IN DEGREE PROJECT VEHICLE ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2017

Degree Project in AeronauticsConceptual design, flying and handling qualities of a supersonic transport aircraft.

NIKOLAOS PERGAMALIS

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES

www.kth.se

Abstract

The purpose of this project is the design of a supersonic aircraft that is able tomeet the market’s requirements, be economically viable and mitigate the currentbarriers. The initial requirements of the design have been set according to theunderstanding obtained from a brief market research, taking into account themarket needs, in addition to the economical and environmental restrictions. Theconceptual design proposed is a supersonic transport able to execute transatlanticflights carrying 15 passengers. The aerodynamics, propulsion data and weight ofthe design have been estimated using empirical relations and experimental datafound in references. The design has been evaluated regarding its performance,stability, flying and handling qualities. The relevant models have been createdusing the software Matlab, while the flight testing has been executed at theMerlin MP521 engineering flight simulator. Finally, a discussion is made aboutthe environmental impact of the supersonic transport, focusing on the aerodynamicnoise, generated by the sonic boom, and the air pollutants emissions.

Contents

1 Introduction 11

2 Conceptual Design 122.1 Market Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Initial Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Desired Requirements . . . . . . . . . . . . . . . . . . . . 142.2.2 Initial takeoff weight estimation . . . . . . . . . . . . . . . 142.2.3 Mission profile and segments weight fractions . . . . . . . 152.2.4 Thrust-to-weight ratio . . . . . . . . . . . . . . . . . . . 172.2.5 Wing loading . . . . . . . . . . . . . . . . . . . . . . . . 182.2.6 Constraint analysis . . . . . . . . . . . . . . . . . . . . . 192.2.7 Initial sizing results . . . . . . . . . . . . . . . . . . . . . 202.2.8 Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.9 Tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.10 Fuselage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.11 Landing gear . . . . . . . . . . . . . . . . . . . . . . . . 272.2.12 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.13 Aircraft model . . . . . . . . . . . . . . . . . . . . . . . . 352.2.14 Control surfaces . . . . . . . . . . . . . . . . . . . . . . . 37

3 Aerodynamics 383.1 Airfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1.1 Airfoil selection . . . . . . . . . . . . . . . . . . . . . . . . 383.1.2 Subsonic aerodynamic coefficients . . . . . . . . . . . . . 393.1.3 Supersonic aerodynamic coefficients . . . . . . . . . . . . 40

3.2 Subsonic Lift-Curve Slope . . . . . . . . . . . . . . . . . . . . . . 413.2.1 Wing - Fuselage Assembly . . . . . . . . . . . . . . . . . . 413.2.2 Horizontal Tail . . . . . . . . . . . . . . . . . . . . . . . . 423.2.3 Total aircraft . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3 Supersonic Lift-Curve Slope . . . . . . . . . . . . . . . . . . . . . 443.4 Maximum Lift Coefficient . . . . . . . . . . . . . . . . . . . . . . 45

3.4.1 Clean configuration . . . . . . . . . . . . . . . . . . . . . 453.4.2 High lift devices . . . . . . . . . . . . . . . . . . . . . . . 483.4.3 Horizontal tail . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5 Subsonic Parasite Drag Coefficient . . . . . . . . . . . . . . . . . 503.5.1 Equivalent skin-friction method . . . . . . . . . . . . . . . 50

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3.5.2 Component buildup method . . . . . . . . . . . . . . . . . 503.6 Supersonic Parasite Drag Coefficient . . . . . . . . . . . . . . . . 523.7 Critical Mach number . . . . . . . . . . . . . . . . . . . . . . . . 563.8 Drag due to Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.9 Miscellaneous Drag . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.9.1 Flaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.9.2 Spoilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.9.3 Landing gear . . . . . . . . . . . . . . . . . . . . . . . . . 60

4 Weights 614.1 Weights Estimation Refined Method . . . . . . . . . . . . . . . . 614.2 Center of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 Stability and Control 645.1 Subsonic Static Longitudinal Stability . . . . . . . . . . . . . . . 64

5.1.1 Aircraft Pitching Moments . . . . . . . . . . . . . . . . . 645.1.2 Subsonic Neutral Point . . . . . . . . . . . . . . . . . . . 655.1.3 Longitudinal Control and Trim Analysis . . . . . . . . . . 66

5.2 Supersonic Static Longitudinal Stability . . . . . . . . . . . . . . 695.2.1 Supersonic Neutral Point . . . . . . . . . . . . . . . . . . 695.2.2 Trim Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3 Longitudinal Center of Gravity Location . . . . . . . . . . . . . . 705.4 Directional Stability . . . . . . . . . . . . . . . . . . . . . . . . . 71

