737 aircraft tested in a wind tunnel will be compared exactly the same with an actual full-scale airplane in free flight in dynamically similar flow conditions.

2.3 Propulsion Systems An aircraft needs a propulsion system to generate thrust which is required to balance or overcome the drag of the airplane. The propulsion system of an aircraft generally consists of an aircraft engine and some means to generate thrust, such as a propeller or a propulsive nozzle Figure 4.

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Piston Turboprop Turbofan

Turbojet Turbojet afterburner Figure 4: Aircraft propulsion systems [12] The general types of aircraft propulsion systems are reciprocating engine with propeller, turbojet, turbofan and turboprop. In selecting a propulsion system for an airplane, the designer considers factors such as installed weight, installed thrust and drag, fuel consumption, variation of thrust and fuel consumption with factors such as altitude, temperature, humidity and air speed, and noise. In other words, a trade-off analysis of thrust versus efficiency is required for the choice of a proper power plant for an aircraft.

The reciprocating engine/propeller is usually used for aircraft with low design Mach numbers below 0.5. High by-pass-ratio turbofan systems are commonly found in jet transport aircraft which have design Mach No of 0.7-0.85. Refer to Figure 5 for a turbofan engine manufactured by Honda for applications in light business jet such as a Honda HA-420 HondaJet. Turboprop systems are utilized for aircraft which can go up to around 0.6 Mach. And Turbojet or low-bypass-ratio turbo fan power plants are deployed in supersonic aircraft with design Mach No of greater than 2. [1]

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Figure 5: A Turbofan Engine (Honda’s HF120) [13] When dealing with performance parameters of powerplants of turbofan aircraft, terms such as N1, N2 are used to describe the level of thrust settings an engine has for appropriate phases of flight. N1 is the low-pressure spool or the "first stage" at the front of an engine with which the forward set of core compressor blades spin. The rearmost turbine blades also spin at the N1 spool because they are attached to the same shaft.

N2 is the speed of the high-pressure spool with which the rest of the core compressor blades not spun by the N1 spool spin. The forward most turbine blades closest to the combustion process also are connected to the N2 spool.

Pratt and Whitney engines use the term Engine Pressure Ratio (EPR) while setting thrust on the aircraft which deploy their engines while manufacturers such as General Electric, Rolls-Royce and CFM use N1%, N2% etc to describe the same thing. At takeoff power, the % for N1 and N2 is usually around 100% with a give or take of 10% depending on exact specifications of engines. [14]

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2.3.1 Specific Fuel Consumption (SFC)

The engine burns fuel to produce the power required for its motion. Specific fuel consumption is a technical figure for an engine of how efficiently it is burning fuel and converting it to power. It is thought of as the mass of fuel needed to provide the net thrust for a given period. The power produced at the shaft of the aircraft engine (reciprocating engine) is referred to as shaft brake power. However, for turbojet and turbofan engines, the measurable primary output is jet engine thrust, and hence it is referred to as thrust specific fuel consumption when dealing with efficiency of its engine. Almost all of the modern day jet transport aircraft are equipped with jet engines which have a degree of by-pass for optimum efficiency. Increasing overall pressure ratios on jet engines tends to decrease the specific fuel consumption. [6]

2.3.2 Effects of Velocity and Altitude on Specific Fuel Consumption (SFC) For jet engines, the velocity of the aircraft causes a significant impact on the specific fuel consumption. “The thrust of a civil turbofan engine has a strong variation with velocity especially at lower altitudes; thrust decreases as velocity increases”. The thrust also decreases as altitude increases. “At high altitudes, thrust is relatively constant for the narrow Mach number range from 0.7 to 0.85”.[15]

The thrust specific fuel consumption of a turbo fan increases distinctly as velocity increases. As altitude increases, the specific fuel consumption of a turbofan engine decreases. However, the thrust specific fuel consumption for a turbo jet is almost constant with increase in velocity in supersonic region.

2.4 Equations of Motion The movement of a given aircraft through the atmosphere is based on the four forces of flight, lift, drag, weight and thrust and is governed by a set of equations called the equations of motion.

2.4.1 The Four Forces The four forces of flight are sketched as shown in Figure 6. The airplane aerodynamic forces: lift and drag, act perpendicular and parallel to the free-stream velocity which is the flow velocity relative to the airplane. The weight acts towards the centre of the

14 | P a g e earth. Thrust is produced by the propulsion system of the airplane and is sometimes installed at an angle relative to the flight path.

Figure 6: Four forces of flight [12] 2.4.2 Modelling the Equations of Motion The equations of motion can be developed in two ways. One takes into account the acceleration due to gravity with distance from centre of the earth which is known as the spherical earth model while the other method assumes the flat earth model and the gravitational acceleration is taken to act downwards vertically. The distances involved in flights with acceleration are negligibly small and hence rotational velocity of the earth (Coriolis acceleration) can be neglected in considering the aircraft motion. This is acceptable up to the supersonic speed regimes, but not when dealing with hypersonic. [16] This is, however, out of the scope of this research and analysis in the research is limited up to the transonic region with assumptions that the aircraft is a rigid body, has constant mass, and is not subject to Coriolis acceleration.

In un-accelerated flights, the forces at a given instance of time are integrated to obtain distance covered. It is important to take the altitude as height above the surface of the earth and the distance measured is on spherical radius plus the height.[17]

2.4.3 Reference Frames Since the airplane equations of motion are developed by applying the Newtonian principles of conservation of linear and angular momentum, an inertial reference (axis) system one in which Netwon’s law of motions are valid needs to be specified. [18] Figure 7 shows the body-fixed axis system (fixed at the Centre of Gravity (CoG) of the

15 | P a g e airplane) and the earth fixed reference system (fixed at an arbitrary point on the flat earth surface).

Figure 7: Body fixed and earth fixed axis systems [18]

The quantity ϱA represents the local mass density of the aircraft and each mass element is subject to the acceleration due to gravity which is denoted by g and a combined aerodynamic and thrust force per unit area, F in Figure 7. These forces are assumed to be the only external forces acting on the airplane when modelling the equations of motion.[18]

An earth fixed reference frame is selected with its origin at the surface of the earth, assuming it is a flat earth. In the Earth-fixed reference frame, the origin is at an arbitrary location on the ground. The Z axis points towards the ground. The X axis is directed North. The Y axis can again be determined using the right-hand rule.

The body-fixed reference frame is often used when dealing with aircraft. The origin of the reference frame is the centre of gravity (CoG) of the aircraft. The X axis lies in the symmetry plane of the aircraft and points forward. The Z axis also lies in the symmetry plane, but points downwards and is perpendicular to the X axis. The Y axis can again be determined using the right-hand rule.

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When modelling the equations of motion to analyse flight dynamics, the stability reference system is generally used. The stability reference frame is similar to the body- fixed reference frame. It is rotated by an angle about the Y axis of the body-fixed reference frame so that the X axis is aligned with the relative wind vector. Projection of this vector onto the plane of symmetry of the aircraft is then the direction of the X axis of the stability reference frame. The Z axis still lies in the plane of symmetry and the Y axis is still equal to that of body-fixed reference system. The relative wind vector lies in the XY plane of the stability reference frame Figure 8. [18]

Figure 8: Stability axis system (non zero side slip) [18] 2.5 Flight Dynamics and Control In order to fly an aircraft from one location to another in a particular manner, it must be controllable in three critical flight dynamics parameters. These parameters are known as roll pitch and yaw and dictate the angles of rotation in three dimensions about the aircraft’s centre of gravity Figure 9.

2.5.1 Roll, Pitch and Yaw Roll is the rotation about the aircraft longitudinal axis and determines the bank angle of the aircraft to change the horizontal direction of flight. Pitch is the angular movement about the aircraft’s lateral axis, in other words it determines the aircraft nose attitude. Yaw is about the vertical body/stability axis and is used to either create or tackle side slip developed by the aircraft. It is also used in conjunction with roll motion while an aircraft is doing a co-ordinated turn.

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Figure 9: Roll, pitch and yaw motion of an aircraft [19] 2.5.2 Control Surfaces These control movements are achieved by manipulation of control surfaces located on wings, horizontal and vertical wings through movement of control column in the cockpit. The control surfaces can generally be divided into two distinct classes: primary control surfaces and secondary control surfaces. The primary control surfaces are such that when they fail, the whole aircraft becomes uncontrollable. Elevators, ailerons and rudders are primary control surfaces in an aircraft. The failure of secondary control surfaces does not generally result in catastrophic loss of control as potentially will be the case with the failure of the primary control. The example of secondary control surfaces includes flaps, spoilers, speed brakes and trim tabs Figure 10.

The flying or handling qualities of the aircraft are determined by characteristics such as controllability to maintain steady state, straight line flight throughout its design flight envelope, maneuverability from one steady state flight condition to another safely, acceptable cockpit control forces for different flight configurations and ability to trim efficiently in flight conditions. [18]

Figure 10: Control surfaces of Airbus A320 [20]

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2.6 Range and Endurance The range and endurance of an aircraft are directly related to the quantity of fuel the aircraft can carry and the rate at which it burns the fuel to travel in the air. An aircraft flies at different speeds in various flight environments for different flight segments during a flying operation. The weight of the aircraft is also decreasing continuously in flight as fuel is burned. It means that W = L= CLqS where CL varies with Angle of Attack and q varies with ρ and V.

It is governed by Breguet range and endurance equations. In modelling range and endurance, there are three typical flight profiles that are used commonly. They are constant angle of attack - constant Mach number, constant angle of attack - constant altitude, and constant altitude - constant Mach number.

2.6.1 Range and Endurance - Constant AoA – Constant Mach In constant angle of attack – constant Mach number scenario, the only variable changing is the weight of the aircraft due to fuel being burnt as the flight progresses, allowing aircraft to follow a cruise climb flight situation. It is not very practical in civil operations as change in altitude may be restricted in controlled airspace. [21]

2.6.2 Range and Endurance - Constant AoA – Constant Altitude In constant angle of attack and constant altitude, the Mach No of the aircraft is constantly adjusted as the weight decreases due to fuel burn to achieve the range required. [21] This flight profile is good for patrol and surveillance operations as it improves endurance too but is not very fuel efficient.

2.6.3 Range and Endurance - Constant Altitude – Constant Mach In this flight profile, the AOA of the aircraft is allowed to decrease as the weight decreases, which in turn requires a progressive decrease in thrust to maintain the Mach number. The equation used to calculate range in this method is more complex than the two methods discussed above. The range is found by integrating drag over the weight change, and the cruise speed for the optimal range is a function of fuel ratio. [21]

2.7 One Engine Inoperative (OEI) Condition When one of the engines on a multi-engine aircraft stops working the one engine inoperative (OEI) condition exists. The most common multi-engine aircraft in current civil aviation operations are twin jet aircraft whose engines are installed on the wings. 19 | P a g e

There are other multi-engine aircraft with more than two engines currently in operation throughout the world. Some of the aircraft have their engines mounted at the rear of the fuselage such as Boeing 727 (out of production) depending on their design purposes.

2.7.1 Thrust Asymmetry Effect The engine and fin locations affect the asymmetric thrust due to OEI. There is a more pronounced thrust asymmetry effect in the aircraft which have wing mounted engines than those which have the rear mounted engines in OEI. [22] This is because the greater lateral distance of the thrust line of the wing mounted engines from the centre of gravity creates the greater moment arm.

The asymmetric thrust causes the aircraft to develop yaw rate towards the direction of failed engine which needs to be corrected by application of rudder. This thrust asymmetry also induces asymmetric lift as one wing produces more lift than the other which creates roll.

The dihedral and wing blanking effects in combination with resulting side slip also play their role in contributing towards the rolling moment towards the direction of the dead engine. “On propeller airplanes, an additional rolling moment develops due to the loss of propulsive lift of the wing section behind the failed propulsion system. Turbojet/ -fan airplanes do not have blown wing sections because the engines are mounted below or above the wings, but the sideslip angle reduces the frontal area of the downwind swept wing considerably, increasing the rolling moment”. [23] There is also a roll due to the rudder deflection. A certain amount of aileron deflection is required to achieve zero rolling moment.

2.7.2 Spillage Drag In addition to this asymmetric yaw caused by loss of thrust from one engine, there is a drag due to an inoperative engine which is known as spillage drag which adds to the yawing moment. [4] The spillage drag is a propulsion performance penalty of turbo fan or jet engines which occurs when inlet of the engine spills air around the outside instead of conducting the air to the compressor. However, this drag is partially cancelled out by the phenomenon known as lip suction effect produced by passing of spilled air over the external cowl lip which makes the air accelerate and the pressure decreases. When an engine is shutdown or fails, the difference between the actual engine airflow and the

20 | P a g e maximum air flow demanded by the inlet of the engine is great, producing the spillage drag.

The drag from the engine can be minimised by reducing the spillage through allowing a windmilling engine, which passes more air through it. In modelling the drag for OEI, the wind milling drag can be estimated based on the inlet diameter of the engine, Mach number, mean nozzle exit velocity and free stream velocity using Torenbeek’s method.[24]

2.7.3 Trim Drag “Trim drag is defined as that extra drag required to, produce a condition of zero moments on the airplane. In OEI, it is increased by the requirement to produce lift (side force) on the vertical tail(s) to assure zero yawing and rolling moments and is dependent upon the thrust line location”. [6] The control inputs required to keep the aircraft trimmed contribute towards the increased total drag of the aircraft as trim drag which needs to be overcome with remaining thrust available, affecting the range calculations. Figure 1 illustrates the drag characteristics of typical transport aircraft over different lift coefficient.

Figure 11: High drag characteristics of the Airbus A320-200 and Boeing 737-800[6] 2.7.4 Range and Endurance Performance with One Engine Inoperative (OEI) The maximum range of an aircraft at its optimum altitude with OEI is less than that with all engines operating (AEO) condition. [25] Due to the loss of overall thrust, the remaining engines must have a higher thrust to sustain level flight. However, that is not 21 | P a g e possible at high altitudes and high speeds as there will be insufficient thrust to overcome the high transonic drag. “A descent to a lower altitude and an adjustment in speed is usually necessary” [25] to maximise the range the aircraft can fly in the OEI condition. There has been a large volume of analysis directed towards analysis of effects of an engine failure in a multi-engine airplane, with focus more on emergency issues in commercial flights as required by stipulations mandated by civil aviation authorities. Although every multi engine aircraft has OEI and range endurance performance charts derived from flight test and/or analysis, very little research has been done before in published literature on OEI range and endurance performance from the perspective of purposely shutting down an engine to extend range and endurance. In those emergency situations, the aircraft will adopt pre-determined procedures and land at the nearest air field as soon as possible.

However, in reality, there are situations where an aircraft is required to fly without all engine operating (AEO) such as in long endurance missions in a P-3 Orion where a long endurance and time on station is required over high speeds.

In aircraft such as P-3 which has its four turbo prop engines mounted on its wings, asymmetric flight is not a concern for (OEI) operations because asymmetric thrust can be balanced by remaining engines; the left outboard engine of P-3, which has no generator is often shutdown, so is the right outboard engine occasionally, for loiter operations. Two or three engine operating loiter profiles are applied to reduce fuel consumption in order to extend the time the aircraft remains on station. [26] The propellers of the offline engines are also usually feathered during such operations. The pilot will have to deflect flight control surfaces to offset the unbalanced moment created by the asymmetry in thrust. It can be noted that a feather propeller usually has much less drag than a windmilling turbofan.

2.8 Relevant Literature In regards to control and performance during asymmetrical powered flight in a multi- engine plane, the paper written by Harry Horlings [23] based on airplane design methods and flight test techniques reviewed some of the forces and moments that act on multi-engine planes after engine failure with an emphasis on importance of design techniques deployed by engineers for sizing the vertical tail. It discussed factors influencing controllability and performance in asymmetrical flight condition as well as 22 | P a g e experimental flight tests to determine minimum control speed. The paper concluded with some flight operation aspects in this situation and recommends a few improved and important first steps from the perspective of emergency management.

Three recovery options were discussed: two of which are relevant to takeoff and go around while the third one is attributed to many accidents. They are straight flight with wings level, straight flight with zero sideslip and straight flight with no or partial rudder. In first scenario, since the aircraft is kept wings-level for easier flying, this results in a sideslip which creates additional drag and affects performance such as climb rate. This calls for the need to reduce the sideslip as much as possible.

Hence the second method, straight flight with zero sideslip where rudder generated side force is used to balance the asymmetric thrust with the help of a small bank angle towards the operative engine was proposed.

In third scenario, when the rudder is only partially used, the aircraft will yaw and sideslip with increased drag and hence climb performance. This is pronounced at high power settings and low airspeed and bank angle in excess of the commonly approved 5 degree is required to balance side forces, resulting in a large side slip angle that might result in a fin stall. This had never been flight tested and was not recommended to fly in the paper.

The paper discussed the best option for maintaining controllability and performance in high power settings and low airspeed configuration which is to deflect the rudder as much as required to maintain the heading (zero yaw rate), applying small bank angle in the order of 2-3 degree towards the operative engine.

Jan Roskam and William Anemaat [27] also produced a technical paper which looked at a user friendly method for analysing longitudinal and later-directional trim problems for airplane with all engine operating and one engine inoperative. The approach is programmed into advanced aircraft analysis (AAA) software with equations of flight equilibrium based on methods applied in Jan Roskam’s Airplane Flight Dynamics and Automatic Flight Controls text. The software was produced by DARcorp for industry, tertiary and individual applications and provides a powerful framework to support the iterative and non-unique process of aircraft preliminary design”. It is used for

23 | P a g e preliminary design of airplanes, stability and control analysis of new and existing airplanes.

The paper covered aspects of airplane flying qualities which are affected by several detail design aspects of flight control systems using a small turboprop airplane as an example. It discussed several example applications of longitudinal and lateral- directional trim calculations for the aircraft using the software.

Another relevant literature was Stability and Control derivative estimation and engine- out analysis produced by Joel Grasmeyer of Virginia Polytechnic Institute and State University. [28] The article described the estimation of stability and control derivatives using the methods of Jan Roskam given in reference [29] which is based on the USAF DATCOM. [30] It also discussed the approach in establishing engine out constraint based on the required yawing moment coefficient. The left engine out scenario was used as an example application while using Boeing 747 data for stability and control derivatives for validation purpose. The author suggested applying a correction factor based on the deviation of the predicted results and the flight test data to calibrate the derivatives for better accuracy.

Further work stemmed from the above literature was the work done by Michael Cavanaugh [31] to calculate the single engine minimum control speed in air of a jet powered aircraft which was partly from his research work on design study to reduce the single engine minimum control speed of the twin engine business jet. The report discussed the minimum control speed theory associated with asymmetric flight, adopting a bank angle of 5 degree towards the operative engine as per FAR23.149 requirement. A MATLAB routine was proposed to find the airspeed, rudder and aileron deflections which balance the lateral flight equilibrium for different gross weights at sea level. Aileron and rudder limited minimum control speed in air were estimated using the Boeing 747-100 as the sample aircraft assuming a failure of right outboard engine. The minimum control speed calculated in this literature only considered control surface deflection limited control speeds as it can be defined by control force limits.