6 Performance 736.1 Climb Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.1.1 Minimum Time to Climb . . . . . . . . . . . . . . . . . . 746.1.2 Minimum Fuel to Climb . . . . . . . . . . . . . . . . . . . 76

6.2 Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.3 Descent and Loiter . . . . . . . . . . . . . . . . . . . . . . . . . . 776.4 Takeoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.5 Landing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.6 Total Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7 Test Flight 827.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.2 Flying and Handling Qualities . . . . . . . . . . . . . . . . . . . . 83

7.2.1 Modes excitation . . . . . . . . . . . . . . . . . . . . . . . 837.2.2 Dynamic Stability Requirements . . . . . . . . . . . . . . 857.2.3 Longitudinal Dynamic Stability . . . . . . . . . . . . . . . 877.2.4 Lateral-Directional Dynamic Stability . . . . . . . . . . . 90

8 Environmental Impact 958.1 Sonic Boom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958.2 Air Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

8.2.1 Air Pollutants Identification . . . . . . . . . . . . . . . . . 998.2.2 Environmental Concerns of Supersonic Flight . . . . . . 101

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9 Discussion - Conclusions 107

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List of Figures

2.1 Mission profile division. . . . . . . . . . . . . . . . . . . . . . . . 162.2 Fuselage top view. . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3 Fuselage side view. . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4 Fuselage-wing assembly top view. . . . . . . . . . . . . . . . . . . 262.5 Fuselage-wing side view. . . . . . . . . . . . . . . . . . . . . . . . 272.6 Airbus A320 main landing gear retraction and stowage. . . . . . 272.7 Main landing gear logintudinal location [17]. . . . . . . . . . . . . 282.8 Diagram of nose landing gear location estimation. . . . . . . . . . 292.9 Supersonic air inlets. . . . . . . . . . . . . . . . . . . . . . . . . . 302.10 Three-shock external inlet. . . . . . . . . . . . . . . . . . . . . . . 312.11 Oblique shock wave. . . . . . . . . . . . . . . . . . . . . . . . . . 322.12 Concorde rectangular ramp intakes. . . . . . . . . . . . . . . . . 332.13 EJ200 turbofan engine. . . . . . . . . . . . . . . . . . . . . . . . . 352.14 Aircraft model top view. . . . . . . . . . . . . . . . . . . . . . . . 352.15 Aircraft model side view. . . . . . . . . . . . . . . . . . . . . . . 362.16 Aircraft model front view. . . . . . . . . . . . . . . . . . . . . . . 362.17 Rudder illustration. . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 NACA 64-006 lift curve for Re = 9·106 (XFOIL). . . . . . . . . . 393.2 NACA 64-009 lift curve for Re = 9·106 (XFOIL). . . . . . . . . . 403.3 Wing supersonic CNα for taper ratio of 0.2 [13]. . . . . . . . . . . 443.4 High aspect wing and airfoil maximum lift coefficient ratio at 0.2

Mach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.5 Stall angle of attack increment at subsonic Mach numbers of 0.2

- 0.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.6 Trailing and leading edge high lift devices. . . . . . . . . . . . . . 483.7 Wing TE flaps (red), LE flaps (magenta) and ailerons (cyan). . . 493.8 Sear-Haacks body volume distribution [9]. . . . . . . . . . . . . . 543.9 Wing-body area rule design [9]. . . . . . . . . . . . . . . . . . . . 543.10 Aircraft cross-section area distribution. . . . . . . . . . . . . . . . 553.11 Wing critical Mach number in two-dimensional flow. . . . . . . . 573.12 Wing control surfaces (blue) and spoilers (red). . . . . . . . . . . 59

5.1 Wing-body and tail mean aerodynamic centers [28]. . . . . . . . 655.2 CG position influence on Cm at 0.5 Mach. . . . . . . . . . . . . . 66

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5.3 Variation of δt to trim with the flight speed and the static marginat SL flight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.4 Variation of δt to trim with the flight speed and the flight altitudefor the subsonic Mach number range. . . . . . . . . . . . . . . . . 68

5.5 Variation of αtrim with the flight speed and the flight altitude forthe subsonic Mach number range. . . . . . . . . . . . . . . . . . . 68

5.6 Variation of δt to trim with the flight speed and the flight altitudefor the supersonic Mach number range and static margin of 0.1. . 69

5.7 Variation of δt to trim with the flight speed and the flight altitudefor the supersonic Mach number range and static margin of 0.35. 70

5.8 Variation of αtrim with the flight speed and the flight altitude forthe supersonic Mach number range. . . . . . . . . . . . . . . . . . 70

6.1 SEP contours diagram (dry thrust). . . . . . . . . . . . . . . . . 746.2 Flight path for minimum time to climb at cruise conditions. . . . 756.3 Flight path for minimum fuel to climb at cruise conditions. . . . 766.4 Illustration of takeoff path and distance. . . . . . . . . . . . . . . 786.5 Illustration of landing path and distance [13]. . . . . . . . . . . . 80

7.1 Short-period mode frequency requirements [39]. . . . . . . . . . . 867.2 Elevator impulse input flight recording of the short period mode

for 0.6 Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . 887.3 Body axis pitch rate flight recording of the short period mode for

0.6 Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . 887.4 Elevator step input flight recording of the phugoid mode for 0.6

Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.5 True airspeed flight recording of the phugoid mode for 0.6 Mach

at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.6 Euler roll angle flight recording of the spiral mode for 0.6 Mach

at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.7 Aileron input flight recording of the roll subsidence mode for 0.6

Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917.8 Euler roll angle flight recording of the roll subsidence mode for

0.6 Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . 927.9 Body axis roll rate flight recording of the roll subsidence mode for

0.6 Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . 927.10 Rudder input flight recording of the dutch roll mode for 0.6 Mach

at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937.11 Body axis roll rate flight recording of the dutch roll mode for 0.6

Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937.12 Body axis yaw rate flight recording of the dutch roll mode for 0.6

Mach at 30 kft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

8.1 Drawing and specifications of the baseline configuration [41]. . . 968.2 Drawing and specifications of the low boom configuration [41]. . 978.3 Three view of a low boom SBJ concept [44]. . . . . . . . . . . . . 988.4 Air pollutants formation [48]. . . . . . . . . . . . . . . . . . . . . 100

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8.5 Atmosphere ozone concentration and temperature till the altitudeof 100,000 ft [54]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

8.6 NOx emissions index for SST design (red) and for a typical subsoniclong haul airliner (blue). . . . . . . . . . . . . . . . . . . . . . . . 105

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List of Tables

2.1 Summary of aircraft requirements. . . . . . . . . . . . . . . . . . 142.2 Summary of aircraft specifications. . . . . . . . . . . . . . . . . . 212.3 Summary of wing basic dimensions. . . . . . . . . . . . . . . . . . 232.4 Summary of tail basic dimensions. . . . . . . . . . . . . . . . . . 242.5 Fuselage basic dimensions. . . . . . . . . . . . . . . . . . . . . . . 262.6 Properties of the designed 4-shock external inlet for freestream

Mach number M1=1.7. . . . . . . . . . . . . . . . . . . . . . . . . 322.7 EJ200 engine specifications. . . . . . . . . . . . . . . . . . . . . . 342.8 Propulsion system basic dimensions. . . . . . . . . . . . . . . . . 352.9 Aircraft exposed and wetted areas. . . . . . . . . . . . . . . . . . 36

3.1 NACA 64-006 aerodynamic coefficients ( Re = 9·106). . . . . . . 393.2 NACA 64-009 aerodynamic coefficients ( Re = 9·106). . . . . . . 403.3 Lift-curve slope of wing - body assembly for subsonic Mach number

range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.4 Lift-curve slope of horizontal tail, downwash angle derivative and

horizontal tail CLα contribution to the aircraft, respectively, forsubsonic Mach number range. . . . . . . . . . . . . . . . . . . . . 43

3.5 Aircraft lift-curve slope for subsonic Mach number range. . . . . 433.6 Wing-body and horizontal tail lift-curve slope for supersonic Mach

number range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.7 Horizontal tail downwash angle derivative and CLα contribution

to the aircraft, respectively, for supersonic Mach number range. . 453.8 Aircraft lift-curve slope for supersonic Mach number range. . . . 453.9 Subsonic aircraft maximum lift coefficient and stall angle of attack. 473.10 Subsonic horizontal tail maximum lift coefficient and stall angle

of attack. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.11 Subsonic parasite drag coefficients for the stated Mach number

and altitude flight conditions. . . . . . . . . . . . . . . . . . . . . 523.12 Supersonic skin-friction drag coefficient component for the stated

Mach number and altitude flight conditions. . . . . . . . . . . . . 533.13 Supersonic parasite drag coefficient component for the stated Mach

number and altitude flight conditions. . . . . . . . . . . . . . . . 563.14 Supersonic drag-due-to-lift factor. . . . . . . . . . . . . . . . . . . 583.15 Drag coefficients of high lift devices during takeoff and landing. . 59