The stability and control derivative estimation can be performed in more than one way. The approaches used by the authors in the two previous literatures were based on Roskam [29] which was adapted from the USAF stability and Control DATCOM [30]. 24 | P a g e

Vortex-lattice method (VLM) can also be applied to estimate baseline stability and control derivatives for a high speed civil transport. The estimations using this method were then augmented by the DATCOM method. [3]

There was also a research thesis conducted by Benjamin Abrahams [32] under supervision of Dr. Rik Heslehurst on single engine subsonic range performance of the F-22. The initial F-22 performance was modelled using AAA software mentioned previously in this section. One Engine Inoperative range performance optimization based on Breguet Range equations was conducted for supercruise and subsonic flight conditions. The author presented that the range performance in subsonic condition is superior to that in super cruise condition, and that an OEI condition does not improve subsonic range performance of the F-22. Range improvements of 72% for the normal subsonic and 4% for OEI flight conditions when compared with the supercruise condition were achieved. This occurs due to the smaller drag acting on the F-22 in normal subsonic conditions and increased trim drag in OEI as opposed to supercruise conditions where wave drag becomes relevant to range calculations. The optimum range performance with OEI for the F22 was observed to occur at 25,000 feet (cruise) which is only an improvement of 2.6% over the 30,000 feet with AEO.

2.9 Summary The current literature relating to the One Engine Inoperative flight highlights the emergency perspective of the situation especially in civil transport operations even though this is a practical application in maritime patrol and surveillance operation with an aircraft such as P3-Orion.This chapter has discussed the background literature on aerodynamics, propulsion systems, equations of motion and flight equilibrium, and flights dynamics and control. It has also been described that there are an infinite number of possible range and endurance flight profiles an aircraft is able to fly and that trim drag resulted from recovery to balanced flight in OEI condition affects the range and endurance performance. The relevant literature covering practical piloting techniques and some of the previous work conducted in both transport and military types of aircraft has been reviewed. The next chapter will outline the history and technical details of the aircraft model used throughout the research as well as estimation of parameters and stability and control derivatives for the aircraft for analysis presented in subsequent chapters.

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3. CHAPTER 3: AIRCRAFT MODEL USED IN RESEARCH: B737- 300 3.1 Introduction This chapter of the thesis will discuss brief history of the class of aircraft model used in the research, a Boeing 737-300, its design features, detailed specifications and estimation of parameters necessary for analysis presented in the subsequent chapters. This chapter involves collation of known data for the aircraft model from well- recognized sources in aerospace/aviation realm, and estimation of unknown data through techniques and design approaches of Jan Roskam.

3.2 Brief History Boeing 737 is a short range twin narrow body jet type aircraft which entered service in 1968 as a complement model for the 707 and 727. [33] Initial design studies were started since 1964 for a short haul jetliner as 727 and 707 models were medium and long range aircraft. It is the most commercially successful jetliner in the history of civil air transportation, which is still being developed some 40 years later. [34] Its competitors at that time were the Douglas DC-9 and the BAC111. One of the key design features in terms of passenger carrying ability of the 737 was its six abreast seating: its contemporary DC-9 had six abreast seating. It was made possible by mounting the engines under the wings, increasing the passengers per load. Its ability to operate in harsh conditions such as remote, small airports with not much facilities attracted attention from airline operators around the world. It was also the beginning of the era of the modern day standard two-person flight decks.

The launch variant is the 737-100 and the Boeing 737 has developed into a family of nine passenger models with a capacity of 85 to 215 passengers. The 737-200 is the lengthened version of the launch model which entered service in 1968. The Boeing 737- 300/-400/-500 variants of 1980s are referred to as Boeing 737 Classic series which carry features such as improved wing designs incorporated CFM56 turbofan engines and added passenger carrying capacity. Since 1996, the 737 family has entered another phase in development with the introduction of the next generation variants 737-600/- 700/-800/-900ER. Boeing is currently developing 737-MAX as its fourth generation variant to succeed the Next Generation series with scheduled first delivery in 2017.[35]

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In this research, the 737-300 (classic series) is chosen for analysis presented in the subsequent chapters as it is the middle generation variant.

Boeing 737-300 (Classic Series) succeeded its successful predecessors -100 and -200 variants with increased capacity (payload), shorter runway requirement and superior range, incorporating improvements to upgrade to modern specifications while maintaining commonality with previous variants. It is featured with fuel efficient and less noisy CFM56 turbo fan engines with extended wing tips for improved aerodynamics. The flight deck was furbished with an Electronic Flight Instrumentation system. It has a seating capacity from 128 to 149.[35]

3.2.1 Wings The wings of the Boeing 737 are made of an aluminium alloy and adopt a two-spar structure. The front and rear spars support shear loads while the upper and lower skin panels carry bending loads, forming a wing box which serves as an integral fuel tank. The wings of -300/-400/-500 series are built with an aerofoil which is made up of four specially designed Boeing aerofoil sections splined into one smooth surface as shown in Figure 12. They have 0.2m wingtip extensions and a slightly modified aerofoil section for the LE slats which yields a 4% improvement in maximum lift to drag ratio and a 3% reduction in block fuel at 1500nm range. [36]

Figure 12: Airfoil sections used in Boeing 737-300 aircraft wings [36] With a goal of improving range, the Boeing 737-300 wings are designed with shorter chord to accommodate flush wing mounted engines (as opposed to pylon mounted in earlier aircraft). This satisfies the ground clearance requirement as well as helps

27 | P a g e alleviate the bending moment due to lift of the wings, allowing reduction in the spar weights.

“It also had much less sweep than its predecessors (25º compared to 35º on the 727) because speed was not considered important for a short range jet”. [36] Winglets are installed on some 737-300 airplanes as an after-market airline option as they improve climb/cruise performance fuel performance and hence increasing range.

3.2.2 Fuselage The 737-300 is a second-generation stretched version of the original 737s and is 109 ft 7 in long. The fuselage of -300 is constructed by adding two sections to the 737-200 fuselage; a 44in section forward of the wing and a 60in section aft of the wing. [37] The design features of the aircraft can be seen in Figure 13. There are four vortex generators on each side of the rear fuselage above the horizontal stabiliser as a mean of reducing drag to gain a slight performance advantage. There are also 10 other small vortex generators installed above the fibreglass radome (radar dome) of the aircraft which purpose are to reduce cockpit noise from the windshield. [36]

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3.2.3 Engine The 737-300 (also -400/-500) aircraft are equipped with high bypass ratio engines (CFM56- 3) which are quiet, economical to operate and maintain. The higher thrust capability of the engines in combination with modified flight control surfaces allows the 737-300 to operate on shorter runways than its earlier versions. The engines are mounted in such a way that they stay protruded forward when viewed from top and the top of the nacelle sits level with the upper surface of the wing. The engines in -300 are tilted 5 degrees up which helps the ground clearance requirement as well as thrust vectoring effect to assist take- off performance. “The CFM56-3 is said to be almost 20% more efficient than the JT8D used in Boeing 727s”. [38]

Figure 13: Design Features of the Boeing 737-300 [38] 3.2.4 Control Surfaces

3.2.4.1 Roll Control Ailerons in the 737-300s are operated by dual hydraulic systems with manual reversion capability from both control columns in case of failure of both systems. Spoilers are differential system and can be operated hydraulically if aileron system is jammed. The ailerons have balance tabs/panels for trimming functionality. [36]

3.2.4.2 Pitch Control Elevators in the 737-300 are also hydraulically operated by two independent systems. A manual reversion can be triggered from both control columns in case of failure of both hydraulic systems. The balance tabs/panels on both elevators assist in trimming the 29 | P a g e aircraft with a secondary purpose of controlling the pitch if the elevator system fails. [35]

3.2.4.3 Yaw Control Yaw control in 737-300 is through rudder which is controlled through a Power Control Unit (PCU). The PCU deploys a hydraulically operated dual servo to move the rudder with no manual reversion ability. In 737-300, a Yaw damper system is fitted for passenger comfort. It allows a maximum of 3 degree deflection either side of the trimmed position. [36]

3.2.5 High Lift Devices The Boeing 737-300 leading edge devices are comprised of 4 Krueger flaps and 6 slats installed inboard and outboard of the engines respectively. The slats run from engine pylon to wingtip on the wings, yielding an average chord increase of 4% over the whole wing. This gives the classics similar approach speeds to the originals. The trailing edge flaps are of triple-slotted type in 737-300 aircraft. The leading edge slats may be extended when the trailing edge flaps are not. [36]

3.3 Aircraft Schematics Three view schematic drawings of the Boeing 737-300 aircraft can be seen in Figure 14, Figure 15 and Figure 16. They provide overall dimensions of the aircraft which are very useful in estimating parameters relevant to the research and analysis presented in the subsequent sections.

Figure 14: Front view of Boeing 737-300[39]

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Figure 15: Side view of Boeing 737-300 [39]

Figure 16: Plan view of Boeing 737-300 [39] 3.4 Aircraft Details The details of the aircraft: powerplant specifications, aircraft geometry, weights and performance parameters are presented in the following sections.

3.4.1 Powerplant Details The powerplant deployed for the -300 variant of the Boeing 737 aircraft is of CFM56-3. Its performance specifications can be referred to in Table 1.

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Model CFM56-3 Type -B2 Takeoff Thrust (kN) 98.1 Cruising Thrust (N) 22419 Bypass Ratio 5.9 SFC (cruise) lb/lb.hr 0.67 Engine Length (m) 2.36 Engine weight (kg) 1951 Fan diameter (in) 60 No of nacelles 2 Max Nacelle Width (m) 2 Length of Nacelle (m) 3.3 Cross sectional area (m2) 3.14 Table 1: Details of powerplant used in Boeing 737-300 [40] 3.4.2 Wing Geometry The geometrical details of the main wings used in the Boeing 737-300 aircraft are as follow: Span (m) 28.88 Gross Area (m2) 105.4 Root Chord (m) 7.32 Tip Chord (m) 1.62 Mean Aerodynamic Chord (m) 3.41 Quarter chord Sweep (deg) 25 Dihedral (deg) 6 Aspect ratio 7.91 Taper ratio 0.240 Wing Twist (deg) 3 Incidence (deg) 1.4 Table 2: Details of wing design used in Boeing 737-300 [35] 3.4.3 Horizontal Tail Geometry The details for the Horizontal tail of the aircraft are tabulated as shown in Table 3. Span (m) 12.7 Gross Area (m2) 31.4 Elevators Area (m2) 6.55 Root Chord (m) 3.8 Tip Chord (m) 0.99 Mean Aerodynamic Chord (m) 2.5* Quarter Chord Sweep (deg) 30 Aspect Ratio 5.14 Taper Ratio 0.260 Table 3: Details of horizontal tail of Boeing 737-300 [35]

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3.4.4 Vertical Tail Geometry The vertical tail of the aircraft possesses the following measurements. Table 4 Span (m) 6.15 Gross Area (m2) 23.13 Rudder Area (m2) 5.22 Root Chord (m) 5.7 Tip Chord (m) 1.8 Mean Aerodynamic Chord (m) 4.1 Quarter Chord Sweep (deg) 35 Aspect Ratio 1.49 Taper Ratio 0.31 Table 4: Details of vertical tail of Boeing 737-300 [35] 3.4.5 Fuselage Details The details of the fuselage of the aircraft are presented below. Length (m) 32.18 Maximum diameter (m) 4.01 Table 5: Fuselage details of Boeing 737-300 [35] 3.4.6 Weights The weight data specified for the Boeing 737-300 aircraft are tabulated in Table 6 Maximum take Off weight (kg) 62820 Maximum landing weight (kg) 51710 Maximum zero-fuel weight (kg) 47625 Maximum ramp weight (kg) 56700 Fuel capacity (kg) 14410 Max payload (kg) 14805 Table 6: Boeing 737-300 weights [35] 3.4.7 Performance Details The performance specifications known for the aircraft are presented in Table 7. Wing Loading (kg/m2) 596.29 Thrust loading (kg/kN) 353.48 Thrust to Weight Ratio 0.2884 CLmax (T/O) at MTOW 2.16 CLmax (Landing) at MLW 2.88 Cruise Mach 0.745 Ceiling (ft) 37000 Range with max payload (nm) 2950 Table 7: Performance details of Boeing 737-300 [36] 3.5 Estimation of Parameters The estimation of parameters necessary for calculating and analysing performance parameters presented in subsequent chapters is discussed. In particular, methods for parabolic drag polar estimation, trim drag calculation, and stability and control derivatives are touched on the following sub-sections.

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3.5.1 Drag Polar Estimation Drag polar is a parabolic representation for the variation of drag coefficient with respect to lift coefficient. It is not exact but accurate enough for the purpose of performance calculation especially in subsonic condition. [41]

The drag polar of Boeing 737-300 is estimated as shown in below. [42, 43]

2 CD  CD0  KCL Equation 1 Where, 1 K  eAR

0.68 0.15 e  4.61(1 0.0045AR )[cos(LE )]  3.1

2 It is composed of two terms; zero-lift drag, CDo and induced drag, KCL (related to producing lift). The zero-lift drag is proportional to V2 while the induced drag is inversely proportional to V2. The zero lift drag is to do with aerodynamic cleanness with respect to friction, shape, protuberances (cockpit shape, antenna, external fuel tanks). The induced drag contributes highest at low velocities and decreases with increasing flight velocities.

K, e and AR are the induced drag correction factor, Oswald efficiency factor and the wing aspect ratio respectively. A procedure to estimate zero-lift drag, CDo, is outlined in Appendix A.

The analysis presented in subsequent chapters look at range and endurance performance of the aircraft at various speeds at different altitudes. The drag polar estimation above will determine the estimated lift and drag parameters the aircraft is subject to at a particular condition. The estimated drag polar parameters for the Boeing 737-300 aircraft is presented in Chapter 4.

3.5.2 Trim Drag Estimation The trim drag for the aircraft is the increase in induced drag of the tail. It is a type of drag increment mainly resulted from production of a horizontal tail load in order to balance the aircraft longitudinally around its centre of gravity. For one engine inoperative (OEI) flights, additional profile and induced drag due to required control surface deflections to keep the aircraft level and co-ordinated contribute towards the

34 | P a g e total drag of the aircraft. The profile drag and induced drag for a wing can be estimated using equations as shown below. S  C  (c )cos( ) wing_ flapped D _ c.s _ profile dp c c.s  S  4  wing  Equation 2  S  C  K C 2  wing_ flapped  Di _ wing wing Lreq  S   wing  Equation 3 3.5.3 Estimation of Stability and Control Derivatives Stability and control derivatives measure change in forces and moment acting on the aircraft as variables related to stability such as airspeed, altitude, and angle of attack change. The stability and control derivatives of the Boeing 737-300 and their dependent variables are presented as shown in Table 8. The details of formula used to calculate each derivative is included in Appendix B.

It is worthwhile knowing the relationship between each stability and control derivative and its dependent variables. The stability and control derivatives can have dependence on each other as flight condition changes. Table 8 summarizes the derivatives and their dependent variables with estimated values for each derivative to be used in the later sections of the thesis estimated for sea level and at minimum control speed.

Derivative Nomenclature Dependent components Value estimated Longitudinal Stability Derivatives

Lift curve slope CL Wing-body combination 0.1025 Horizontal tail Dynamic pressure ratio H.T to Wing area ratio Angle of attack Cmα Centre of gravity location -0.05875 pitching moment Aerodynamic centre location coefficient CLα Longitudinal Control derivatives Stabilizer incidence lift CLih Horizontal Tail lift curve 0.0168 coefficient H.T to Wing area ratio Elevator deflection lift CLδe Flap deflection lift coefficient 0.0091 coefficient H.T to Wing area ratio Stabilizer incidence Cmih Horizontal tail lift curve -0.012936 pitching moment Distance between CoG and A.C coefficient of H.T Elevator deflection Cmδe Elevator lift curve -0.04131 pitching moment Distance between CoG and A.C coefficient of H.T

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Average chord H.T Lateral Stability Derivatives Sideforce Cyβ Wing, fuselage and vertical tail -0.0141 coefficient(sideslip angle) Rolling moment Clβ Wing-body, horizontal tail, -0.0013 coefficient vertical tail Yawing Moment Cnβ Wing, fuselage and vertical tail 0.0019 coefficient Lateral Control Derivatives Sideforce coefficient Cyδa zero 0 Rolling moment Clδa Rolling effectiveness 0.000805 coefficient Aileron lift effectiveness Yawing moment Cnδa Wing planform or surface taper 0.000112 coefficient ratio, aspect ratio, dynamic pressure ratio Directional Control Derivatives Sideforce coefficient Cyδr flaps, V.T and wing geometry 0.003054 Rolling moment Clδr Sideforce coefficient, angle of 0.0025 coefficient attack, wingspan, vertical tail volume, distance between CoG and AC of V.T Yawing Moment Cnδr Sideforce coefficient, angle of -0.0044 coefficient attack, wingspan, V.T volume, distance between CoG and A.C of V.T Table 8: Stability and control derivatives and their dependent variables [28] 3.6 Summary The technical details and design features of the aircraft model used in this research have been discussed. The estimation procedure of important parameters such as drag polar and stability and control derivatives and why they are important and how each of these is dependent on other variables have been outlined. The next chapter will discuss analysis of the performance of the aircraft with emphasis on range and endurance with all engines operating (AEO).

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4. CHAPTER 4: ALL ENGINE OPERATIVE FLIGHT ANALYSIS 4.1 Introduction This section of the thesis will discuss the results and analysis of all engine operative (AEO) flight performance. In order to perform the analysis, variations of thrust and specific fuel consumption (SFC) with altitudes need to be determined. The mathematical models for thrust available (cruise thrust) and SFC developed are presented. Range and Endurance performance estimation using Breguet’s equations is then performed and discussed in this section of the thesis. The details of the thrust and SFC models presented in this chapter can be referred to in Appendix C and Appendix D.

4.2 Objectives The performance analysis presented in this chapter of the thesis is intended to aid in developing One Engine Inoperative (OEI) performance analysis in the next chapter of the thesis. The main objects of this analysis are as follows:  Estimate parabolic drag polar of the Boeing 737-300 for flight performance analysis at subsonic speeds. (M < 0.8)  Determine aerodynamic characteristics of the Boeing 737-300 in straight level and symmetric flight during cruise for subsonic flight region. This will primarily determine the lift and drag characteristics of the aircraft which will then be used for performance analysis.  Investigate optimum range and endurance performance of the Boeing 737-300 at various altitudes for subsonic flight when all engines are operating.

4.3 Scope The following performance related characteristics are determined to carry out the all engine operative (AEO) performance analysis as per the objectives outlined above.  Thrust available model. This is to estimate thrust produced by the aircraft power plants at a given speed and altitude.  Thrust versus specific fuel consumption (SFC) model. These models allow altitude versus thrust and altitude versus SFC plots at various speeds to be produced.

 CL and CD values for varying altitudes and speeds.

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 Range and endurance performance using the Breguet’s Range and Endurance equations. These equations take into account the fact that the aircraft weight drops as fuel is burned and average of the maximum take-off weight and the weight at the end of the flight (with 10% as reserve and not taking into account descent, landing and taxing phases of the flight) is used.

4.4 Thrust Model The variations of thrust and SFC with speed and altitude are estimated based on engine characteristic data taken from Chapter 9. [44] Performance data are read off the curves given for engines with high bypass ratios of 6.5 for cruise ratings. (The bypass ratio of the engines used in B737-300 is 5.9). The values presented in the curves in the reference are non-dimensionalised thrust ratio and hence multiplied by known static thrust at sea level of 98.1 kN per engine. Second order polynomial curve fit models are then derived to estimate the variation of thrust and SFC with speed and altitude.

There are other mathematical models developed for high bypass turbo fan engines such as ones presented by Brandt [45] Asselin [46] and Eshelby [21]. However, the above mentioned approach is adopted as there are both Thrust and SFC data available for same engine with by-pass ratios of 6.5 within a single reference for different flight phases such as climb or cruise. The curves are also presented in non-dimensional thrust ratio form which makes it easier to work with. Refer to Appendix C.

The mathematical model estimated for thrust available per engine for cruise situations at a given altitude and speed for turbofan engines with high bypass ratio in the order of 6.5 is derived as follows (from engine data):

2 TAalt  TAstatic_ S.L (AM  BM  C) Equation 4 Where, A  30(e )3  45(e )2  20(e )  2

B  36(e )3  54(e )3  24(e )  2

C  1.6(e ) 1.4

In Equation 4, TAstatic S.L denotes the sea-level static thrust and M is the Mach number. The coefficients A, B and C are calculated as above and σ represents the density ratio

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(ρalt/ ρS.L). Figure 17 presents the plot of thrust available across a range of speed at various altitudes.

4.5 Specific Fuel Consumption Model The specific fuel consumption of a turbo fan engine is essentially a function of thrust available by the engine and Mach number. Altitude affects the density, pressure and temperature of the ambient atmosphere the engine is operating in. This in turns affects the thrust the engine is required to produce to achieve or maintain a speed. The specific fuel consumption for the high bypass ratio turbofans at a given altitude and speed can be derived from actual data as follows: SFC  c  0.616(A(TA /T  )2  B(T  )  C) alt,Machno f alt staticSL staticSL Equation 5 Where,

A  1.6M 3 1.6M 2  0.5M  0.5 B  2.1M 3  2.5M 2  0.25M  0.5 C  0.7M  0.4

In Equation 5, θ represents the temperature ratio (θalt/ θS.L) and δ is the pressure ratio

(δalt/ δS.L). Cf is a correction factor built in to adjust for better accuracy of the thrust specific fuel consumption model based on particular engine’s sea level static and cruise specific fuel consumption figures published. The known figures for static sea level SFC and cruise SFC are given to be 0.39/hr and 0.67/hr respectively. Normalizing model’s SFC with these figures results in the correction factor. In this thesis, the correction factor for the engine used in -300 variant of the Boeing 737 is estimated to be 1.425. Figure 18 presents the plot of SFC for different speeds at various altitudes based on the mathematical models given in Equation 4 and Equation 5. Details of Thrust and Specific Fuel Consumption models estimation are included in Appendix C and Appendix D respectively.

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Figure 17: Thrust available for different Mach number at various altitudes (2x Engine)

Figure 18: SFC for different Mach No at different altitudes (2x Engine)

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Turbofan engines do not like to operate at less than maximum thrust setting. When lesser thrust is set by throttling back, there is a proportional reduction in fuel flow as such SFC increases. The SFC also decreases with altitude and increases with Mach No.

Specific fuel consumption and the aircraft fuel load determine the maximum flight time and the maximum range of an aircraft. Engines with larger thrust require greater fuel flow rate and the fuel to air ratio which is effectively the multiplication of SFC with specific thrust. Ideally, this can be achieved by increasing these two parameters but is not practical as combustion process and materials used in the engine set limits on values of fuel to air ratio [17].

4.6 Drag Polar The drag polar of Boeing 737-300 is estimated for subsonic Mach numbers as given in Equation 6 using aircraft data gathered as presented in Chapter 3 and procedures outlined in Appendix A. The cruise Mach number for the type of airplane is known to be around 0.745 [40]. Above this Mach number, CDo and K become function of Mach number. Table 9 presents CDo and K values for take-off, clean and landing configurations. Figure 19 shows the parabolic drag polar plots for these configurations. The two term drag polar used in the estimation may not be accurate enough especially for take-off and landing configurations when camber is high. However, the research emphasizes more on cruise phase of the flight.

C  C  KC 2 D D0 L Equation 6

Flight Configuration CDo K Take-off 0.01728 0.0476 Landing 0.01792 0.04244 Clean 0.016 0.0476

Table 9: CDo and K values for take-off, landing and clean configurations

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Figure 19: Estimated drag polar for the B737-300 for different configurations 4.7 Equations of Flight Equilibrium In non-dimensional form, the equations of flight equilibrium using the aircraft stability axis system are: [18]

mgsin 1  (CD0  CD1  CDihih1  CDe e1 )q1S T1 cos(T 1 ) Equation 7

mg cos 1  (CL0  CL1  CLihih1  CLe e1 )q1S T1 sin(T 1 ) Equation 8

0  (Cm0  Cm1  Cmihih1  Cme e1 )q1Sc T1dT Equation 9

 mgsin1 cos 1  (Cy 1  Cya a1  Cyr r1 )q1S  FyT1 Equation 10

0  (Cl 1  Cla a1  Clr r1 )q1Sb  LT1 Equation 11

0  (Cn 1  Cna a1  Cnr r1 )q1Sb  NT1 Equation 12

There are nine variables in the six equations. At least three variables need to be specified to solve for the other unknowns. The steady state thrust, can be specified based on the specifications of the engine used in an aircraft. Usually, the steady state bank angle, ϕ1 and the steady state stabilizer incidence angle, ih1 are specified in most practical applications. Since several of the variables are inter-related, by using the iterative method, the equations of flight equilibrium can be solved for solutions to the remaining variables.

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4.7.1 Stability and Control Derivatives The stability and control derivatives used in the following analysis are estimated using Roskam’s methods of estimation outlined in Appendix B. The derivatives only concerned with longitudinal steady straight line flight are listed in this section as tabulated in Table 10. They are computed in stability axis system. The sign conventions for control surfaces displacement are assigned as shown in Figure 20 for the analysis in this chapter of the thesis.

0.119 0.1868

0.1025 -0.05875

0.0091 -0.04131

0.0168 -0.0129 Table 10: Estimated longitudinal derivatives required for analysis

Figure 20: Control surfaces sign conventions 4.8 Straight and Level Performance In a steady level flight, since the acceleration is zero, the summation of forces in both horizontal and vertical direction is zero. Since this is for All Engine Operative (AEO) flight condition and assuming this is a straight and level symmetrical flight, the lateral set of equations of flight equilibrium, Equation 10, 11 and 12 can be neglected for this analysis. The longitudinal set of equations of flight equilibrium, Equation 7, 8 and 9 can be rewritten in following simplified forms:

mgsin 1  (CD )q1S T1 cos(T 1 )

mg cos 1  (CL )q1S T1 sin(T 1 )

0  (Cm )q1Sc T1dT

Assuming that thrust inclination, and angle of attack, are quite small, the terms,

and can be set to 1 and 0 respectively. Thrust line projection distance, is also assumed to be negligible. Flight path angle, , is also set

43 | P a g e to ‘0’ as it is a steady straight and level flight. Thrust available from the aircraft engines must be sufficient enough to cancel out the Total Drag developed by the aircraft in a particular flight condition. At the same time, Lift produced by the aircraft in that flight condition must be equal to Weight of the aircraft to maintain steady straight and level symmetrical flight. Hence, the total lift coefficient required to main the steady straight and level flight is: W C  L q S 1 Equation 13

The total drag developed by the aircraft can then be calculated using the parabolic drag polar Equation 6 estimated as shown in Figure 19.

4.8.1 Variation of Minimum and Maximum Speeds with Altitude In order to determine the minimum and maximum speeds, the plots of total thrust available (from both engines) and total drag of the aircraft at various altitudes need to be produced as shown in Figure 21. The graphical methods of determining speeds at which the two curves intersect at a given altitude yields minimum and maximum speeds which the aircraft needs to be flying to maintain the straight and level flight. Table 11 presents the values obtained from graphical interpretation and these are also used in producing the plots shown in Figure 22.

Figure 21: Thrust available (cruise) Vs Drag at 10,000 ft (AEO)

In level flight, since CL cannot exceed CLmax, there is a flight speed below which level flight cannot be maintained and this speed is the stall speed, Vs as calculated by:

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2 W  Vs    Equation 14 CL max  S 

Based on the aircraft data gathered as presented in Chapter 3, CLmax, for take-off configuration with flaps is 2.16 while it is 2.88 for landing configuration. The CLmax value for cruise configuration without flaps is 1.4. Hence CLmax= 1.4 is used to calculate to arrive at the stalling speeds for various altitudes given in Table 11.

The weight of the aircraft used is the Maximum Take-off Weight (MTOW) which is 2 62,820 kg. The wing loading, W/S, for the aircraft is hence 5869 N/m . The variation of minimum and maximum speeds with altitude is plotted as shown in Figure 22.

As can be seen in the figure, the stalling speed, Vs increases with altitude as air density,

 decreases with increase in altitude. Minimum speed, Vmin the aircraft is required to fly to overcome drag is found to be slower than stalling speed at altitudes below 30,000 ft. At cruising altitudes, this minimum speed is found to be higher than the stalling speed. It should also be noted that maximum speeds at altitudes are found to be very close or higher than known cruising speed of the aircraft. This may be attributed to some inaccuracy in estimating drag polar or thrust available at higher speed regions as transonic wave drag conditions were not taken into account in deriving the models.

Figure 22: Variation of minimum and maximum speeds with altitude (AEO)

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Altitude Vstall Vstall Vmin Vmin Vmax Vmax [ft] [Mach No] [KTAS] [Mach No] [KTAS] [Mach No] [KTAS] S.L 0.22 145 0.13 86 0.78 516 5,000 0.24 156 0.16 104 0.79 514 10,000 0.27 172 0.19 121 0.8 510 20,000 0.33 203 0.27 166 0.8 491 30,000 0.42 247 0.43 253 0.8 471 35,000 0.47 270 0.69 396 0.8 459 Table 11: Thrust Available Vs Drag at various altitudes (AEO) 4.9 Range and Endurance Performance This analysis is conducted for the aircraft flying with clean configuration such as in cruise flight and when both engines are operating. This configuration produces the lowest drag coefficient of all possible normal flight conditions as it has the clean profile and no wave drag component is included as the analysis is for subsonic speed regimes. This results in the lowest thrust being required for straight and level flight, allowing for application of thrust and specific fuel consumption models developed as they are based on cruise thrust. Range and endurance are calculated using the Breguet equations. The integral forms of the equation are given in Equation 15 and Equation 16 below.[42]

WlandingV C 1 Range  L dW Equation 15 Wtakeoff c CD w Wlanding1 C 1 Endurance  L dW Equation 16 Wtakeoff c CD w

W stands for weight in the equations while V is velocity; c is specific fuel consumption;

CL is lift coefficient; and CD is drag coefficient.

The range and endurance of an aircraft is a direct function the quantity of fuel the aircraft can carry and the rate at which it burns to travel in the air. An aircraft flies at different speeds in various flight environments for different flight segments during a flying operation. The weight of the aircraft is also decreasing continuously in flight as fuel is burned.

4.9.1 Range and Endurance – All Engine Operative – Constant Altitude- Constant Speed The range and endurance at constant speed and altitude for the (AEO) flight are calculated for a range of speeds at varying altitudes using Equation 17 and Equation 18. [42] The results are plotted as shown in Figure 23 and Figure 24 respectively.

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  V 1 K 1 K Range  tan Winitial  tan W final  Equation 17 c KCD0  q CD0 q CD0    1 1 K 1 K Endurace  tan Winitial  tan W final  Equation 18 c KCD0  q CD0 q CD0 

Figure 23: Range vs. Speed at different altitudes with AEO (at MTOW) A maximum take-off weight (MTOW) of 62,820 kg and fuel weight of 14,410 kg (10% of which is taken as fuel reserve) are used in calculating Winitial and Wfinal parameters in the equations. The speed to fly the aircraft in this flight condition for the best range and endurance will have to fall between Vstall or Vmin and Vmax. Refer to Table 12.

As can be seen in the plots given in Figure 23, the maximum range of the aircraft is about 2600nm at 35,000 feet without taking into account taxing, climb and descent. It is also assumed that the amount of fuel mentioned above is used between beginning and end of cruise. The aircraft will have to fly at a Mach No close to 0.8 or 459 KTAS at that altitude to achieve that. This corresponds to an endurance of about 5.5 hours. Refer to Figure 24.

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Figure 24: Endurance vs. Speed at different altitudes with AEO (at MTOW) However, for the optimum endurance performance of the aircraft in this same flight condition, it will have to fly at a lesser speed of 0.7 Mach or 403 KTAS. The optimum endurance is 6 hours with this flight profile.

The airspeed is directly proportional to square root of weight, and inversely proportional to square root of density and square root of lift coefficient. As the flight progresses and fuel is progressively burned, the weight decreases and hence the airspeed decreases. This may be viewed as a constant Angle of Attack (AoA) flight.

In order to satisfy the constant speed - constant altitude constraints, lift coefficient must remain proportional to weight throughout the flight. This means as the weight decreases, the lift coefficient must be decreased by decreasing the angle of attack. This in turn reduces the induced drag (smaller induced drag, zero-lift drag is unchanged) and throttle may need to be adjusted to lower settings as the flight progresses. It can be observed from the plots that with AEO both range and endurance performance improve as the altitude increases although endurance is not a strong function of altitude. It can be explained from the fact that the SFC decreases as the altitude increases and as the throttle setting is adjusted to close to maximum (more efficient) settings. Table 12 lists optimum range and endurance performance at various altitudes with corresponding speed information.

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(ft)

(hr)

(nm)

(Mach No) (Mach No) (Mach No) (Mach No) (Mach No) (Mach

SL 0.22 0.13 0.78 1288 5.0 0.45 0.34 5000 0.24 0.15 0.79 1395 5.01 0.51 0.36 10000 0.27 0.18 0.8 1527 5.06 0.56 0.41 20000 0.33 0.26 0.8 1894 5.34 0.67 0.51 30000 0.42 0.42 0.8 2372 5.88 0.74 0.61 35000 0.47 0.64 0.8 2562 5.99 0.78 0.69 Table 12: Optimum range and endurance at different altitudes with corresponding speeds (AEO at MTOW) 4.9.2 Trim Angle of Attack and Elevator Deflections This analysis is performed to observe what sort of angle of attack and control surface defections (elevator deflection in this straight, level and symmetric flight scenario) are required for the aircraft to be in trim while flying at the speeds dictated by optimum range and endurance performance with constant altitude – constant airspeed profile in AEO condition.

The longitudinal set of equations of flight equilibrium, Equation 7, Equation 8 and Equation 9 from section 4.8 are recalled here. Assuming that there is always sufficient thrust to overcome the drag, the drag equation given by Equation 7 can be treated as superfluous. Hence, the Equation 8 and Equation 9 can be rewritten in the following matrix form:

CL CLe 1  CL1  CLo  CLihih       C C    C  C i  m me  e1   mo mih h1  Equation 19

The trim angle of attack and elevator deflections can then be solved for using iterative matrix techniques. The plots of trim angle of attack and elevator deflections with respect to speed at various altitudes are presented as shown in Figure 25 and Figure 26. A sanity check of the solutions needs to be carried out as deflection angle of more than 25- 30 degrees for elevator would stall the horizontal tail of the aircraft, hence setting up the limits for the maximum amount of deflections beyond which the solution is impractical. Same is also true for the trim angle of attack and the angle of attack greater than 20 degrees can be regarded invalid.

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It can be observed that if the aircraft is flying at a speed of 0.75-0.78 Mach which is the optimum range speed at 35,000 ft, the elevator deflection required to hold the angle of attack of about 3 degree to keep the aircraft in trim will be -2 degree. It means a slight downward deflection of elevators is required to pitch the nose of the aircraft down to fly with an angle of attack of 3 degree.

Figure 25: Trim angle of attack vs. speed at different altitudes

Figure 26: Trim elevator deflection vs. speed at different altitudes

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4.10 Limitations The analysis presented in this section assumed a number of variables constant or negligible. These assumptions are made to achieve the most realistic results but may affect the accuracy of the analysis. These are:  Thrust vectors from both engines are assumed to be in the same horizontal plane as the aircraft centre of gravity (CoG), with horizontal stabilizer incidence angle and thrust inclination taken as zero.  Thrust available is assumed to be always sufficient to overcome the drag which neglects the drag equation in the longitudinal set of equations. This in turns ignores the trim drag.  A straight and level, un-accelerated and symmetric flight profile (zero sideslip angle) is assumed in estimating range and endurance. This allows easier drag analysis but does not reflect reality as the aircraft could be flying with some sideslip for certain part of the cruising phase of the flight. However, to account for each and individual change of drag profile will be a tedious process, and hence this assumption.  Required engine related data such as thrust and specific fuel consumption are obtained from references given by measuring or reading off relevant curves, and human errors can contribute to inaccuracy of some of the data.  Elements such as weather phenomena or non standard atmospheric conditions which influence the performance of the aircraft are not taken into consideration.  Limitation on reliability of analytical aerodynamic relationships/ estimation/ formulas could exist as the analysis followed and obtained these from established literature.

4.11 Summary In this chapter an analysis of basic flight performance for all engine operative condition has been presented. It has covered engine thrust and specific fuel consumption derived and drag polar estimated for the aircraft used in research. The process of obtaining minimum, maximum, and stalling speeds at the aircraft maximum take-off weight for various altitudes has also been discussed. An analysis of range and endurance performance using Breguet equations for constant speed- constant altitude flight profile has been performed. A discussion on longitudinal equations of flight equilibrium has also been included with an analysis on longitudinal control surfaces deflection required 51 | P a g e for trimmed flight at various altitudes. The next chapter presents a study into one engine inoperative (OEI) range and endurance performance of the Boeing 737-300 aircraft.

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5. CHAPTER 5: ONE ENGINE INOPERATIVE FLIGHT MODELLING 5.1 Introduction This chapter discusses performance issues concerning One Engine Inoperative (OEI) flight for the Boeing 737-300. Thrust reduction and asymmetric thrust are two important considerations in determining aircraft performance under OEI circumstances as the resulting unbalanced state of the aircraft needs to be counteracted by systematic control inputs from skilful pilot, affecting stability and control of the aircraft. It also presents the Range and Endurance optimization to determine the optimum flight altitude and attitude for the best range and endurance performance of the aircraft with the OEI condition.

5.2 Objectives The main aims of this chapter of the thesis are as follows:  Investigate force and moment equilibrium associated with lateral stability and control in OEI condition.  Analyse control surface deflections required to fly the aircraft with a certain attitude in OEI condition.  Analyse drag contributions caused by control surface deflections required towards overall drag of the aircraft with OEI.  Determine flight condition (altitude, attitude, and speeds) for optimal range and endurance performance in OEI condition.

5.3 Assumptions There are a number of assumptions made with the OEI range and endurance estimation to achieve realistic results and for ease of analysis. The major assumptions made in this section, and the reasoning behind each of them is listed as follows:  It is assumed that the aircraft is recovered from OEI condition with appropriate control surface deflections and flies a straight and level steady un-accelerated flight profile with zero degree of side slip with OEI. In real life scenarios, the aircraft could be flying with a side slip angle at different stages of its flight, but it will be a tiresome process to model the detail drag profile for each stage with a side slip angle and hence this assumption.