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4.1 Aircraft weights estimation. . . . . . . . . . . . . . . . . . . . . . 614.2 CG vertical location of basic aircraft components. . . . . . . . . . 63

5.1 Directional stability derivatives for the subsonic Mach numberrange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.1 Short-period mode damping ratio limits. . . . . . . . . . . . . . . 867.2 Phugoid mode stability requirements. . . . . . . . . . . . . . . . . 877.3 Minimum time to double amplitude limits for spiral mode. . . . . 877.4 Roll subsidence mode time constant limits. . . . . . . . . . . . . 877.5 Dutch roll mode damping ratio and frequency limits. . . . . . . . 877.6 Variation of short-period pitching mode characteristics with speed

and altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.7 Variation of phugoid mode characteristics with speed and altitude. 897.8 Variation of spiral mode characteristics with speed and altitude. 917.9 Variation of roll subsidence mode characteristics with speed and

altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.10 Variation of dutch roll mode characteristics with speed and altitude. 94

8.1 Carbon dioxide emissions of subsonic airliner and SST design(6050 km distance flown). . . . . . . . . . . . . . . . . . . . . . . 103

8.2 Water vapor emissions of subsonic airliner and SST design (6050km distance flown). . . . . . . . . . . . . . . . . . . . . . . . . . . 103

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Nomenclature

A Area, m2

a Acceleration, m/s2

AR Aspect ratiob Span, mC Thrust SFC, g/KNsc Chord. mCD Drag coefficientCf Skin-friction coefficientCL Lift coefficientCm Pitching moment coefficientCP Pressure coefficientD Drag, ND Diameter,md Distance, mE Endurance, secEI Emissions indexe Oswald efficiency factorg Gravitational acceleration, m/s2

h Height, mI Area moment of inertia, m4

i Incidence angle, degK Drag-due-to-lift factorL Lift, NL Length, ml Length, mM Mach numberm Mass, kgm Mass flow, kg/sn Load factorP Pressure, Pap Roll rate, deg/secq Pitch rate, deg/secq Dynamic pressure, Pa

R Range, mr Yaw rate, deg/secr Radius, mRe Reynolds numberS Area, m2

T Thrust, NT Temperature, KT Period, sect Time, sect Thickness, mTR Throttle ratioV Speed, ms−1

W Weight, Nx Longitudinal position, my Span-wise (lateral) position, mz Vertical position, mα Angle of attack, degγ Flight path angle, degδ Control surface deflection, degε Downwash angle, degη Elevator deflection angle, radζ Rudder deflection angle, radζ Damping ratioθ Angle, degΛ Sweep angle, degλ Taper ratioµ Rolling friction coefficientξ Aileron deflection angle, radρ Density, kg/m3

σ Sidewash angle, degφ Euler roll angle, degω Angular frequency, rad/s

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1. Introduction

In recent years, the prospect for an supersonic passenger jet operation hasrisen again. The progress achieved in jet propulsion engines and the possibilityof composite materials usage at the aircraft structure are the main reasons thatthe success of the supersonic flight has become much more feasible nowadayscompared to the past.

NASA has already began to work on the preliminary design for a low-boomsupersonic passenger with the project Quiet Supersonic Technology (QueSST)[1], which has aroused its interest in the supersonic transportation, after the HighSpeed Research (HSR) program that phased out in 1999. Moreover, a newlyfounded company, named Boom Technology Inc., has started the developmentof a supersonic transport aircraft being able to fly at a speed of 2.2 Mach andcarry up to 45 passengers [2]. The aim of the Boom Technology design is toachieve fares comparable to the subsonic airliners business class and increasethe aircraft’s utilization and passengers load factors through the reduced seatcapacity of the aircraft, in comparison with the Concorde’s economic failure inthis aspect.

Apart from the economic feasibility for the supersonic passenger jet success,the environmental restrictions and impact comprise important factors as well.The overland flight ban, which has been implemented due to the sonic boom,and the increased air pollutants emissions have been primary concerns as regardsthe relevant regulation process and the mission accomplishment limitations.

In this project, an effort is made for a supersonic transport aircraft conceptualdesign, which could be viable in the current market, as a result of the increasinginterest on this aeronautical domain. The whole conceptual design process isdemonstrated and the design is evaluated regarding its performance, stability,and flying and handling qualities. Difficulties and problems that refer to thedesign process and the requirements satisfaction are addressed, and improvements,solutions are implemented or proposed, where possible.