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 The model developed is based on right engine out situation and thus force and moment directions are depicted for the corresponding engine out situation. The model may be used for left engine out situation and the fore and moment directions will be opposite to those of the right engine out situation.  It is also assumed that rudder is used to counter yaw moment due to thrust asymmetry and ailerons are used to counter roll moment induced by side force on vertical tail. The condition that aircraft is banked 5 degrees towards the operating engine (to lift the inoperative engine) which is usually requirement by aviation authorities to demonstrate aircraft’s minimum control speed with OEI is also imposed in analysis of optimum range and endurance.  The maximum take-off mass (MTOW) of 62,820 kg and the fuel mass of 14,410 kg as given in chapter (3) are used in the calculations. It is assumed that 10% of the total fuel the aircraft carries is reserve.  The range and endurance model covers the subsonic flight regime and assumes that the steady state drag value for all speeds (below Mach 0.8) and altitudes follows the parabolic drag polar presented in the previous chapter. This steady state drag value is applicable for normal flight with AEO (zero control surface deflections and balanced flight). With OEI, the control surface deflections are required for the balanced steady straight line flight and hence additional drag contributions are added to this steady state value. The wave drag calculations are not required.  The range calculated is the gross still air range. It assumes that the aircraft starts the flight at the initial cruising altitude above the departure point and runs out of fuel above the arrival or destination point.  The maximum lift coefficient used in the model for clean cruise configuration is taken to be 1.4 as per Chapter 3. The lift coefficient value of 2.16 for take-off with flaps configuration and 2.88 for landing with flaps configuration are assumed.  It is also assumed that the thrust inclination angle is zero, i.e. the thrust line coincides with the horizontal plane passing through the aircraft Centre of Gravity (CoG).

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5.4 Lateral Stability and Control with One Engine Inoperative When one engine fails in a multi-engine aircraft, asymmetric thrust develops, resulting in a yaw rate in the direction of failed engine. The thrust available is approximately halved and control surface deflections (aileron inputs to lift the inoperative engine and rudder inputs to balance the side slip) required to keep the aircraft flying as efficiently as possible with OEI will produce additional drag on the steady state condition. This requires the existing operating engines to have sufficient continuous thrust to compensate for such drag. [46] In addition to this asymmetric yaw, there is also an increased drag on the inoperative engine side due to wind-milling effect of a jet engine which adds to the yawing moment. This drag for a turbofan is usually small. Figure 27 shows the forces associated with lateral stability of the aircraft in OEI condition. (Right engine out)

Figure 27: Forces associated with OEI (Right Engine Out) [41]

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5.4.1 Lateral Equations of Flight Equilibrium The lateral equations of flight equilibrium for a steady straight line flight as given in

Chapter 4 are recalled. For a steady straight line flight, the flight path angle, , is assumed to be zero. Neglecting the thrust inclination and projection angles of the engines, side force due to thrust, and rolling moment due to thrust, can also be set to zero. In non-dimensional matrix form, the simplified lateral equation of motion can be rewritten as given in Equation 20. [18]

 1   (mg sin1 cos  1  FyT1 )  q1S C y C ya C yr         L C C C     T1  Equation 20  L La Lr  a   q Sb     1 C N C Na C Nr  r     1   N Twme  q1Sb 

5.4.2 Wind Milling Drag due to Inoperative Engine and Yawing Moment In an OEI situation, especially for a turbo fan aircraft such as the Boeing 737-300, the dominating forces to the total yawing moment of the aircraft are wind milling drag generated by the inoperative engine and the thrust from the operating engine.

The wind milling drag of the inoperative engine can be estimated using Torenbeek’s method given in by Equation 21. [24]

Dwme  q1Sref CDwme Equation 21 Where,

The drag coefficient due to wind milling engine, CDwme is given by [23]: 2  V V 0.0785d 2  d 2 n (1 n ) i (1 0.16M 2 ) 4 i V V CDwme  Sref

In the above equation, di is the inlet diameter of the engine. M is the Mach number and Vn/V represents the ratio of mean nozzle exit velocity to free stream velocity. [24]

The total aircraft yawing moment caused by wind milling engine and thrust from the operating engine can then be estimated by Equation 22. [24] The coefficient CNTwme is yawing moment coefficient due to thrust and wind milling engine, and le is lateral distance of the engines from centre of gravity. 56 | P a g e

NTwme  q1Sref bCNTwme  (T1  Dwme )le Equation 22

5.4.3 Yaw and Rudder Control In OEI condition, the developed yaw (due to thrust asymmetry plus wind milling drag) continues to increase until the thrust yawing moment is balanced by opposite yawing moments due to the resulting side slip. This is also known as weather cock stability of an aircraft. The maximum side slip angle an aircraft reaches in OEI condition before any corrective inputs can be calculated as given in Equation 23. [18] Figure 28 illustrates the side slip situation the aircraft will be subject to in right engine inoperative condition. βmax values at a range of speed for the B-737-300 aircraft at maximum take- off weight in OEI condition assuming a right engine failure are plotted as given in Figure 29.

 N   Twme Equation 23 max 1 CN q1Sb

Figure 28: Force and moment the aircraft is subject to with OEI and side slip [41]

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Figure 29: Maximum sideslip Vs speeds at different altitudes (Right Engine Inoperative at low altitudes) Once the weather cock stability equilibrium sideslip angle is achieved, the yawing does not increase further. However, the resultant side force developed by the vertical tail due to side slip continues to accelerate the aircraft laterally towards the side of inoperative engine. This needs to be balanced by opposite side force, usually in the form of rudder control input which will reduce the side slip angle. The amount of rudder deflection required for a desired sideslip (assuming no aileron inputs) can be solved by Equation 24Equation 24. [41]

1  CN   NTwme q1Sb  r  Equation 24 CNr

Figure 30 illustrates the rudder deflection required to achieve zero side slip over a range of airspeed at different altitudes (low altitudes). It can be noted that positive sign of rudder deflection estimated means left rudder or yawing moment towards operative engine.

Figure 30: Rudder deflections required for zero side slip at different speeds at different altitudes

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5.4.4 Roll and Aileron Control In addition to the yawing phenomenon, the aircraft with (OEI) also suffers from a roll rate developed due to the difference in speed at which each side of the wings travels through the air. The dihedral and wing blanking effects in combination with resulting side slip also play their role in contributing towards the rolling moment. In jet aircrafts, the side slip angle reduces the frontal area of the downwind swept wing considerably, increasing the rolling moment. [23] A certain amount of aileron deflection is required to achieve zero rolling moment. The amount of aileron deflection required to achieve zero rolling moment can be found as given in Equation 25. [18] Figure 31 shows a range of aileron deflections required at max side slip condition to achieve zero rolling moment at different speeds and altitudes.

LT1  CL  max  q1Sb  a  Equation 25 CLa

Figure 31: Aileron deflections (for zero rolling moment) Vs speed at different altitudes at max side slip 5.4.5 Minimum Control Speed with One Engine Inoperative In (OEI) situations, the only aerodynamic controls available as far as lateral equilibrium is concerned are ailerons, and rudder as well as the engine thrust; directional controls can somewhat be maintained by manipulating power levers/throttles. Hence, in order to be able to recover to steady straight line and controllable flight, the airspeed is required to be high enough such that recovery inputs such as rudder and ailerons deflection are effective to generate required opposite yawing and rolling moments to recover lateral equilibrium.

The additional trim drag resulting from the required control inputs to balance the aircraft with OEI for steady straight line flight calls for certain minimum control speed.

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It is the slowest speed at which the aircraft is able to recover to steady straight line flight with zero side slip with the maximum rudder deflection applied usually with a small bank angle towards the operating engine. This speed should not be slower than the stalling speed.

Figure 32 and Table 13 show the stalling speeds of the aircraft with cruise configuration and minimum control speed (at maximum rudder) with OEI at different altitudes. On the other end of the speed range, there is also maximum flyable speed dictated by “drag to overcome Vs thrust available by the remaining engine” criteria at an altitude.

This minimum control speed in air, for effective recovery to steady straight and controlled flight in (OEI) condition is found as given in Equation 26. [18]

Figure 32 illustrates the minimum control speeds for different altitudes assuming a maximum rudder deflection of 15 degree. It is based on thrust available at Mach 0.2 as yawing moment due to the whole thrust asymmetry situation is directly proportional the speed at which the aircraft flies. If the aircraft is flying at a higher speed and OEI condition occurs, the minimum control speed to recover with the mentioned configuration will be higher than those shown in Figure 32.

2(NTwme ) Vmca  Equation 26 CNr r max Sb

Figure 32: Minimum Control Speed at different altitudes with max rudder deflection of 15 deg

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Altitude (ft) Vmca (Mach No) Vmca (KTAS) Vstall (Mach No) (cruise) Vstall (KTAS) S.L 0.196 130 0.23 152 2000 0.199 131 0.24 157 4000 0.2 131 0.26 170 5000 0.21 137 0.26 169 8000 0.21 135 0.29 186 10000 0.22 140 0.3 191 Table 13: Minimum Control Speed and Stalling Speed (cruise clean configuration) at different altitudes with OEI 5.4.6 Trim Drag One of the significant factors in achieving more accurate and realistic range and endurance performance model in OEI situations is the estimation of trim drag resulted from deflected control surfaces. Under normal balanced flight with AEO, the drag polar is assumed to be valid for different altitudes at speeds up to cruise Mach. In other words, the zero-lift Drag coefficient and lift due to drag factor are assumed constant for all the flight scenarios in the subsonic region.

With OEI, it is important to take into account additional profile and induced drag contributed towards the total drag of the aircraft in a particular flight condition. The profile and induced drag contributions due to deflected control surfaces (ailerons and rudder) are estimated as given in Equation 2 and Equation 3 of section 3.5.2. [7]These additional drag contributions (profile and induced) are then added to the steady state drag value based on the drag polar derived for the normal balanced flight to arrive at the total drag of the aircraft with required deflected control surfaces for a particular flight condition with OEI.

The profile and induced drag associated with elevator, rudder and aileron deflections are calculated by treating the wings-ailerons and vertical tail-rudder pairs as deflected plain flaps as given in part VI of Roskam’s Airplane Design. In Equation 2, the term ΔCdp is the profile drag increment for ailerons/rudders and estimated as per the graph given in Figure 33.

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Figure 33: Profile Drag Increment: Plain Flaps [47] The total drag (coefficients) for the Boeing 737-300 aircraft with required deflected control surfaces for balanced steady straight line flight with OEI is given by Equation 27. [7] The percentage increment of total drag is plotted for different speeds at various altitudes. Figure 34

CDoei  CDss  CDp _ rudder  CDp _ ailerons  CDi _ rudder  CDi _ ailerons Equation 27

Figure 34: Trim Drag with OEI over a range of speeds at different altitudes

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5.5 OEI Flight Analysis Assuming a right engine failure, by specifying a negative bank angle (to lift the dead right engine) of 5 degree, δa and δr values required to fly with zero side slip at different altitudes across a range of speeds are plotted as shown in Figure 35. In most of the practical flight operations of multi-engine aircrafts, it is a regulatory requirement of an aircraft to be controllable in a straight line flight with (OEI), with a given maximum bank angle and minimum speed. [28]

The speed at which the aircraft is travelling determines the required amount of rudder input. However, for both aileron and rudder, it is important to note that the amount of deflection should be consistent with conditions of attached flow. The realistic maximum deflection for both aileron and rudder is 25 degrees. Conventional rudders with deflection of more than 25 degrees would stall the vertical tail. [18]

Assuming as small as possible side slip (zero side slip in this analysis) is desired for the least drag during an asymmetric flight recovery at 10,000 ft, the rudder deflection needs to be in the region of positive 5 degrees at the speed slightly above the stall speed of the aircraft as can be deduced from Figure 35. This is also based on the assumption that the aircraft is held at a negative 25 degrees aileron deflection. This means that the aircraft needs to be flying with a bank angle in the region of negative 3 degree. The bank angle balances the side force with a component of the aircraft weight which in turns balance the rolling moment equilibrium Figure 36.

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Figure 35: Aileron (constant) and rudder deflection for zero side slip at different speeds at different altitudes with OEI

Figure 36: Bank angle for zero side slip at different speeds at different altitudes with OEI The minimum control speed at this altitude is 0.22 Mach while the stalling speed with cruise configuration is 0.3 Mach. Hence, the ability of the rudder deflection to balance the aircraft at the altitude to keep straight and level with zero side slip is sufficient as the aircraft will stall first before having any ineffective rudder authority. 64 | P a g e

In this OEI situation, the aircraft is flying with one engine and thrust available is halved. It is required to determine how the minimum speed dictated by thrust available versus drag (OEI) to overcome requirement compares with this speed. Figure 37, Figure 38, Figure 39 and Figure 40 show the thrust available versus drag required at 20,000 ft, 10,000 feet, 5,000 feet and S.L for the aircraft with comparison between AEO and OEI drags.

The OEI drag curves in the plots take into account additional trim drag resulted from balancing the flight equilibrium with OEI. The minimum and maximum speed dictated by the thrust available model and drag required curve are 0.31 Mach and 0.5 Mach respectively at 10,000 ft. Hence, the minimum speed the aircraft is able to fly to maintain this altitude should not be lesser than 0.31 Mach (Vmin) and greater than 0.5

Mach (Vmax) with one engine inoperative (OEI). The optimum range and endurance performance with OEI at this altitude will have to occur at speed between these boundaries. Table 14 shows the minimum and maximum speeds the aircraft can fly with OEI at different altitudes.

V V V V Altitude mca V stall V min V max V (Mach mca (Mach stall (Mach min (Mach max (ft) (KTAS) (KTAS) (KTAS) (KTAS) No) No) No) No) S.L 0.196 130 0.23 152 0.21 139 0.44 291 5,000 0.21 137 0.26 170 0.25 163 0.48 312 10,000 0.22 140 0.3 191 0.31 198 0.5 319 20,000 ------30,000 ------35,000 ------Table 14: Vstall, Vmca, Vmin, Vmax with OEI at different altitudes

It is advisable to keep the aircraft close to zero degree sideslip as the increased drag would impact the aircraft ability to climb out with one engine operating as well as the range and endurance.

Thus, to fly with a zero or close to zero side slip angle, the aircraft needs to fly at speed regime close to max speed available. This will require only a smaller rudder deflection and aileron deflection, reducing the trim drag and hence total drag.

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Figure 37: Thrust Available Vs Drag over a range of speed at 20,000 ft

Figure 38: Thrust Available Vs Drag over a range of speed at 10,000 ft

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Figure 39: Thrust Available Vs Drag over a range of speed at 5,000 ft

Figure 40: Thrust Available Vs Drag over a range of speed at S.L

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5.6 Range and Endurance with OEI The range and endurance performance of the Boeing 737-300 aircraft with OEI are analysed. The analysis explores the range and endurance performance in three different flight schedules: constant speed-constant altitude schedule, constant lift-constant speed schedule, and constant lift-constant altitude schedule. As discussed previously, the range and endurance performance are a function of three critical parameters in speed, density and lift coefficient. If one of the parameters is varied while the two others are held constant, the mathematical estimation will yield a better correlation with the physical results.

5.6.1 Range and Endurance with OEI – Constant Speed and Constant Altitude The range and endurance in this flight schedule are estimated based on the assumption that the aircraft will fly almost the entire segment (except for descent/landing segment) of post (OEI) condition with a constant speed at a definite altitude which would result in the best range and endurance. It is also assumed that the specific fuel consumption is constant throughout the flight in this schedule [7] and the aircraft is recovered to straight line controlled status from transient asymmetric flight at its maximum takeoff weight (MTOW) right after one of the engines fails, right engine in this case. The range and endurance performance for constant speed – constant altitude flight schedule are calculated as given in Equation 17 and Equation 18 respectively. [42]

Figure 41: Range Vs Speed at different altitudes (OEI) (constant speed – constant altitude) 68 | P a g e

Figure 42: Endurances Speed at different altitudes (OEI) (constant speed – constant altitude) The range and endurance at constant speed and altitude for the (OEI) flight are plotted for a range of speeds at varying altitudes as shown in Figure 41 and Figure 42. The speed options to fly the aircraft in (OEI) condition for the best range and endurance fall between Vmca/ Vstall/Vmin and Vmax given in Table 14. It can be seen from Figure 37 that there is no sufficient thrust available from the remaining engine to fly at an altitude of 20,000ft and higher and hence no speed data as well as range and endurance estimation for altitudes of 20,000ft onward in Table 15.

It can be observed that for optimum range performance in (OEI) condition in this constant speed – constant altitude schedule, the aircraft needs to be flying at a speed close to maximum available speed at a constant altitude at altitudes of 12,000 ft and below. Figure 43

At 10,000 ft, the best range performance with OEI is 1587nm and occurs at maximum speed of about 0.5 Mach assuming the same weight assumptions as in AEO range estimation in the previous chapter. It is a slight improvement from range performance with AEO (1527nm) at the same altitude.

On the other hand, for the best endurance performance, the aircraft will need to fly at a slower speed of about 80% of the best range speed at a constant altitude. At 10,000 ft, 69 | P a g e the optimum endurance is about 5.76 hours and the best endurance speed is 0.4 Mach. This is also a slight improvement from 5.06 hours estimated with AEO at the same altitude. The best endurance speed with AEO is about the same as that of OEI.

Figure 43: Thrust available Vs Drag curve with OEI at 12,000 ft

) ) ) ) ) )

(ft)

(hr)

(nm)

Mach No Mach No Mach No Mach No Mach No Mach No Mach

( ( ( ( ( (

S.L 0.196 0.23 0.21 0.44 1318 5.57 0.44 0.29 5,000 0.21 0.26 0.25 0.48 1454 5.69 0.47 0.34 10,000 0.22 0.3 0.31 0.5 1587 5.76 0.53 0.4 12,000 0.225 0.32 0.34 0.52 1634 5.79 0.54 0.44 20,000 ------30,000 ------35,000 ------Table 15: Best range and endurance with corresponding speeds at each Altitude

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5.6.2 Range and Endurance –Constant Lift (AoA) and Constant Speed Under the constant speed and constant lift (angle of attack) flight schedule, the range and endurance performance can be estimated as given in Equation 28 and Equation 29. [42]

V L  W  Range  ln i    Equation 28 c D W f  1 L  W  Endurance  ln i    Equation 29 c D W f 

As can be seen in Equation 28, the range performance depends on L/D which is the aerodynamic efficiency of the aircraft and the specific fuel consumption, c while velocity, V is held constant. The ratio (Wstart/Wend) also affects the range and optimising it, gives a greater range. As the fuel is consumed and the weight gets smaller, the aircraft is required to fly in less denser altitude while the velocity and lift are being maintained. Hence, the altitude must increase as the flight progresses with this flight schedule. This method is known as “drift up” or “cruise climb” and is often used in practical aviation situations so as to cater to certain air traffic control requirements. [6]

In addition, it may be required to adjust the throttle so that the airspeed remains constant. This is more pronounced especially for flight in the troposphere. As the temperature falls with altitude in such circumstances (below 11km or troposphere), the thrust available decays less rapidly. [6]

As the altitude gets lower, the range gets progressively worse due to TSFC changes. This is because increased density increases thrust (drag) due to at lower altitudes. In the stratosphere, where the temperature is constant, the engine thrust will decrease with altitude at the same rate that the drag is reduced with altitude as the thrust available is proportional to the density and CL/CD needs to be held constant Hence, the throttle can remain unadjusted. It can also be observed that endurance performance improves as the altitude increases at constant speed.

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5.6.3 Range and Endurance – Constant Altitude and Constant Lift (AoA) The range and endurance performance are also analysed for constant altitude and constant lift (hence constant angle of attack) method. They are estimated as given in Equation 30 and Equation 31 respectively. [6]

2 2 CL Range   Wi  Wf  Equation 30 c pS CD 2 2 CL Endurance   Wi  Wf  Equation 31 Vc pS CD

By inspecting Equation 30, it can be deduced that the range performance will be maximum if the SFC, c is minimum, the aircraft flies at highest possible altitude (lowest possible density), the term, ratio of square root of CL to CD is maximum and Wi – Wf is maximum.