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2. Conceptual Design

2.1 Market Research

Flying supersonic has always been a very promising and tempting idea. Aflight duration could become two or three times less in comparison to the relevantones of subsonic aircraft. After the Concorde retirement in 2003,the supersoniccivil transportation is not existent any more. Although the required technologyto construct supersonic aircraft exists, the economic sustainment of the concept,as the case of the Concorde, has shown is not feasible [3]. The supersonicoverland flight ban has also imposed one more important constraint. For theabove reasons, an excessive turn of the civil transportation from subsonic tosupersonic is highly improbable at least in the upcoming two or three decades.

However, the need for over-haul flights is expected to increase significantlyduring the next twenty years. According to the Airbus forecast about the globalmarket for the period from 2016 to 2035 an increase of 95 % is anticipatedfor the long-haul traffic [6]. Moreover, Boeing’s current market outlook (2015- 2034) is also forecasting a grow of 5 % annually in the long-haul traffic overthe relevant time period [7]. These forecasts regarding the market growth andthe increased demand in intercontinental flights set a quite promising ground forthe supersonic flight involvement, where its biggest advantage of diminishing theflight time could be maximally exploited.

Large supersonic transport aircraft, like the Concorde, will more likely notbe successful, since the added cost will be a significant hindering factor for thecommon passenger to choose it. For this reason, the supersonic aircraft willprobably recruit exclusively business class passengers from the regular airlineflights, since the ticket price could be in this case competitive. Therefore,operating full and smaller aircraft could be economically viable and profitable.Small supersonic airliners carrying about 15 to 25 passengers could allow theeconomic success of the concept, since the development risk and expenditurewill be significantly lower, as well as the potential market share [4].

Private individuals who are keen to buy business jets could be potentialcustomers for small supersonic aircraft too. In the upcoming ten years (2016 -2025) period, Bombardier forecasts a total of 8300 new business aircraft deliveries,when 2800 of them would be of medium size [8]. As the majority of them,according to this prediction, is going to be delivered to North America andEurope, fast and comfort transatlantic flights with a prestigious aircraft could

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be an interesting choice for some wealthy individuals, not caring so much foroverall cost. Other potential customers could be government agencies, sinceofficials could save this way valuable time, and big corporations.

Regarding the overland ban, the solution of planning routes that cover longoverseas distances seems the more realistic. Such routes can be for examplethe London – New York or the Paris – New York, which are now two of themost busy intercontinental routes in operation. Moreover, routes in south-eastAsia are expected to increase over the upcoming years, since Asia is forecasted,according to Boeing, to be the continent with the biggest demand in new aircraftdelivery with a global share of 38 % [7]. The growth that will be realized in thisarea offers also new opportunities for long-haul supersonic flights. An exampleis the Dubai – Singapore route, which can be performed almost overseas, by justmaking a small detour (less than 5 % in total distance covered) compared tothe direct route [4]. The possibilities given for mostly overseas long-haul flightsdecreases the necessity for an extreme low-boom design, which would reduce thesonic boom sound intensity level into the acceptable range for human hearing.Developing this kind of design would add extra development costs and woulddeteriorate in general the aerodynamic performance of the aircraft, resulting inreduced fuel efficiency, thus increasing further the cost, which has to be keptas low as possible. The environmental consequences due to increased pollutantemission to the atmosphere would be another important factor to be considered.

In conclusion, using all the above observations, the most feasible supersonictransport design, considering mainly the financial and secondly the technicallimitations, would be the construction of a quite small supersonic aircraft thatcould carry 15 passengers and have a range of 7200 km in order to executetransatlantic flights. The cruise speed would be 1.7 Mach, which is about thedouble of the regular cruise speed of a subsonic airliner. Although a higher Machnumber is preferred as more enticing for the clients, the choice of a moderatespeed would result in building an aircraft with reduced weight, having a positiveeffect in fuel consumption and noise generation [5].

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2.2 Initial SizingThe initial design process includes the specification of the desired requirements

according to the aircraft mission and role. Then, the mission profile sections haveto be defined. According to this mission profile, an initial estimation will be donefor the maximum take-off weight.

2.2.1 Desired Requirements

The desired requirements for the supersonic transport to be designed arepresented in Table 2.1.

Cruise speed 1.7 MachMaximum speed 1.7 Mach

Minimum payload mass 1900 kgCruise altitude 15 km

Range 7200 kmLoiter time 20 min

Landing distance 3500 mTakeoff distance (SL) 3500 m

Thrust specific fuel consumption (cruise) 26.9 g/KNs

Table 2.1 – Summary of aircraft requirements.

The payload mass corresponds to the 15 passengers plus the pilot, the co-pilotand two crew members. An average of 100 kg is assigned for each person on-boardincluding the luggages.

2.2.2 Initial takeoff weight estimation

The first step is to make an initial estimation of the takeoff weight (W0 ).The takeoff weight consists of the empty weight (We), the payload weight (Wp)and the fuel weight (Wf ) as shown in equation (2.1). The payload weight isdefined by the requirements, when the fraction of empty weight over the takeoffweight is given by the empirical relation (2.2) found in reference [9].

W0 = Wp +Wf + We

W0W0 (2.1)

We

W0= 0.32 + 0.66m−0.13

0 AR0.3(T

W0

)0.06 (W0S

)−0.05M0.05max in fps units (2.2)

The fuel weight is computed after calculating the weight fractions for thedifferent mission segments, since the total aircraft weight drop corresponds onlyto consumed fuel weight. The final fuel weight is then increased for safety reasons

14

by 6 %. The relevant weight fractions are calculated according to estimationsderived from historical data or with approximating relations. For each missionsegment i, the weight of the burned fuel is given by the relation

Wfi =(

1− Wi

Wi−1

)Wi−1 (2.3)

while the total amount of fuel for all n segments of the mission is estimated as

Wf = 1.06n∑i=1

Wfi (2.4)

Finally, the take-off weight can be computed using an iterative method forsolving the equations (2.1), (2.2) and (2.4), making an initial estimation for W0 ,which will then converge to the actual value.

In order to estimate the empty weight faction (We/W0 ), the aspect ratio(AR,), the wing loading (W0/S) and the thrust-to-weight ratio (T/W0 ) haveto be defined. For the supersonic transport a low aspect ratio of 3.2 is selected,since a long wing would result in a large value of the wave drag. Moreover, it isnot feasible to construct a light wing which could be structurally strong enoughto resist the relevant bending and torsional stresses in such high airspeeds andto be free of the aeroelastic phenomena effects.

The thrust-to-weight ratio and the wing loading will be defined in the relevantfollowing subsections. It should be stated here that the selection of the appropriatevalues for the two aforementioned parameters is a compromise. A large wingloading is more preferred for the supersonic aircraft, which results in smallervalues of thrust-to weight ratio and thus lower thrust requirements. However,the wing loading is limited from a reasonably low stall speed requirement andconsequently from the landing and takeoff distance restrictions.

2.2.3 Mission profile and segments weight fractions

In Figure 2.1 the different segments of the mission profile for the transportaircraft are presented. The typical mission of the aircraft includes:

• taxi, warm-up and takeoff, 1

• climb, 2

• cruise, 3

• loiter, 4

• descend, 5

• landing and taxi back, 6

15

Figure 2.1 – Mission profile division.

The weight fractions for the different mission segments are calculated usingthe following relations [9]

W1W0

= 0.97 (2.5)

W2W1

= 0.991− 0.007Mcruise − 0.01M2cruise (2.6)

W3W2

= e−

RC

V (L/D)cruise (2.7)

W4W3

= e−

EC

V (L/D)max (2.8)

W5W4

= 0.99 (2.9)

W6W5

= 0.992 (2.10)

For the weight fraction estimation (eq. 2.7) of the cruise phase, the Breguetrange equation is used. The specific fuel consumption C for the cruise is the onedefined from the requirements before, while for the loiter the typical value ofthe 22.7 g/KNs has been used [9]. The maximum lift to drag ratio (L/Dmax) isequal to the relevant value of the loiter phase for a jet aircraft. The correspondentvalue for the condition of the most efficient cruise is 86.6% of the L/Dmax for ajet aircraft [9] and is approximated using the relation [11](

L

D

)cruise

= 11M−0.5 (2.11)

16

2.2.4 Thrust-to-weight ratio

Cruise

The required T/W during cruise can be simply approximated using the rigidequations of motion for steady flight. In this case, the thrust should equal thedrag and the lift should equal the weight, assuming that the thrust installationangle is zero (thrust vector aligned with the velocity vector) and disregardingthe angle of attack influence. Thus(

T

W

)cruise

=(L

D

)−1

cruise(2.12)

The above equation is a good initial approximation, although it underestimatesthe drag, since during the level and unaccelerated flight the angles of attackexperienced are quite small.