With this profile, when the flight progresses and the fuel is burned up, the airspeed decreases due to aircraft’s reducing weight. Hence, the velocity is the variable for this flight schedule and the throttle needs to be reduced as the flight progresses and required Lift reduces. This way, the aircraft will be able to fly at constant height (hence altitude) as CL will be held constant as fuel is consumed and weight reduces. The range performance in this schedule is less than for “cruise-climb” profile discussed in the following section for same CL /CD because the speed needs to be reduced progressively during the cruise. This also causes some variation in SFC, c. The total range can then be estimated by using average value of SFCs or treating the calculation as sum of steps. An approximation to “cruise climb” profile discussed in the previous section can be achieved if each of the steps are flown at an increased altitude.

It can be seen in the plots presented for both AEO and OEI conditions that the range performance improves with altitude and the optimum range speed increases with altitude. As the aircraft becomes lighter it requires reduced dynamic pressure. Since this flight schedule requires the aircraft to fly at constant altitude with constant lift (angle of attack), the speed at which the aircraft flies is the variable to satisfy the constraints. The endurance performance does not vary significantly with altitude although it follows the similar trend with range in that it slightly improves with altitude.

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5.6.4 Range and Endurance performance comparison AEO and OEI The following table summarizes the range and endurance performance comparison between AEO and OEI conditions at various altitudes. The model developed in this thesis predicts OEI range and endurance performance which are slightly superior to those with AEO at low altitudes where single engine flight is possible. It can also be observed that the speeds required to achieve optimum range and endurance performance are slower with OEI than that with AEO.

With OEI, the predicted range and endurance performance is about 2 to 5% and 11 to 15% superior respectively to AEO.

AEO OEI

) ) ) )

(ft)

(hr) (hr)

(nm) (nm)

Mach No Mach No Mach No Mach No Mach

( ( ( (

S.L 1288 5.0 0.45 0.34 1318 5.57 0.44 0.29 5,000 1395 5.01 0.51 0.36 1454 5.69 0.47 0.34 10,000 1527 5.06 0.56 0.41 1587 5.76 0.5 0.4 20,000 1894 5.34 0.67 0.51 - - - - 30,000 2372 5.88 0.74 0.61 - - - - 35,000 2562 5.99 0.78 0.69 - - - - Table 16: Range and Endurance comparison for AEO and OEI at different altitudes 5.6.5 Weight Sensitivity on Range and Endurance The Breguet range and endurance equations have been used in Chapter 4 and 5 to estimate and to compare range and endurance performance in various flight schedules as discussed in respective chapters. It assumed beginning and end of cruise as two limits in closed form Breguet range and endurance equations in an approximate manner. Generally for more accurate calculation and when closed form solutions to Breguet’s range and endurance equations cannot be obtained, numerical integration method in calculating range and endurance is normally used.

The following section investigates the sensitivity of weights in calculating range and endurance performance and compares the results of integration method and Breguet’s

73 | P a g e equations. It discusses range and endurance performance of the two methods for both AEO and OEI situations by selecting 10,000 feet as the altitude for the analysis.

Range

5 Wcruise end

W 4 cruise begin 6

2 3 7 1

Wlanding Wramp Wtake-off Wclimb

1) Engine Start and warm-up 2) Taxi 3) Take off 4) Climb (to cruising altitude) 5) Cruise 6) Descent 7) Landing, taxi, shutdown Figure 44: Typical passenger aircraft flight profile [18] A typical airplane mission profile is shown in Figure 44. In previous range and endurance performance analysis using Breguet equations, the maximum fuel capacity of the aircraft is taken as the weight of the fuel at the beginning of the cruise. It was assumed that 90% of the fuel would be used at the end of the cruise in estimating range and endurance performance with Breguet equations.

However, for more accurate estimations, operating empty weight, payload including crew weight can be taken into consideration to work out the ramp weight of the aircraft. The take-off weight of the aircraft can then be calculated by subtracting weight of the fuel required to start up the engines and perform run-ups and that required to taxi to the taking off runway. Then, the amount of fuel required for take-off and climbing to cruise altitude can be calculated to arrive at the weight of the aircraft (or fuel weight) at the beginning of the cruise. For the accurate range performance of the whole flight for the mission profile, the range the aircraft covered during the climb phase and landing phase would need to be added to the range calculated for the cruise phase. However, for the purpose of this analysis, only the flight between beginning of cruise and end of cruise will be considered.

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The weight of the aircraft at the start of the initial cruise and at the end of cruise are determined. 1, 2, 5, 10, 15 and 50 weight/time steps are then used to calculate average specific range of each step using the following Specific Range and Endurance equations. By summing range values of each step, the total range the aircraft covers during cruise is estimated. [6]

R  (S.R) W  ave Equation 32 V V S.R   Equation 33 cTreq . W F

E  (S.E)aveW Equation 34 1 1 S.E   Equation 35 cTreq . W F

Weightfuel=14410 kg AEO AEO (10% assumed (numerical integration method) (Breguet’s method) reserve) Weight Steps Average Max Average Max Max Max Max SR Range Range Speed Range Range (nm/kg) (nm) (Mach No) (nm) Speed (Mach No) 1 0.1176 1525 0.56 2 0.1177 1527 0.56 5 0.1177 1527.3 0.56 1527 0.56 10 0.1177 1527.4 0.55 15 0.1177 1527.4 0.55 50 0.1177 1527.4 0.56 Table 17: Weight sensitivity on Range with AEO at 10,000 ft

Weightfuel=14410 AEO AEO kg (numerical integration method) (Breguet’s method) (10% assumed reserve) Weight Steps Average Max Average Max Max Max SE Endurance Max Endurance Endurance (hr/kg) (hr) Endurance (hr) Speed Speed (Mach No) (Mach No) 1 0.0003898 5.05 0.4 2 0.0003911 5.07 0.4 5 0.0003915 5.08 0.4 5.06 0.41 10 0.0003916 5.08 0.4 15 0.0003916 5.08 0.4 50 0.0003916 5.08 0.4 Table 18: Weight sensitivity on Endurance with AEO at 10,000 ft 75 | P a g e

It can be observed from that a higher number of weight segments does not have significant bearing on difference between integration method and Breguet equations. It is sufficient to assume 5 weight steps with numerical integration method if extreme accuracy is desired. The details of specific range and endurance plots using weight segments for AEO condition can be referred to in Figure 45, Figure 46, Figure 47 and Figure 48.

Figure 45: Plot of specific range vs. speed at 10,000 ft using 5 weight steps (AEO)

Figure 46: Plot of specific endurance vs. speed at 10,000 ft using 5 weight steps (AEO)

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Figure 47: Specific range vs. weights at 10,000 ft (at Max Range Mach No) (AEO)

Figure 48: Specific endurance vs. weights at 10,000 ft (at Max Range Mach No) (AEO) The speeds at which maximum range occurs at the altitudes are comparable to one another with weight steps method registering around 0.51 Mach while Breguet’s method a 0.53 Mach for OEI condition. The optimum range performance calculated using Breguet’s equation is 1587 nm whereas that of using weight steps method outputs a figure in the region of 1610 nm. The specific endurance performance is also comparable with both numerical method and Breguet’s methods yielding figures close to each other.

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Refer to Table 20. Plots of specific range and endurance using 5 weight steps for OEI condition are depicted in Figure 49, Figure 50, Figure 51 and Figure 52.

Weightfuel=14410 kg OEI OEI (10% assumed (numerical integration method) (Breguet’s method) reserve) Weight Steps Average Max Average Max Max Max Max SR Range Range Speed Range Range (nm/kg) (nm) (Mach No) (nm) Speed (Mach No) 1 0.124 1608 0.51 2 0.124 1608 0.51 5 0.1246 1616.2 0.51 1587 0.53 10 0.1246 1616.2 0.51 15 0.1246 1616.2 0.51 50 0.1246 1616.2 0.51 Table 19: Weight sensitivity on Range with OEI at 10,000 ft

Weightfuel=14410 OEI OEI kg (numerical integration method) (Breguet’s method) (10% assumed reserve) Weight Steps Average Max Average Max Max Max SE Endurance Max Endurance Endurance (hr/kg) (hr) Endurance Speed Speed (Mach No) 1 0.0004523 5.87 0.38 2 0.0004534 5.88 0.375 5 0.0004537 5.88 0.38 5.76 0.4 10 0.0004538 5.88 0.378 15 0.0004538 5.88 0.377 50 0.0004538 5.88 0.38 Table 20: Weight sensitivity on Endurance with OEI at 10,000 ft

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Figure 49: Plot of specific range vs. speed at 10,000 ft using 5 weight steps (OEI)

Figure 50: Plot of specific endurance vs. speed at 10,000 ft using 5 weight steps (OEI)

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Figure 51: Specific range vs. weights at 10,000 ft (at Max Range Mach No) (OEI)

Figure 52: Specific endurance vs. weights at 10,000 ft (at Max Range Mach No) (OEI) 5.7 Validation of Results In analyzing the aircraft performance parameters mentioned throughout this thesis, a number of assumptions as stated throughout thesis were made in accordance with recommended techniques presented in the references used. However, the methods presented in the references may be considered to be widely recognized from a conceptual design and analysis point of view. As such, an alternative way of estimating

80 | P a g e the performance parameters, in particular range and endurance performance of the aircraft, is sought to validate the results estimated in preceding section.

A performance planning manual used by airlines for -300 variant of the Boeing 737 [47] is consulted to validate the Range and Endurance results. The manual contains in flight data for use as general reference in airplane performance monitoring, flight planning studies and as a supplement to information provided in the operations manual. The power plants used for the aircraft according to the manual are CFM56-3 series with a sea level thrust rating of 98.1 kN. Relevant data and information utilized to validate the results of the thesis are included in Appendix E.

This section of the thesis looks at the range and endurance performance data of the Boeing 737-300 flight planning and performance manual to validate the performance obtained in the previous sections. The data provided in the Long Range Cruise Tables in the manual is used to estimate the fuel flow per engine of the aircraft based on weight, speed and altitude. It also indicates %N1 parameter to set to with a provision for adjustment for deviation from standard atmospheric conditions.

5.7.1 Range Validation Specific range is calculated based on fuel flow and speed data provided at each altitude. A fuel load of 12,969 kg which is 90% of the maximum capacity of 14,410 kg assumed throughout the thesis with the aircraft’s gross weight being 62,820 kg. For comparison purpose in this section, it is assumed that the aircraft’s maximum gross mass is 60,000 kg with a fuel mass of 11,111 kg 10% of which is assumed reserve. This is to align the data given in the manual with approach used by the model. The average of the fuel flow and speed data of the manual for the weight specified above is used. Specific range performance at each altitude is calculated based on the flight planning manual for the reference aircraft which is denoted as manual’s data in the tables below. The results are then compared with those predicted by the thesis model for the new weight configurations as can be seen tabulated in Table 21 and Table 22.

5.7.2 Endurance Validation For validation of endurance results, Long Range Cruise En-route Fuel and Time graphs provided in the performance planning manual are utilized. Nil wind and standard ISA conditions are assumed in extracting endurance performance from the given graphs.

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Range values deduced from the Long Range Cruise Table are used to arrive at endurance values (with fuel required data to cross check). Refer to Figure 53 for sample estimation from the graph given in the flight planning manual. Hence, the endurance values are for the altitude and airspeed at which Range was estimated. Refer to Appendix E for details of the long range cruise en-route data.

Figure 53: AEO Endurance estimation from Long Range Cruise En-route Fuel and Time [47] 5.7.3 AEO Range and Endurance Validation Discussion It is observed that the difference between SR calculated from the flight planning manual and that predicted by the model is not significant with percentage errors falling within 11% for range performance at the same airspeeds. The thesis model seems to predict more optimistic figures registering a range figure which is 10% more than that of the manual at 35,000ft. Refer to Figure 55.

The specific endurance performance comparison also yields similar results in higher altitudes (<10%) but the difference is significant (20%) in lower altitudes (20,000 ft and

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10,000ft). This can be attributed to the fact that the Long Range Cruise En-route Fuel and Time data given in the manual also takes into account the descent phase which explains why specific endurance (time and fuel directly) read off the curves are higher than those of the thesis model. Refer to Table 21.

AEO (Manual data) AEO (Thesis) Altitude Speed S.E S.R S.E FF/Eng (kg/hr) S.R (nm/kg) (ft) (Mach No) (hr/kg) (nm/kg) (hr/kg) 35000 1197 0.75 0.179 0.00043 0.199 0.000427 30000 1261 0.745 0.174 0.00042 0.184 0.000382 20000 1379 0.66 0.148 0.00041 0.147 0.000327 10000 1491 0.56 0.121 0.00038 0.1211 0.000299 Table 21: Range and Endurance comparison (Flight planning manual data vs Thesis) (AEO)

AEO Range Comparison

Manual Specific Range (nm/kg) Thesis Specific Range (nm/kg) %error 0.25 12

10 0.2 8 0.15 6 4

0.1 2 error % 0 0.05

Specific Range (nm/kg) Range Specific -2 0 -4 5000 10000 15000 20000 25000 30000 35000 40000 Altitude (feet)

Figure 54: AEO Range Comparison Plot

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Figure 55: AEO Specific Range Vs Speed Plot

Figure 56: AEO Specific Endurance Vs Speed Plot 5.7.4 OEI Range and Endurance Validation Discussion According to the flight planning manual, the long range cruise altitude capability with OEI data indicates a pressure altitude of 12300 ft as its maximum at 60,000 kg. This is given as maximum continuous thrust with 100 ft/min residual rate of climb with atmosphere condition of ISA + 10C and below. Plots of thrust available and drag with OEI presented in the previous sections also suggest a similar limitation with OEI with thrust available curve not intersecting the drag curve any more as altitude goes higher than 12,000 ft. 84 | P a g e

The range performance comparison with OEI was also carried out and observed to be within 10% error. However, it can be noted that the thesis model predicts a more pessimistic figures as compared to the AEO comparison. Figure 57

Similar trend to that discussed in AEO validation section exists for OEI endurance performance comparison. Table 22 summarizes the range and endurance performance comparison for OEI condition. Figure 58 and Figure 59 can be referred to for plots of specific range and specific endurance with OEI at altitudes the remaining operative engine is capable of powering the aircraft. It can be observed the OEI endurance performance error when compared with the manual data ranges from 1 to 21%. The lower the altitude, the greater the discrepancy becomes.

OEI Range Comparison

Manual Specific Range (nm/kg) Thesis Specific Range (nm/kg) %error 0.16 0

0.14 -1

-2 0.12 -3

0.1 -4 0.08 -5

0.06 -6 %error -7 0.04

Specific Range (nm/kg) Range Specific -8 0.02 -9 0 -10 5000 6000 7000 8000 9000 10000 11000 12000 13000 Altitude (feet)

Figure 57: OEI Range Comparison Plot

OEI(Manual data) OEI (Thesis) Altitude FF/Eng Speed S.R Endurance S.R S.E (ft) (kg/hr) (Mach No) (nm/kg) (hr) (nm/kg) (hr/kg) 12000 2511 0.54 0.137 0.00045 0.128 0.00037 11000 2516 0.53 0.134 0.00045 0.125 0.00036 10000 2521 0.52 0.132 0.00045 0.123 0.00036 8000 2531 0.5 0.128 0.00044 0.12 0.00035 6000 2543 0.49 0.124 0.00045 0.113 0.00033 Table 22: Range and Endurance comparison (Flight planning manual data vs Thesis) (OEI)

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Figure 58: OEI Specific Range Vs Speed Plot

Figure 59: OEI Specific Endurance Vs Speed Plot

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While thrust available limits the aircraft to fly at its normal crusing altitude with OEI, it can be observed that the flight planning manual also suggests a slightly improved range and endurance performance at altitudes closer to maximum capable with OEI.

5.8 Summary In this chapter issues concerning lateral stability and control when the aircraft is in OEI condition have been presented. It has covered on thrust asymmetry, minimum control speed, trim drag associated with OEI condition. Range and endurance performance are again estimated for constant altitude – constant speed flight profile for comparison with AEO condition from the previous chapter. It also discussed range and endurance options for constant speed – constant angle of attack and constant altitude – constant angle of attack flight profiles. An analysis of weight sensitivity in determining range and endurance performance by comparing numerical integration method and Breguet’s approach has been also covered in this section. It concludes with validation of results obtained in the thesis with data available for flight planning and performance manual of a Boeing 737-300 used by airlines. The next chapter builds upon the chapters presented thus far to briefly study into OEI turning performance of the Boeing 737-300 aircraft.

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6. CHAPTER 6: LATERAL CONTROL AND MANEOUVERABILITY WITH ONE ENGINE INOPERATIVE 6.1 Introduction This chapter discusses issues of turning performance with One Engine Inoperative (OEI) of the Boeing 737-300. Asymmetric thrust brought about by the inoperative engine in a multi-engine aircraft causes the aircraft to fly out of balance. The resulting unbalanced state of the aircraft must be countered by use of control surfaces which affects stability and control of the aircraft. This part of the thesis looks at yawing moment to balance with thrust available from remaining operative engine and available lateral control deflections during a turning flight. It looks at the turning performance for right engine inoperative condition with left turning in comparison with right turning flight. It also discusses minimum control speed as the aircraft is allowed to slow down to maintain later flight equilibrium and corresponding control surface deflections required during turning flights.

6.2 Objectives This chapter aims to provide a basic performance analysis on turning flights with OEI as shutting down one engine on purpose for better range and endurance performance is generally applicable for loiter or surveillance mission situations. In those situations, the aircraft is required to fly a certain mission profile with a series of turns in both directions at a prescribed altitude. The objectives of this chapter of the thesis are:  Analyse aerodynamics and limitations associated with lateral control and manoeuvrability  Analyse turning performance with (OEI) (right engine inoperative)  Look at issues of asymmetric thrust and it’s mechanisms  Compare turning performance for left turn with right turn in right engine inoperative scenario  Determine preferable turning manoeuvre with OEI at different altitudes and speeds with different gross weights

6.3 Lateral Control and Maneuverability To maneuver the aircraft outside of the longitudinal plane, the ailerons and rudder are typically used in combination with the elevator to control both the magnitude and direction of the lift. The performance of the aircraft in a steady and level coordinated

88 | P a g e turn is one in which controls are coordinated so that vector sum of the aircraft acceleration and the acceleration of gravity produces a force that falls in the aircraft’s plane of symmetry. The steady and coordinated means that it is achieved while maintaining airspeed with angular velocity held constant. To accomplish this, the aircraft is required to undergo a banking maneuver towards the direction of the desired turn usually by aileron control inputs.

For the aircraft to turn right, right aileron inputs are applied. This causes the right aileron to go up while the left aileron goes down pushing the right wing down. This causes the aircraft to tip to the right and start to turn. With the aircraft in bank, the lift of the wings is tilted in the direction of the roll, breaking it into two components: a vertical component which is acting opposite to the weight through the aircraft centre of gravity and side force which is unopposed and in the direction of the bank and perpendicular to the flight path. The unopposed side force of the aircraft is constant while the aircraft is in bank, resulting in a circular arc motion.