Takeoff

Having estimated the thrust-to-weight ratio required for the cruise condition,the correspondent value for takeoff can be calculated with the relation(

T

W

)TO

=(T

W

)cruise

(Wcruise

WTO

)(TTOTcruise

)(2.13)

where (Wcruise

WTO

)=(W2W1

)(W1W0

)= βc (2.14)

The fraction (TTO/Tcruise) can be computed using the installed engine thrustlapse equations for maximum thrust presented in [10], for cruise at the desiredaltitude and for sea level flight. These equations apply to the expected performanceof the advanced engines in the 2000 era and beyond. The flight altitude in theserelations are introduced as the ratio between the static temperature (θ) and thestatic pressure (δ), respectively, at the flight altitude to the corresponding valuesat sea level, as shown in equations (2.15) and (2.16).

θ = Talt/TSL (2.15)

δ = Palt/PSL (2.16)

The nondimensional temperature (θ0) and pressure (δ0) are defined using thecorrespondent total temperatures and pressures at flight altitude, respectively,as

θ0 = Ttalt/TSL = θ

(1 + γ − 1

2 M2)

(2.17)

17

δ0 = Ptalt/PSL = δ

(1 + γ − 1

2 M2) γγ−1

(2.18)

The specific heat ratio (γ is equal to 1.4 for atmospheric air. The thrustlapse (α) is defined as the maximum thrust at flight altitude over the maximumthrust at sea-level flight and can be calculated from the equations (2.19) and(2.20). For a low-bypass ratio turbofan engine, the so-called dry thrust lapse,without the usage of afterburner, is estimated as

αdry ={

0.6δ0 for θ0 ≤ TR0.6δ0(1− 3.8(θ0 − TR)/θ0) for θ0 > TR

(2.19)

and the so-called wet thrust lapse, using the afterburner, is estimated as

αwet ={δ0 for θ0 ≤ TRδ0(1− 3.5(θ0 − TR)/θ0) for θ0 > TR

(2.20)

The term TR appeared in the above equations is the throttle ratio, whichis equal to the so-called value θ0 ,break [10]. These equations are valid for valuesof the theta break greater than one. The theta break relates two importantconstraints of the turbine engine, the compressor pressure ratio and the turbineinlet temperature, being actually the point where the engine control system mustswitch from limiting the compressor pressure ratio to limiting the turbine inlettemperature. The θ0 ,break should be chosen by the designer so that it provides thebest balance of engine performance over the expected range of flight conditions.In this case of the supersonic transport, the throttle ratio should be greater thanone in order to fulfill the supercruise requirement. For this reason, it is set to1.2, so that it operates closer to the optimal value of θ0 , as given by the cruisecondition, thus sustaining thrust to higher values of Mach number.

2.2.5 Wing loading

Having estimated the thrust-to-weight ratio at takeoff, the wing loading willbe estimated for the most critical conditions of the mission, which are the takeoff,stall and landing. After computing the relevant values, the minimum wingloading obtained will be used to calculate the wing reference area.

Stall

For the calculation of the wing loading for the stall condition, an initialmaximum lift coefficient (CLmax) has to be estimated. For a supersonic aircrafthaving a low aspect ratio wing and a large leading edge sweep, the value forCLmax would be quite small. In this case, a CLmax of 1.6 will be assumed, whichis a typical value for supersonic wings. Since a moderate value for CLmax canonly be obtained for the supersonic aircraft configuration, in order to avoid a

18

low wing loading resulting in a large wing area, a very low stalling speed cannotbe achieved. However, it should be kept as low as possible so that the landingdistance requirement can be fulfilled too. For this reason, a stalling speed of 68m/s has been selected at sea-level flight. Therefore the wing loading at stall canbe calculated as (

W

S

)stall

= 12ρSLV

2stallCLmax (2.21)

Takeoff

The wing loading at takeoff is given from the relation [9](W

S

)TO

= (TOP )σCLTO(T

W

)TO

in fps units (2.22)

where σ is the air density ratio (density at takeoff altitude over density atsea-level), set in this case equal to one, assuming operation from airports atalmost zero altitude, like the Heathrow in London and the John F. Kennedyin New York. The takeoff speed is specified from the FAR Part 25 regulationsfor civil aircraft as 1.1 times the stall speed. Hence, the takeoff lift coefficient(CLTO) is obtained by dividing the maximum lift coefficient (CLmax) with 1.21.The takeoff parameter (TOP) can be obtained solving equation (2.22), whereincreasing the TOP results in a requirement for increased takeoff distance. Inthis case, the TOP should be chosen so that the aircraft fulfills the takeoffdistance requirement, while keeping the wing loading as high as possible.

Landing

The maximum wing loading at landing will be estimated using the maximumlanding distance requirement. A relation that connects the two parameters isthe following [9](

W

S

)land

= 180

(dland1.67 − da

)σCLmax in fps units (2.23)

where the landing distance (dland) is divided by 1.67 to provide the requiredsafety margin set by regulations (FAR 25) and da is the obstacle-clearancedistance, which is equal to 1000 ft for an airliner-type aircraft.