When the aircraft is brought back to wings level attitude by opposite aileron inputs, the side force is eliminated and the aircraft flies in a steady straight line. Elevator inputs are usually accompanied with aileron inputs while the aircraft is turning to compensate for the loss in the vertical component of the lift by means of increasing the angle of attack of the wings because some of the lift is diverted to cause the plane to turn. [2]

The magnitude of the banking angle and speed determine turning radius. Hence, the aircraft is turned by the component of the lift force brought about by banking and rudder is not primarily used for turning. However, there is a phenomenon called adverse yaw which is the side effect of aileron induced turns, the details of which have been discussed in previous chapters. Thus, rudder is used during the turn to coordinate the turn to maintain the nose of the aircraft pointed along the flight path. Otherwise, the adverse yaw which causes the aircraft to yaw away from the direction of the turn due to difference in drag between the two wings while the aircraft is in turn is encountered. [18]

6.4 Turning Performance The performance of the Boeing 737-300 aircraft in a steady coordinated level turn for both AEO and OEI situations are analyzed. The turning performance of an aircraft is 89 | P a g e limited by aerodynamic properties and structural limitations such as stall, positive or negative design load factor, and thrust.

The equations of flight equilibrium are studied, and load factor and associated bank angles during level turn are determined. Two performance characteristics of greatest importance in turning flights: Turn radius and rate of turn for the aircraft are analyzed for different altitudes.

6.4.1 Flight equilibrium during turning flight The forces and geometry of the aircraft in level coordinated turn are depicted in Figure 60. The force equilibrium for the level turning flight can generally be expressed as given in, Equation 37 and Equation 38 respectively. [1]

Fx  T  D  0 Equation 36

Fy  W sin  Z cos  0 Equation 37

Fz W cos  L  0 Equation 38

L -Zcos φ

Zsin φ

r = v/ω

Z=mvω Wcos φ φ φ

ω Wsin φ z

W

y

Figure 60: Force components and geometry in level coordinated turning flight [1] 6.4.2 Load factor and bank angle When the aircraft is in a level turn, it is banked through a roll angle, and the necessary condition for a level turn is Lcosϕ = W so that the altitude will remain constant. In another words, the resultant force must be equal to vector sum of Lift and Weight components. The load factor encountered by the aircraft in flight is given by Equation 39. [42]

q  T qC  n  (T/W) x (L/D)    Do  K(W / S) W (W / S)    Equation 39

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In a turning flight with bank angle, , the load factor, n, is found from the following relationship.[42]

  cos 1 (1/ n) Equation 40

The lift coefficient of the aircraft required in maintaining a level flight for a given altitude and speed is calculated as given below.

2(W/S) C  Equation 41 L V 2

However, the value of CL cannot be too large or small as the maximum load factor which the aircraft is designed for should not exceed in any turning manevouer of the aircraft. Hence, the following conditions are set up in determining the lift coefficient of the Boeing 737 for turning performance.

 If CLmax / CL > nmax , CLT = nmax

 If CLmax / CL < nmax , CLT =

The maximum load factor for the Boeing 737-300 aircraft for this turning performance analysis is taken to be 3.5 while CLmax value is 1.4. CLT refers to the lift coefficient in turning flight. [6] The first condition can be referred to as CLmax limited turn performance while the second condition is the design load factor limited turn performance.

The CLT value is then used to estimate drag coefficient of the aircraft in turning flight,

CDT based on the drag polar estimated in Chapter 4. For the OEI flight schedule, the

CDT value takes into account the trim drag resulted from the control surfaces deflection required to fly the aircraft at level altitude with zero side slip as discussed in Chapter 5. The total drag required for level flight in turning flight is then

1 D  V 2 SC Equation 42 T 2 DT

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When the aircraft is flying with OEI, the thrust available is halved and certain flight conditions will require greater thrust to overcome the larger drag. This is the case for the flight at higher altitudes of 12,000 ft and more with OEI as can be observed in chapter (5). Hence, another condition is set up to allow for this limitation.

If DT > TAOEI ,

TAOEI CDT  qS Equation 43

CDT  CD0 CLT  K Equation 44

Applying the equations and the conditions set up, the load factor the aircraft is subject to during the turn is plotted for different flight speeds at different altitudes Figure 61.

It can be seen that the load factor increases linearly as the speed goes up at lower end of the speed regime. This part is due to the max lift coefficient limited turning performance at lower speeds and this analysis assumes the maximum lift coefficient value for this condition. The aircraft is not allowed to fly slower than the speed corresponding to this lift coefficient as it will stall.

It can be observed that the higher the altitude, the airspeed required to fly to achieve the same load factor increases. As the aircraft flies at higher altitude, the sustained load factor is reduced. This is because the density decreases as altitude goes higher.

The maximum load factor occurs at the peak of the curves as shown. The curves follow a pattern which increase at first, then reaches a local maximum (denoted by ‘B’) and then decreases with airspeed as can be seen in the figure. Left of the maximum point is the region where induced drag dominates which decreases with airspeed. Right of the point is where parasitic drag dominates which increases with airspeed.

At the maximum load factor point, the aircraft is flying at its maximum Lift to Drag ratio. As velocity decreases, lift coefficient has to increase. However, that cannot

92 | P a g e happen indefinitely as it is limited by stall/ maximum lift coefficient. The velocity at that maximum lift coefficient is denoted by point ‘A’. Below that speed, point ‘A’, the maximum load factor is constrained by maximum lift coefficient.

As the aircraft’s bank angle is increased, the magnitude of the lift must increase. As lift increases, the drag due to lift increases. Hence, to maintain a sustained level turn at a given airspeed and bank angle, the thrust must be increased from its straight & level flight value to compensate for the increase in drag. If this increase in thrust pushes the required thrust beyond the maximum thrust available from the engine, then the level turn cannot be sustained at the given bank angle and it will have to be decreased in order to decrease the drag.[1]

Figure 61: Load factor variation with respect to speed at different altitudes (AEO) (MTOW) 6.4.3 Radius of turn The turn performance of the aircraft is dependent on the load factor, n as can be seen in the following equation of motion for a level turn.   cos 1 (1/ n) . The smallest possible radius is always desired in turning flights and it can be obtained when the load factor is the highest and airspeed is the lowest. [42] V 2 r  g tan Equation 45

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6.4.4 Minimum Turn Radius The turn radius for the Boeing 737-300 aircraft are analysed for different flight speeds at different altitude at maximum gross weight with all engine operative as can be seen in Figure 63. The minimum turn radius for the aircraft is calculated using Equation 46. [42]

4K(W/S) R min  (T/W)g 1- 4KC /(T /W )2 D0 Equation 46

The load factor corresponding to the minimum turn radius is calculated from the following equation.

4KC D0 n Rmin  2 - (T ) 2 W Equation 47

Figure 62: Turn Radius with respect to speed at different Altitudes (AEO) (MTOW) The velocity at which the minimum turn radius is achieved is estimated from the following equation. [42]

4K(W/S) VRmin  (T /W ) Equation 48

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Figure 63: Turn radius with respect to speed at different altitudes (AEO) (MTOW) (Zoomed)

It can be seen from Figure 63 that as the altitude increases, the turn performance curves shift upwards. The minimum turn radius occurs at lower speed regimes. As the altitude gets higher, the minimum turn radius increases. This is due to the need for higher airspeed to maintain lift at less denser higher altitudes.

It can also be observed from the turn radius curves that there is a region at the low end of the speed where the turn is restricted by the max lift coefficient and hence stall speed. One of the design features of the aircraft is it will stall before the maximum design load factor can be exceeded. For a given true airspeed, the Mach number will increase with increasing altitude (because the speed of sound decreases with increasing altitude).

Compressibility increases lift curve slope close to critical Mach no and CLmax is reduced. The net result is a further increase in the stall speed with increasing altitude mostly due to change in density. However there is a speed at which minimum turn radius is achieved as can be observed in Figure 63.

The maximum allowable drag is limited by thrust available and this region can be seen as the part of the curves towards the high speed range. With speed held constant at higher speed range, the higher the bank angle, the smaller the radius of turn will be. However, this is restricted by maximum design load factor and stall speed of the aircraft. When the aircraft is at a bank angle, the stalling speed is increased above that of straight and level flight with load factor 1. Hence, the stalling speed increases 95 | P a g e proportionally to square root of n when the aircraft is in a level coordinated turn with a load factor greater than 1.

6.4.5 Sustained Rate of turn The sustained turn rate (rad/s) of the aircraft is calculated as given in Equation 49 and the plot of the turn rate corresponding to the turn radius at different altitudes for a range of speeds is presented as shown in Figure 64. [42]

g n 2 1   V Equation 49

Figure 64: Sustained turn rate Vs speed at different altitudes (AEO) (MTOW)

Table 23 summarizes predicted turning flight performance of the Boeing 737-300 aircraft at sea level with all engine operative.The plots of load factor, turn radius and rate of turn vs. speed at different altitudes when the aircraft is at its assumed maximum take-off weight with OEI are also included as shown in Figure 65, Figure 66 and Figure 67.

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Max Speed Lift Rate of Rate of Load Bank Radius of (Mach Coefficient Turn Turn Factor Angle Turn (m) No) (during turn) (rad/s) (deg/s) (deg) 0.3 1.2 1.21 34 1505 0.06 3.4 0.4 1.8 0.67 56 1192 0.11 6.3 0.6 2.0 0.3 60 2196 0.09 5.2 0.7 1.97 0.22 59 3265 0.07 4.0 0.75 1.78 0.19 56 4048 0.06 3.4 Table 23: Summary of turning performance of B737-300 at 10,000 feet with AEO

Figure 65: Load Factor vs speed at different altitudes (OEI) (MTOW)

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Figure 66: Sustained turn radius vs speed at different altitudes (OEI) (MTOW)

Figure 67: Sustained turn rate vs speed at different altitudes (OEI) (MTOW) 6.5 Lateral flight equilibrium with OEI The moment caused by thrust asymmetry in OEI is opposed by a rudder input which creates a counter moment. This rudder force is opposed by the side force generate by a side slip angle the aircraft is at. The yawing moment of the inoperative engine known as wind milling drag is a function of basic engine parameters, temperature and pressure altitude. The forces and moments in lateral flight equilibrium are a function of air speed and bank angle.

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Out of the lateral set of flight equilibrium equations, yawing moment equation and sideforce equations, Equation 10, Equation 11 and Equation 12 presented in section 4.7 are the primary balancing equations for directional control with OEI. The rolling moment equation is relatively less critical but it can limit the lateral controllability of the aircraft with its roll control power.

The equilibrium of the aircraft with right engine inoperative is analysed with assumption that desired sideslip angle is zero and roll control power is at its maximum. The bank angle is varied in both directions, towards the working engine (left bank with right engine inoperative) as well as the inoperative engine (right bank with right engine inoperative). Then, the yawing moment to balance the flight equilibrium in both circumstances are investigated and compared. These yawing moments are the moments required to balance with a rudder control deflection to create a counter yawing moment to keep the later flight equilibrium Hence, it is limited by the rudder control power of the aircraft, and the minimum control speed the aircraft is allowed to slow down to in this condition determines the turn performance of the aircraft. The optimum turn performance is achieved when the velocity is the minimum with the highest bank angle as possible.

6.5.1 Yawing moment with One Engine Inoperative For a given set of asymmetric thrust conditions, the minimum control speed is the speed below which aerodynamic controls are insufficient to maintain equilibrium. At each altitude, there is a maximum value of aerodynamic yawing moment coefficient which can balance the net yawing moment caused by roll, bank angle, asymmetric thrust and side slip angle.

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Figure 68: Thrust moment, and yawing moment the aircraft is subject to at different speeds at different altitudes (negative bank angle of 5 deg, zero sideslip, max aileron)

Figure 68 shows the moment due to thrust moment from operative engine on left hand combined with the wind milling drag of the inoperative engine at different altitudes at maximum gross weight. It also illustrates the yawing moment and rolling moment developed which are to be balanced with aileron and rudder control inputs at different speed range with right engine inoperative.

Similarly, the net yawing moment the aircraft is subject to with right engine inoperative when banked towards the inoperative engine is plotted as can be seen in Figure 69.

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Figure 69: Thrust moment, yawing moment and rolling moment the aircraft is subject to at different speeds at different altitudes (positive bank angle 5 deg, zero side slip, max aileron) 6.5.2 Effect of bank angle The effect of bank angle on yawing moment developed at different altitudes at maximum gross weight is also analysed for OEI condition. Assuming a right engine inoperative condition, and that maximum available aileron is held, the net yawing moment developed by the aircraft which is to be balanced with the rudder deflection to achieve zero side slip are plotted as a function of bank angle for different altitudes. Figure 70 shows the yawing moment to balance in a left bank situation with right engine inoperative condition. The same analysis is also done for the right engine inoperative condition with right bank as shown in Figure 71.

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Figure 70: Bank angle effect on yawing moment developed at different altitudes with OEI (Right Engine Inoperative with Left bank turn at max gross weight)

It can be noted from the plot that as the bank angle increases banked lift coefficient increases and net yawing moment to balance decreases. This corresponds to a decrease in minimum control speed as the yawing moment available at the maximum rudder deflection can be achieved at a lower speed.

Figure 71: Bank angle effect on yawing moment developed at different altitudes with OEI (Right Engine Inoperative with right bank at max gross weight)

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For the yawing moment developed with OEI, there is a counter yawing moment available from the rudder deflection to balance that at a given altitude, weight and bank angle. The amount of deflection required depends on minimum speed the aircraft is allowed to slow down to at a bank angle without stalling the aircraft or exceeding the design load factor.

It can also be observed that the net yawing moment developed for left bank and right bank cases with OEI are not the same. At 10000 feet, when the aircraft is banked 10 degrees towards the operative engine (left), the yawing moment to balance with the rudder is 0.0004 in coefficient form. Refer to Figure 70. The sign negative means that the counter yawing moment required is towards the direction of operative engine (left) and a positive rudder deflection is required.

In comparison, that of the right bank condition at the same flight condition is a greater magnitude of 0.002539. It indicates that a greater rudder deflection may be required assuming zero side slip is the desired condition with ailerons held at its maximum limit.

6.5.3 Minimum control speed when banked with OEI The minimum control speeds the aircraft is allowed to slow down to with OEI during a banking turn at different altitudes are investigated in this section. The cases with bank angle of 30 and 60 degree for both left and right directions are analysed for minimum allowable control speed in comparison to stalling speed.

Figure 72 to Figure 79 present the minimum control speed based on aileron limited condition and rudder limited condition for left banking as well as right banking flight conditions with right engine inoperative. It is plotted for different altitudes as function of true air speed. The maximum limit for rudder and aileron deflections is 15 and 25 degree respectively. “Maximum rudder” on the graph denotes the flight regime with variable aileron control (+25 to -25) with fixed maximum rudder (+15 or -15) and “maximum aileron” denotes that with variable rudder control while the aileron is fixed at its maximum limit of (+25 or – 25).

The following observations can be drawn from the plots:  Stalling speed increases with bank angle.  Stalling speed increases as the altitude goes higher 103 | P a g e

 The higher the weight, the greater the stalling speed is.  Minimum control speed goes up as weight increases during the banked manoeuvre. This could be because the higher the aircraft weight, the greater the side slip angles the aircraft can develop, thus resulting in the need for higher minimum control speeds. This may be limited by the amount of aileron and rudder deflections.  Rudder limited minimum control speeds (i.e. rudder is fixed at its maximum) are smaller than aileron limited minimum control speeds (i.e. aileron is fixed at its maximum), and closer to stall than rudder limited minimum control speeds. However, from practical allowable control surface deflections, operating ailerons while rudder is fixed at maximum is not enough to maintain equilibrium at high bank angle maneuveurs. Hence, in determining minimum control speeds for OEI (right engine out in this case), it makes more sense to stick with max aileron solutions. As can be seen in Figure 72 to Figure 79 following the control surface deflections of rudder with max aileron are within physical allowable limits. (+-15 deg)  Aileron limited minimum control speeds get smaller as the bank angle is decreased. (compare Vmca at 60 degree Vs 30 degree).

Minimum control speeds for left banking maneuveurs are compared to be smaller than those for right banking. Neglecting the stalling speed and minimum available speed which could possibly limit the minimum speed the aircraft is allowed to slow down to, the need for slower speeds for left banking maneuveurs with right engine inoperative is a prerequisite for superior turn performance. Another factor that influences the turn performance is the bank angle, and it will be limited by the minimum lift coefficient available at the corresponding minimum control speeds at a given altitude.

It is also important to note that for any flight condition, the flight needs to take place between speed range limited by stalling/minimum/minimum control speed and maximum available speed dictated by thrust available from the remaining operative engine. As discussed in Chapter 5, with one engine inoperative, flights above the altitude of 12,000 ft and above cannot take place due to the lesser thrust available at higher altitudes. Table 24) lists minimum control speeds and stalling speeds with corresponding control deflections for different banked manvouers at different altitudes.

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Altitude Vmca Vmca Rudder Aileron (max (max deflection (max deflection rudder) aileron) aileron) (max rudder) Bank angle = -30 (towards operative engine) SL 0.27 0.61 -2.5 within +-15 deg > +-25 deg 5000 0.31 0.71 -2.7 within +-15 deg > +-25 deg 10000 0.38 > Mcruise -2.85 within +-15 deg > +-25 deg Bank angle = -60 (towards operative engine) SL 0.41 > Mcruise -3.3 within +-15 deg > +-25 deg 5000 0.47 > Mcruise -3.4 within +-15 deg > +-25 deg 10000 0.55 > Mcruise -3.5 within +-15 deg > +-25 deg Bank angle = 30 SL 0.43 0.7 -5.8 within +-15 deg > +-25 deg 5000 0.49 0.8 -5.35 within +-15 deg > +-25 deg 10000 0.56 > Mcruise -5.25 within +-15 deg > +-25 deg Bank angle = 60 SL 0.54 > Mcruise -4.98 within +-15 deg > +-25 deg 5000 0.6 > Mcruise -4.9 within +-15 deg > +-25 deg 10000 0.7 > Mcruise -4.83 within +-15 deg > +-25 deg Table 24: Summary of Stall and minimum control speed with corresponding control surface deflections at various flight conditions

Figure 72: Minimum control speeds and corresponding control surface deflections (-30 deg bank)

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Figure 73: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (-30 deg bank)

Figure 74: Minimum control speeds and corresponding control surface deflections (-60 deg bank) 106 | P a g e

Figure 75: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (-60 deg bank)

Figure 76: Minimum control speeds and corresponding control surface deflections (30 deg bank) 107 | P a g e

Figure 77: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (30 deg bank)

Figure 78: Minimum control speeds and corresponding control surface deflections (60 deg bank) 108 | P a g e

Figure 79: Rudder deflections with maximum aileron at different altitudes for 3 different gross weights (60 deg bank) 6.6 Level coordinated turn with One Engine Inoperative The preceding sections discussed in this chapter were more of an analysis on flight equilibrium in lateral motion. The aerodynamic forces and moments the aircraft is subject to with OEI and respective counter control required to maintain the flight equilibrium with different bank angles for banking maneuveurs were studied in those sections. However, the scenarios discussed were of trim conditions and it did not address performance of control surfaces which are required to maintain level coordinated turn with a bank angle with OEI The following section of the chapter looks at the performance of both longitudinal and lateral controls required to achieve a sustained level coordinated turn at a certain bank angle at different altitudes.

6.6.1 Change in control surfaces required for sustained level coordinated turn Assuming a right engine inoperative condition at sea level and the aircraft is travelling at Mach 0.2, control surfaces are trimmed for steady level flight, ignoring any possibility of stall, the change in aileron, elevator, and rudder deflection angles required to maintain level coordinated turn at the same airspeed and altitude as a function of bank angle is analysed.

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The aerodynamic angles and control surface deflections for steady level coordinated turn is expressed as given in Equation 50. [48]

                      a    a    a  Equation 50        e   e   e         r   r trim  r 

In the above equation, the trim condition is for the steady level flight with right engine inoperative. It is evaluated for sea level and at the same airspeed of Mach 0.2. The flight equilibrium equations recalled from Chapter 5 and then including roll, pitch and yaw rate terms, can be rearranged in matrix form as given in Equation below. [48]

C 0 0 C 0 C cos / cos  C  R C cos sin tan  L Le    w L0 gx Lq       0 C C 0 C  R (C sin tan  C cos sin)  y y a y r  gy yp yr      0 Cl Cl 0 Cl  a    Rgy (Clp sin tan  Clr cos sin)   a r  C C 0 C 0     C  R C cos sin tan   m m me  e   m0 gx mq  C C C 0 C     C  R (C sin tan  C cos sin)   n n n a n r  r trim  nT gy np nr  Equation 51 2 Where Rgx  gcw / 2V 2 Rgy  gbw / 2V

Assuming no bank angle (as opposed to adopting 5 degrees towards operating engine for lesser rudder deflection and improved minimum control speed in most of the civil aviation regulations for One Engine Inoperative operations) with flight path angle set to zero, the trim condition must satisfy the simplified Equation 52. [48]

C 0 0 C 0 C  C  L Le    w L0       0 C C 0 C  0  y y a y r       0 Cl Cl 0 Cl  a    0  Equation 52  a r  C C 0 C 0     C   m m me  e   m0  C C C 0 C     C   n n n a n r  r trim  nT 

The change in aileron, elevator and rudder deflection angles required to maintain the level coordinated turn at the airspeed and at the altitude can be determine using the following equation. [48]

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C 0 0 C 0 C [(cos / cos) 1]  R C cos sin tan  L Le    w gx Lq       0 C C 0 C  R (C sin tan  C cos sin)  y y a y r  gy yp yr      0 Cl Cl 0 Cl  a    Rgy (Clp sin tan  Clr cos sin)   a r  C C 0 C 0     R C cos sin tan   m m me  e   gx mq  C C C 0 C     C  R (C sin tan  C cos sin)   n n n a n r  r   nT gy np nr 

Equation 53

Assuming all control surfaces are trimmed for steady level flight at a constant speed and at an altitude, ignoring any possibility of stall, the change in aileron, elevator and rudder deflection angles required to maintain the level coordinated turn at the same airspeed and altitude can be plotted as function of bank angle for AEO and OEI conditions as shown in Figure 80 and Figure 81 respectively. Table 25 tabulates the trim control deflections and change in control surface deflections required for a 20 deg bank both directions.

Figure 80: Change in control surface deflections required for a level coordinated turn with AEO

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Figure 81: Change in control surface deflections required for a level coordinated turn with OEI

Del Del Trim (20 deg bank) (-20 deg bank) AoA 0.5 0.2 0.2 Sideslip 2.2 2.5 2.75 Aileron 7.4 8.2 9.5 Elevator 2.1 -0.2 -0.2 Rudder 4.4 5.2 5.5 Table 25: Trim control deflections and change in control surface deflections required for 20 degree bank

6.6.2 Observations It can be noted that the magnitude of rudder deflection is not the same for right and left turns in both AEO and OEI cases. Refer to Figure 80 and Figure 81. With all engine operating, there seems to be approximately equal amount of change in rudder deflection required for left and right turns. Given this analysis is being done for a jet transport type aircraft of Boeing 737-300 class, this symmetry in rudder deflection may be considered appropriate. However, this may not be the case with propeller aircraft as there will be an added yawing moment due to right hand rotating propeller in conventional propeller aircraft. In those situations, the change in rudder deflection will be higher for right turns.

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With right OEI, it can be observed that change in rudder deflection to sustain a coordinated turn for right turn is higher than that for left turn. This is due to the thrust asymmetry and wind milling drag of the inoperative right engine. This change in rudder deflection also includes the counter moment to balance the adverse yaw effect which is the tendency of the aircraft to yaw towards the opposite direction of the turn due to the yawing moment produced.

Positive rudder deflection (yaw towards left) required to keep the turn coordinated gradually decreases as the bank angle decreases towards the wing level and transitions into negative deflection (yaw towards right) as the aircraft rolls onto positive bank angles. The rudder deflections are observed to be quite small for both banking directions in this AEO flight condition. However, for OEI (right engine inoperative) case, the rudder deflections required are slightly greater in the region of 5 to 6 degrees for both banking directions. The aircraft needs to be already flying with a positive rudder deflection to counter the asymmetric yaw developed due to the inoperative right engine and to keep the aircraft trimmed. And the change in deflections is required to sustain the level coordinated flight during the turns at Mach 0.2 at sea level.

As the aircraft is banked to execute the turn either to the right or left, elevator deflection is increased as can be seen in Figure 80 and Figure 81 to increase the angle of attack to produce more lift. Negative sign for elevator deflection indicates the elevator up movement for pitch up movement. Since the aircraft is already flying with one engine inoperative condition (Right Engine Inoperative), there is already a rudder deflection for trim condition to maintain lateral equilibrium and added deflection is required to keep the turn coordinated during a level coordinated turn. Table 25

It can be noted that right aileron deflection (positive) is required for left turn and left aileron (negative) for right turn as can be seen in the AEO case shown in Figure 80, which seems illogical. However, this can be explained by the fact that in steady level coordinated turn, the bank angle is held constant and the aircraft is not rolling. The right aileron input is needed to initiate a right turn and this will roll the airplane to the right, increasing the bank angle. However, this cannot go indefinitely and at one point when the desired bank angle is achieved, the aircraft needs to stop rolling and little opposite (left aileron) may be needed briefly.

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Table 25 shows the control surface deflections for initial trim state with OEI, and cases for left and right level coordinated turn at 20 degrees bank angle. For instance, to maintain the aircraft in right OEI condition in a level coordinated left turn at 20 degrees, a slight change in elevator deflection for more pitch up moment, a greater rudder deflection towards the operative engine (more left rudder) and more right aileron (positive) are required. The amount of permissible physical limits of the rudder and aileron deflections determines the maximum available bank angle with OEI during the turns.

6.7 Summary This chapter has reviewed lateral flight equilibrium with OEI to analyse turning performance of the Boeing 737-300 aircraft with OEI. It has looked into wind milling drag and resulting yawing moment from OEI condition to observe how it will affect the direction of turn assuming a right engine inoperative condition. Effects of bank angle and weights on turning performance (left turn vs right turn) as well as minimum control speed while the aircraft is at a bank angle have been analysed. Change in control surface deflections required for a coordinated turn with AEO and OEI have been discussed in this chapter.

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7. CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS 7.1 Conclusion In general, the discussed approach adopts many assumptions to simplify the complexity of the equations and the number of variables involved in them. However, it effectively outlines the procedure associated with optimization of range and endurance parameters for All Engine Operating (AEO) situations as well as One Engine Inoperative (OEI) condition. The research work is also a good representation of estimating range and endurance performance of the P-8 Poseidon using (OEI) profile for missions such as maritime patrol and surveillance. The approach can equally be applied for range and endurance performance analysis of other multi-engine aircraft such as the P-3 Orion, which has more practical sense of operating with (OEI) to conduct similar missions.

7.2 Summary of Findings/ Results The analysis conducted in the thesis assumed ideal conditions and ignored other operation factors which affect the flight such as non standard atmospheric condition, wind etc.

The range and endurance performance estimation was built on the Thrust and SFC models developed based on available turbofan engine data. Drag polar estimation was then carried out to develop required aerodynamic parameters. Breguet range and endurance equations were applied to calculate Range and Endurance performance. For OEI, control surface deflections required to keep the aircraft in level coordinated flight were determined to estimate the additional drag as a result of OEI condition. In addition to the loss of thrust from one engine, windmilling drag was also taken into account to arrive at total drag of the aircraft with OEI. The optimum range and endurance and their corresponding speeds were then calculated in both AEO and OEI for various altitudes.

With One Engine Inoperative, the model predicted that the range and endurance performance of the Boeing 737-300 aircraft improve about 2 to 5% and 11 to 15% respectively over AEO. It is also important to note the thrust restricted maximum altitude of about 12,000 ft applies while flying with OEI and hence these improvements are at lower altitudes of less than 12,000 ft. From perspective of military application, this may represent P8-Posiedon missions which require better range and loiter time

115 | P a g e while carrying more payload. For instance, the P8 on its maritime surveillance sortie can achieve its optimum range and endurance of 0.1224 nm/kg of fuel and 0.00044 hr/kg of fuel by flying OEI at 0.53 Mach and 0.4 Mach respectively at 10, 000 ft. This is an improvement from AEO range and endurance of 0.1177nm/kg of fuel and 0.00039 hr/kg of fuel which can be achieved by flying at its optimum range speed of 0.56 Mach and best endurance speed of 0.41 Mach at the same altitude.

Weight sensitivity analysis using numerical integration method was performed to verify the results obtained using Breguet equations. It was found that they are within 5% (percentage error) of one another.

A performance planning manual utilized by airlines for the same variant of the aircraft used in research was consulted to validate the results from the thesis. It was observed that range performance predicted by the thesis model compares within 11% (percentage error) of the data calculated from the manual for AEO while endurance performance also fares similarly with difference within 8% at higher altitudes. The endurance performance of the model for lower altitudes however is a bit off from that of the manual with the manual predicting a larger figures in order of 20%. This however was due to the data given in the manual taking into account descent phase of the flight.

Similarly, the OEI range comapres within 10% of that dervied from the manual. The OEI endurance percentage deviation ranges from 1 to 21% when comapted with the figures derived from the flight manual. It was also noted that the OEI aircraft should fly at speed of about 15-20% slower than it would with AEO to achieve optimum range and endurance performance.

The analysis conducted for lateral flight equilibrium and turning performance with (AEO) and (OEI) allowed some insight into how the aircraft behaves during turning with one engine inoperative. With right engine inoperative, the left turning performance was observed to be superior to right turning performance. It means loitering at altitudes 12,000 ft and below with turns away from the inoperative engine will improve aircraft range and endurance.

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Boeing 737-300 Results Range OEI range improves 2-5% over AEO Endurance OEI endurance improves 11-15% over AEO Maximum altitude 12,000 ft with OEI (thrust restricted) Numerical integration method yields results which are within 5% of Weight Sensitivity Breguet equations Range Comparison AEO range compares within 11% of the flight manual’s data. (with manual) OEI range compares within 10% of the flight manual’s data Endurance Comparison AEO endurance percentage deviation ranges from 17 to 26% (with manual) OEI endurance percentage deviation ranges from1 to 21 % Optimum speed for best speed of about 15-20% slower than optimum range and endurance range and endurance speed with AEO (best endurance speed < best range speed) Table 26: Summary of OEI and AEO results 7.3 Possible Future Directions for Research This thesis has discussed the Boeing 737-300 performance characteristics in subsonic condition with AEO and OEI with focus on Range and Endurance (loiter) performance. A lot of assumptions and simplifications were necessary to arrive at estimated performance parameters as presented in the aircraft. Other means to improve range can also be investigated more thoroughly and accurately. There are a number of additional details which can be researched further to take into consideration while modelling the flight equilibrium equations and range and endurance performance. Examples of such details may be: 1) Taking into account thrust vectoring, thrust reduction effects, circulation control etc. 2) Taking into account wave drag effects as well as deriving 3rd order drag polar to estimate drag polar more accurately especially towards transonic region. 3) More thorough estimation of stability and control derivatives 4) Consideration of Non-standard atmospheric conditions. 5) More detailed engine data and more robust Thrust and SFC models which takes into account factors such as bypass ratio, engine temperature and pressure ratio effects as one of the input parameters. 6) Effects of engine position on range and endurance performance. (Lateral distance as well as engine inclination angle). 7) Detailed model on effect of throttle settings on SFC.

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8) More reliable data validation methods such as wind tunnel testing, flight test etc. 9) Possible static margin analysis on static stability with OEI. 10) Detailed analysis of contribution of windmilling and spillage drag to the OEI drag.

7.4 Final Comment In conclusion, the main objectives of the thesis outlined since project planning stage of the research were achieved and have been presented over the six chapters in this thesis. This thesis has also explored turning performance analysis with OEI which was not included in original project plan.

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8. REFERENCES [1] J. D. Anderson, Aircraft Performance and Design. USA: McGraw-Hill, 1999. [2] A. C. Kermode, Mechanics of Flight, 10th ed. USA: Pearson, 2006. [3] J. Bertin and M. Smith, Aerodynamics for Engineering Students, 2nd ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 1989. [4] N. G. R. Center. (08 February 2011). Mach No. Available: http://www.grc.nasa.gov/WWW/k-12/airplane/mach.html [5] A. Nebylov and J. Watson, Aerospace Sensors. USA: Momentum Press, 2012. [6] C. Lan and J. Roskam, Airplane Aerodynamics and Performance. USA: DARcorporation, 1988. [7] J. Roskam, Airplane Desing Part III: Layout Design of Cockpit, Fuselage, Wing and Empennage: Cutaways and Inboard Profiles, DARcorporation, USA. USA: DARcorporation, 2002. [8] S. Hoerner and H. Borst, Fluid-Dynamic Lift. Brick Town, NJ, USA, 1975. [9] J. Anderson, A History of Aerodynamics and Its Impact on Flying Machines. USA: Cambridge University Press, 1997. [10] J. Vennard, Elementary Fluid Mechanics. USA: John Willey & Sons, 1957. [11] E. Buckingham, "Model Experiments and the Focus of Empirical Equations," TransASME, vol. 37, p. 263, 1915. [12] N. G. R. Center. Airplane Forces. Available: http://www.grc.nasa.gov/WWW/k- 12/airplane/forces.html [13] Honda. (8 February 2011). Turbofan Engine. Available: http://world.honda.com/HondaJet/Background/TurbofanEngine/ [14] E. Roux, Turbofan and Turbojet Engines Database Handbook: Elodie Roux, 2007. [15] J. D. Anderson, Introduction to Flight. USA: McGraw-Hill, 2005. [16] H. Goldstein, P. Charles, and J. Safko, Classical Mechanics, 3rd ed. USA: Addison-Wesley, 2001. [17] E. Tulapurkara, "Chapter I, Lecture Notes for Flight Dynamics I distributed at the Indian Institute of Technology, Madras," ed, 2002. [18] J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls Part I. USA: DARcorporation, 2002.

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[19] Y. Meng and Y. Lee, "Study of shadowing effect by aircraft maneuvering for air to ground communication," AEU-International Journal of Electronics and Communications, vol. 66, pp. 7-11, 2012. [20] Airbus. (8 February 2012). Airplane Forces. Available: www.airbus.com [21] M. Eshelby, Aircraft Performance: Theory and Practice. USA, 2000. [22] L. Bramhall. (23 June 2013). Performance Estimation of Drag Due to Inoperative Engine. Available: www.esdu.com [23] H. Horlings, "Control and Performance during Asymmetrical Powered Flight," Detailed theoretical paper for Multi-engine Rated Pilots CPL & ATPL, AvioConsult, pp. 7-11, January 2012. [24] E. Torenbeek, Synthesis of Subsonic Airplane Design. Delft, Holland: Delft University Press, 1982. [25] S. Ojha, Flight Performance of Aircraft. USA: AIAA Aerospace Education Series, 2000. [26] (2000, 28 November 2012). P3 Orion. Available: http://www.lynellen.com/p3orion/onstation.html [27] J. Roskam and W. Anemaat, "An Easy Way to Analyze Longitudinal and Lateral-Directional Trim Problems with AEO or OEI," SAE Technical Paper Series 941143, 1994. [28] J. Grasmeyer, "Stability and Control Derivative Estimation and Engine Out Analysis," Virginia Tech VPI-AOE-254, 1998. [29] J. Roskam, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes. Kansas, USA: Roskam Aviation and Engineering Corporation, 1971. [30] The USAF Stability and Control Digital Datcom vol. 1 to 3. USA: McDonnell Douglas Astronautics Company, St Louis Division, 1979. [31] M. Cavanaugh, "A MATLAB m-file to Calculate the Single Engine Minimum Control Speed in Air of a Jet Powered Aircraft," ed, 2004. [32] B. Abrahams, "Evaluation of the F-22 Subsonic Range Performance of F-22," SEIT, University of New South Wales, ADFA, Australia, 2005. [33] J. Brown, Hubbard-The Forgotten Boeing Aviator, 2nd ed. USA: Peanut Butter Publishing, 1996.

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[34] M. Sharpe and R. Shaw, Airliner Color History-Boeing 737-100 and 200. USA: MBI, 2001. [35] Boeing. (2012, 28 November 2012). Boeing 737 Description. Available: www.boeing.com/boeing/commercial/737family [36] C. Brady, "The Boeing 737 Technical Guide," 1999. [37] Flightglobal. (2012, 10 September 2013). Boeings Evolution. Available: http://www.flightglobal.com/blogs/flightblogger/2012/03/boeings-777x- evolution-closer.html [38] Aerospaceweb. (2012, 12 December 2012). Boeing 737 Short to Medium-Range Jetliner. Available: http://www.aerospaceweb.org/aircraft/jetliner/b737 [39] P. Jackson, Jane's All the World's Aircraft 1996-97. USA: Janes Information Group, 1996. [40] C. A. Engines. (2013). CFM56-3 Specifications. Available: http://www.cfmaeroengines.com/engines/cfm56-3 [41] M. Sadraey, Aircraft Design: A Systems Engineering Approach. Australia: Wiley, 2012. [42] D. Raymer, Aircraft Design: A Conceptual Approach, 3rd ed. Washington, USA, 1999. [43] J. Roskam, Methods of Estimating Drag Polars of Subsonic Airplanes. Kansas, USA: Roskam Aviation and Engineering Corporation, 1971. [44] L. Jenkinson, P. Simpkin, and D. Rhodes, Civil Jet Aircraft Design. UK: Arnold, 1999. [45] S. Brandt, R. Styles, R. Whitford, and J. J. Bertin, Introduction to Aeronautics: A Design Perspective. Reston, USA, 1997. [46] M. Asselin, An Introduction to Aircraft Performance. USA, 1997. [47] Boeing, "Flight Planning and Performance Manual 737-300 CFM56-3_22K," ed, 2000. [48] W. Phillips, Mechanics of Flight, 2nd ed. USA: John Wiley & Sons, 2001.

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9. Appendix A: Estimation of Drag Polar Parameters Zero Lift Drag The zero-lift drag coefficient of the Boeing 737-300 is calculated by summing every external aerodynamic component of the aircraft which are all contributing to the aircraft drag as given in Equation 54. CDof, CDow, CDoht CDovt, CDoN, and CDohld represent drag components for fuselage, wing, horizontal tail, vertical tail, nacelle, and high lift devices respectively. [41]

CD0  CD0 f  CD0w  CD0ht  CD0vt  CD0N  CD0hld ... Equation 54

Zero-lift drag coefficient due to fuselage The zero-lift drag coefficient for the Boeing 737-300 fuselage is estimated by the following. [41] S C  C f f wetf Equation 55 0 f f LD M S Cf represents skin friction coefficient and is estimated based on the Prandtl relationship as given in Equation 56 assuming flow over fuselage is of completely turbulent nature. Reynolds number, Re in the equation is dependent on air density, true air speed, the length of fuselage and viscosity. 0.455 C f  2.58 Equation 56 [log10(Re)]

The term fLD is concerned with fuselage length and diameter and estimated from Equation 57. The parameter, L/D in equation below is the fuselage length to maximum diameter ratio.

60 L f LD  1  0.0025( ) Equation 57 (L )3 D D The parameter fM is a function of Mach number and estimated from Equation 58.

Swetf and S represent the fuselage wetted area and wing reference area respectively in Equation 55.

1.45 f M 1 0.08M Equation 58

Zero-lift drag due to Wing, Horizontal Tail and Vertical tail

The zero-lift drag coefficients of wing, CDow, horizontal tail, CDoht, and vertical tail CDovt for the aircraft used in research are estimated as given in Equation 59, 60 and 61.

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0.4  S  C  C  C f f  wetw  dmin w  Equation 59 D0w fw tcw M     S  0.004  0.4  S  C  C  C f f  wetht  dmin ht  Equation 60 D0ht fht tcht M     S  0.004  0.4  S  C  C  C f f  wetvt  dmin vt  D0vt fvt tcvt M    Equation 61  S  0.004 

The parameters Cfw, Cfht,Cfvt are estimated using Equation 56 where Reynolds number, Re, is calculated using Equation 62 and Equation 63. VC Re  Equation 62  2    Equation 63 C  Cr 1    3  1   Where

C = mean aerodynamic chord

Cr = root chord λ = ratio of tip chord to root chord

The term ftc in Equation 59, Equation 60 and Equation 61 is calculated from the relationship given in Equation 64 where (t/c) max represents maximum thickness to chord ratio of the wing. The parameter fM in the equations is calculated as given in Equation 58.

4  t   t  ftc  1 2.7  100  Equation 64  c max  c max

Zero-lift drag coefficient due to High Lift Devices The high lift devices in Boeing 737-300 type are generally classified into two main groups; leading edge high lift devices such as slats and trailing edge high lift devices such as flaps as mentioned earlier in the chapter. They are estimated based on the relationships given in Equation 65 and Equation 66

 Csl  CD   CD Equation 65 0sl  C  0w

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 C  C   f A B Equation 66 D0 flap   f  C  In Equation 65(Csl/C) or (Cf/C) is the ratio of average extended (slat) or (flap) chord to average wing chord whereas CDow is the wing zero-lift drag coefficient without application of high lift devices. The parameters A and B are constant parameters which values depend on the type of the high lift devices the aircraft deploy. The Boeing 737- 300 deploys a triple slotted flap, but the A and B values for double-slotted flap given in [41] are assumed in this estimation as those for a triple slotted flap are not readily available. Hence, A=0.0011 and B=1.

Leading edge device ΔCLmax Double-slotted flap 1.6 Triple-slotted flap 1.9 Single-slotted Fowler flap 1.3c’/c Double-slotted Fowler flap 1.6c’/c Triple-slotted Fowler flap 1.9c’/c

Table 27: ΔCLmax estimation for different type of flaps [41] Zero-lift drag coefficient due to Nacelle The engines of the Boeing 737-300 are located inside nacelle as it acts as an aerodynamic cover to reduce the engine drag. The zero-lift drag coefficient contribution due to a nacelle in the aircraft under study is estimated based on Equation 55 where the nacelle finess ratio (ratio of length to diameter) instead of fuselage length to diameter ratio is used.

Miscellaneous contribution to Zero-lift drag coefficient Other miscellaneous contributions toward the total of zero-lift drag coefficient can be attributed to the followings. [41] 1) Interference effect 2) Antenna 3) Pitot tube 4) Surface roughness 5) Leakage 6) Rivets and screws

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Correction factor The overall zero-lift drag coefficient for the aircraft in study is corrected as shown by Equation 67. Due to the difficulty estimating miscellaneous contribution. [41]specifies the value of Kc to be 1.1 for a passenger aircraft type.

CD  Kc[CD CD CD CD CD CD ...] Equation 67 0 0 f 0w 0ht 0vt 0N 0hld

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10. Appendix B: Stability and Control derivatives estimation Estimation of stability derivatives The stability derivatives required for the analysis in the thesis are estimated as follows:

Variation of Drag Coefficient with Angle of Attack

The CDα,, variation of drag coefficient with angle of attack can be estimated based on the parabolic drag polar estimated for the airplane assuming a local analytical fit to the actual drag polar has been made. [29] C 2C C C  D0  L L Equation 68 D  Ae

Where, W C  L qS

C D0  0  The first term in the equation represents the change of profile drag with angle of attack. Due to its laborious nature of estimation, it is assumed to be equal to zero. A is the aspect ratio of the equivalent wings. Oswald efficiency factor, e is estimated with the aid of Figure 3.2 of [29]

Variation of Lift Coefficient with Angle of Attack: Lift Curve Slope The variation of lift coefficient with angle of attack for the aircraft is estimated from Equation 69. The subscripts WB and H in the equation denote wing-body combination and horizontal tail. ȠH represents the dynamic pressure ratio and a conservative value of 0.9 is assumed for the calculation.

S H  CL  CL  CL  H (1 ) Equation 69  WB  H S 

The first term in Equation 69 is the variation contributed by wing-body combination. An empirical correction factor is applied to wing lift curve to correct for body effect via the following relationship. d is the fuselage diameter and b is the wing span.

CL  KWBCL Equation 70 WB W

Where, 126 | P a g e

d d K 1 0.25( )2  0.025( ) WB b b 2A CL   2 2 2  tan   A  c 2  1 2 )  4 K 2   2    avg _ 2D _lift _ curve_ slope _ of _ airfoil K  2

  (1 M 2 )

The parameter δε/δα in Equation 69 is the downwash ratio at the horizontal tail and estimated as given in Equation 71 below.

CL |M   W |M  |M 0 Equation 71   CL |M 0 W Where,

1.19    |M 0  4.44 K K K H (cos c )   4  1 1 K   A A 1 A1.7 10 3 K   7

hh K 1 b H l 1 (2 h ) 3 b

The values of CL |M and CL |M 0 are calcualted using the following equation. W W

Equation 72

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Variation of Pitching Moment Coefficient with Angle of Attack This derivative for the aircraft is estimated as follows: dC C  ( m )C Equation 73 m L dCL Where,

dCm  X cg  X ac dCL

CL S d X  h  h X (1 ) acWB h ach CL S d WB X ac  CL h Sh d 1 h (1 ) CL S d WB X  X  X acWB acW acCB  X   X  K ac  K acW  2   CR  dM X   d acB qScCL W q n d (dM )  w2 (x ) X d f  f i i 36.5 i1 d

The above equation represents the Multhopp strip-integration method of accounting for fuselage effect on wing aerodynamic centre location. The parameter δM/δα is found using equation in conjunction with Figure 3.12 and 3.13 of [29].

Estimation of Longitudinal Control Derivatives

Variation of Lift Coefficient with Stabilizer Incidence The derivative for the aircraft is computed from:

SH CL  CL Equation 74 iH H S CLαH is calculated from Equation 72.

Variation of Pitching Moment Coefficient with Stabilizer Deflection The variation of pitching moment coefficient with stabilizer deflection for the aircraft is estimated from Equation 75.

lH SH Cm  CL Equation 75 iH H cS

In the equation, CLαH is found from Equation 72 as mentioned above. lH is the distance from the centre of gravity to the horizontal stabilizer aerodynamic centre location. 128 | P a g e

Variation of Lift Coefficient with Elevator Deflection This derivative for the aircraft is found from:

SH CL  (CL ) Equation 76  E  F S In Equation 76 the parameter, CLδf, is the variation of lift coefficient with flap deflection and is computed as give in Equation 77

C |  L M CL CL  Cl ( )[ ]kb Equation 77 F F Cl |M   Cl

The parameter Clδf in above equation is the section variation of lift with control deflection δF and computed from: C l Cl { }(cl )Theory K Equation 78  F (C )  l Theory In equation above Clδf is the theoretical flap-lift effectiveness obtained from Figure 10.5 of [29].

And the ratio Clδ/ClδTheory is an empirical correction factor and obtained from Figure 10.6 of [1]. K’ is an empirical correction factor which is important only if large control deflections are considered and K’=1 is used for estimation for the aircraft.

The parameter CLα|M in Equation 77 is the lift-curve slope at a given Mach no of the unflapped surface as obtained from Equation 72 whereas Clα|M is the section lift curve slope corrected for Mach number as given in equation below. C l Cl |M  Equation 79  1 M 2

In above equation, Clα is the zero Mach number section lift curve slope of the airfoil of the wing.The ratio, αδCL/ αδcl, is the ratio of three dimensional flap-effectiveness parameter to the two-dimensional flap-effectiveness parameter and obtained from Figure 10.2 of [29].

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Variation of Pitching Moment Coefficient with Elevator Deflection This derivative for the aircraft is computed from:

lH Cm  CL Equation 80 E E c

Where,

CLδE is calculated from Equation 76.

Estimation of Lateral Stability Derivatives

Variation of Side Force Coefficient with Sideslip Angle The variation of side force coefficient with sideslip angle for the aircraft is estimated from:

Cy  Cy Cy Cy Equation 81  W B V

The first term in the equation is the contribution due to the wing and is calculated from the following equation

1 Cy  .000157.3(rad) Equation 82  w

In Equation 82, Γ is the dihedral angle of the wing. The second term which is the contribution due to the fuselage is estimated from: S C  2K ( 0 )(rad 1) Equation 83 y B i S

Ki is obtained from Figure 7.1 of [28]. It depends on the position of wing on fuselage and on (2Zw/d) where Zw is the distance from body centre to quarter chord of exposed wing root chord and d is the maximum diameter at wing-body junction. So is the cross sectional area at the point when dS/dx is maximum.

The third term CyβV in Equation 81 is the vertical tail contribution and is found from:

d SV 1 Cy  kCL (1 )V (rad ) Equation 84  V V d S The factor k is an empirical factor and estimated from Figure 7.3 of [29]. The parameter

(1 + dσ/dβ) ȠV is calculated from:

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SV d S Z w (1 )V  .724  3.06 .4 .009A Equation 85 d 1 cos c d 4 The parameter CLαV in Equation 84 depends on the effective aspect ratio of the vertical tail (Aveff) which is computed as follows: A A A  ( VB )A {1 K ( VHB 1)} Equation 86 Veff A V H A V VB

Where,

AV is geometric aspect ratio for the isolated vertical tail. A ( VB ) is the ratio of the aspect ratio of the vertical panel in the presence of the body to AV that of the isolated panel and found from Figure 7.5 of [29]. A VHB is the ratio of the vertical panel aspect ratio in the presence of the horizontal tail A VB and body to that of the panel in the presence of the body alone. This ratio is obtained from Figure 7.6 of [29].

KH is a factor for the relative size of the horizontal and vertical tails and found from Figure 7.7.

Variation of Rolling Moment Coefficient with Sideslip Angle This derivative for the aircraft is estimated from:

Cl  Cl Cl Cl Equation 87  WB H V The first term, contribution of wing-body combination, is found from: C C C C C l l l l l 1 Cl  57.3[CL { KM K f  ( ) A} { KM  } (Cl )Z  tan c ( )(rad ) WB WB C  C     w 4  tan Lc L c 2 4 Equation 88 Where,

CLWB ~= CL is the airplane steady state lift coefficient.

(Clβ/CL)Λc/2 is the wing sweep contribution obtained from Figure 7.11 of [29].

KMΛ is the compressibility (Mach number) correction to sweep obtained from Figure 7.12 of [29]

Kf is a fuselage correction factor obtained from Figure 7.13 of [29]

(Clβ/CL)A is the aspect ratio contribution obtained from Figure 7.14 of [29]

Clβ/Γ is the wing dihedral effect obtained from Figure 7.15 of [29]

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KMΓ is the compressibility correction to dihedral obtained from Figure 7.16 of [29]

ΔClβ/Γ is the body-induced effect on the wing height and estimated from the following equation:

Cl d   0.0005 A( )2 Equation 89  b Where,

avg _ fuselage _ cross  sectional _ area d  0.7854

(ΔClβ)Zw is another body-induced effect on the wing height and found from the equation below:

1.2 A Z 2d (C )   ( W )( ) Equation 90 l ZW 57.3 b b C ( l ) is a wing twist correction factor obtained from Figure 7.17 of [29] and θ is  tan c 4 the wing twist between root and tip sections of the wing.

The second term and third term; contribution of horizontal tail and vertical tail: from Equation 87 are estimated using following equations:

SH bH Cl  Cl Equation 91 H HB Sb

ZV cos lV Sin 1 Cl  Cy ( )(rad ) Equation 92 V V b Where,

lv = distance between Centre of gravity and aerodynamic centre of vertical tail.

Zv = distance of vertical tail aerodynamic centre above centre of gravity.

Variation of Yawing Moment Coefficient with Sideslip Angle The variation of Yawing Moment Coefficient with sideslip angle for the aircraft is estimated as given below:

Cn  Cn  Cn  Cn Equation 93  W B V The first term is neglected assuming there are not any very high angles of attack situations in the study. The second term in the equation, body contribution to the derivative is calculated from the following equation.

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S l C  57.3K K Bs B (rad 1 ) Equation 94 n B N Rl S b Where,

KN is a factor for body and wing-body combination effects and obtained from Figure 7.19 of [29].

KRl is a Reynold’s number factor for the fuselage and estimated from Figure 7.20 of [29]. The vertical tail contribution is estimated from:

lV cos  ZV sin 1 Cn  Cy ( )(rad ) Equation 95  V V b Estimation of Lateral Control Derivatives

Variation of Sideforce Coefficient with Aileron Deflection This derivative is taken as zero. [29]

Variation of Rolling Moment Coefficient with Aileron Deflection The variation of rolling moment coefficient with aileron deflection for the aircraft is estimated by taking into account differential control deflection effect. Each control is considered as one-half of the anti-symmetric value. The total rolling-moment coefficient is then obtained from the following equation.

Cl  [Cl  Cl ] Equation 96  A L R Where, C   C l  l

The parameter C’lδ is computed based on equation below in conjunction with Figure 11.1 of [29] K C C  ( l ) Equation 97 l  K

In Equation 97, βC’lδ/K represents the rolling-moment effectiveness parameter and K is the ratio of the 2-d lift curve slope at a given Mach number to 2π/β, i.e. (clα)M/(2π/β).

The parameter αδ in is based on the deflection of one surface and found from the following equation. C   l Equation 98  C l

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Where, C l Cl  ( )Cl K  Theory Cl Theory (Figure 10.5 and Figure 10.6 of [29])

Clα = average section lift curve slope over aileron span of the wing

Variation of Yawing Moment Coefficient with Aileron Deflection This derivative is computed from:

Cn  KCLCl Equation 99  A  A

Where,

ClδA is found as shown in section 3.5.6.2

CL is the steady state lift coefficient for δA = 0 and K is an empirical factor and obtained from Figure 11.3 of [29]

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11. Appendix C: Thrust Model Derivation

Figure 82: Bypass ratio 6.5 Max Cruise Thrust [44]

Altitude Density Density Ratio Speed of Sound Coefficients (at Mach No) h (ft) ρ (sl/ft3) σ a (ft/s) 0 0.2 0.4 0.6 0.8 0 0.002377 1 1116.450092 0.8 0.61 0.5 0.425 0.39 10000 0.001755 0.738479096 1077.385413 0.625 0.5 0.425 0.375 0.345 15000 0.001496 0.629237537 1057.311963 0.55 0.45 0.39 0.35 0.315 25000 0.001065 0.448118938 1015.975938 0.335 0.305 0.295 0.275 0.2475 30000 0.000889 0.374132241 994.6639469 0.295 0.265 0.25 0.245 0.235 36000 0.000709 0.298108761 968.4706908 0.225 0.2025 0.185 0.18 0.18 40000 0.000585 0.246169918 968.0757661 0.175 0.15 0.14 0.14 0.15 45000 0.00046 0.19358268 968.0757661 0.14 0.125 0.11 0.11 0.12 Table 28: Bypass ratio 6.5 Max Cruise Thrust in table form

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Figure 83: Thrust data curve fit

136 | P a g e h (ft) Sigma exp(-sigma) A B C 0 1 0.367879441 0.616071 -0.99536 0.795286 10000 0.738479 0.477840112 0.383929 -0.64964 0.621714 15000 0.629238 0.532998037 0.267857 -0.49929 0.546429 25000 0.448119 0.638828698 -0.00893 -0.09536 0.331786 30000 0.374132 0.687885939 0.089286 -0.14143 0.293143 36000 0.298109 0.742220611 0.102679 -0.13839 0.225214 Table 29: A, B and C coefficients Vs density ratio for thrust model

A,B,C Vs exp(-sigma) 1 y = -1.568x + 1.3699 0.8 R² = 0.9924 0.6 0.4 y = -35.884x3 + 54.371x2 - 23.679x + 2.1458

0.2 R² = 0.9897

0 A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 B

A,B,C -0.2 -0.4 C -0.6 3 2 y = 29.888x-0.8 - 44.741x + 19.666x - 2.0513 R² = 0.9748 -1 -1.2 exp (-sigma)

Figure 84: Curve fit for A, B and C coefficients for thrust model

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12. Appendix D: Thrust Specific Fuel Consumption Model Derivation

Figure 85: Bypass ratio 6.5 SFC Data [44]

SFC/θ0.606 at Mach No FN/( δ.FN*) 0.2 0.4 0.6 0.8 0 0.32 0.28 0.27 0.29 0.25 0.43 0.375 0.37 0.4 0.45 0.56 0.46 0.45 0.48 0.65 0.7 0.565 0.54 0.57 0.85 0.825 0.69 0.64 0.65 0.95 0.88 0.735 0.675 0.685 Table 30: SFC Data in table form

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Figure 86: SFC curve fit

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A,B,C Vs Mach No

1.5 y = -2.2442x3 + 2.39x2 + 0.3374x + 0.3656 R² = 0.9541 1

0.5 y = 0.7853x + 0.3667 R² = 0.9923 A 0 B A,B,C 0 0.2 0.4 0.6 0.8 1 3 2 -0.5 y = 3.4373x - 4.3697x + 0.1561x - 0.4195 C R² = 0.9952 -1

-1.5 Mach No

Figure 87: Curve fit of A, B, C coefficients Vs Mach No for SFC model

Mach No A B C 0.95 0.96875 -1.29125 1.09875 0.85 0.90625 -1.29 1.045 0.65 1.03125 -1.23875 0.90375 0.45 0.8125 -0.9375 0.7125 0.25 0.53125 -0.57875 0.52375 0 0.375 -0.425 0.39 Table 31: A, B and C coefficients Vs Mach No in table form

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13. Appendix E: Boeing 737-300 Flight Planning and Performance Manual Data

Figure 88: CFM56 Turbofan Engine specifications [14]

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Table 32: International Standard Atmosphere[14]

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Table 33: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (37000 ft to 32000 ft)[47]

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Table 34: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (31000 ft to 26000 ft)[47]

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Table 35: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (25000 ft to 20000 ft)[47]

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Table 36: Long Range Cruise Table Boeing 737-300 Flight Planning and Performance Manual (13000 ft to 8000 ft)[47]

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Table 37: Long Range Cruise Table (One Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual (19000 ft to 14000 ft)[47]

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Table 38: Long Range Cruise Table (One Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual (13000 ft to 6000 ft)[47]

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Table 39: Long Range Cruise Altitude Capability (Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual[47]

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Table 40: Long Range Cruise Table (Engine Inoperative) Boeing 737-300 Flight Planning and Performance Manual[47]

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Figure 89: Long Range Cruise Enroute Fuel and Time (37000 ft to 29000 ft) Boeing 737- 300 Flight Planning and Performance Manual [47]

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Figure 90: Long Range Cruise Enroute Fuel and Time (28000 ft- 10000 ft) Boeing 737-300 Flight Planning and Performance Manual [47]

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Figure 91: Long Range Cruise Diversion Fuel and Time Boeing 737-300 Flight Planning and Performance Manual [47]

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