2.2.6 Constraint analysis

After estimating the thrust-to-weight ratio and the wing loading of the aircraftfor the aforementioned conditions, two important constraints, which relate thetwo parameters, will be evaluated so that the final values for both parametersare specified. These parameters are the takeoff distance and the supercruise

19

requirements. The two conditions will be evaluated using the relevant relationsfrom reference [10].

Takeoff distance

An initial approximation for takeoff distance, consisting of the ground rolland the rotation distance, can be made with relation (2.24) assuming that thethrust force is much larger than the resistance forces in the ground roll

dTO =(

k2TO

gρSLCLTOαdry(TSL/WTO)

)(W

S

)TO

+(trkTO

√2

ρSLCLTO

)√(W

S

)TO

in fps units(2.24)

where kTO is the ratio of takeoff speed over stall speed (1.1 as defined in theprevious subsection) and tR the total rotation time needed for the aircraft tomove from the flat to the nose-up attitude needed for takeoff (normally 3 sec).The wet thrust lapse parameter can be estimated from the equation (2.20).

Supercruise

An important restriction for the supersonic transport is that it should cruiseat the desired supersonic Mach number and altitude, without using the afterburner.This is the so-called supercruise condition and it is essential in order to achieveeconomically feasible supersonic flights at long range. The supercruise condition,stated here, estimates the required thrust-to-weight loading needed at takeoff,which is calculated as

(TSLWTO

)= βcαdry

(Kβcq

(W

S

)TO

+ qCD0βc (W/S)TO

)in fps units (2.25)

where αdry and βc are given from the equations (2.19) and (2.14) respectivelyand q is the dynamic pressure for the given cruise flight speed and altitude.The zero lift drag coefficient (CD0 ) and the K coefficient of the lift-drag polarequation (these two coefficients will be analyzed in more detail later on) areinitially approximated using typical values for the specific cruise conditions as0.03 and 0.3 respectively.

2.2.7 Initial sizing results

The results obtained from the initial sizing analysis are presented in Table2.2. The thrust-to-weight ratio corresponds to the maximum value obtained,which is the one satisfying the supercruise condition.

20

Empty weight fraction 0.4715Fuel weight fraction 0.4641

Takeoff mass 29499 kgWing loading (takeoff) 5110 N/m2

Wing loading (stall) 4539 N/m2

Wing loading (landing) 5629 N/m2

Maximum thrust-to-weight ratio 0.5851Takeoff distance (SL) 2283 m

Table 2.2 – Summary of aircraft specifications.

2.2.8 Wing

Wing geometry

In this section, the geometry of the wing will be defined. The choice forthe wing is the trapezoidal with aspect ratio of 3.2, as stated previously. Otherparameters to be defined are the leading edge wing sweep (ΛLE) and the taperratio (λ).

The wing sweep is being used in transonic flow in order to increase the criticalMach number (the freestream Mach number at which the local Mach numberon the aircraft first reaches the sonic speed) and in supersonic flow in order todecrease the loss of lift, associated with supersonic flight. Another importantfeature for using swept wings at supersonic flows is the delay of the appearanceof aeroelastic divergence, which is critical for a light weight design for such highvalues of dynamic pressure. For this aircraft configuration a LE wing sweepangle of 45 deg has been chosen, which is although a bit larger compared tothe Mach cone angle (arcsin(1/M )), so that the wing is capable of creating thenecessary lift for satisfying the takeoff and landing distance requirements.

The usage of a swept wing results in the requirement of having a highlytapered wing in order to preserve the desired elliptical lift contribution overthe wing. Producing a lift distribution over the wing that resembles the idealelliptical one has the important effect of reducing the lift induced drag. However,a very low taper ratio has the consequence of tip stalling tendency. Moreover,it can be limited by requirements about adequate chord near wing tips for theailerons placement. Recommended values for highly swept wings in supersonicflow are 0.2 - 0.3 [9][16]. For practical and structural reasons, the lower value of0.2 is chosen, since results in a larger chord near wing root, which is needed forengines placement, as well as grater internal volume due to increased maximumthickness, making it possible to house the landing gear and fuel tanks.

The aircraft will have a low-wing configuration mainly for the practical reasonof placing the landing gear. A high-wing configuration is not feasible, sincefor low aspect ratio supersonic wings where thin airfoils are used, there is not

21

enough space for their housing. An external blister would be unacceptable,since it would increase the drag significantly. A mid-wing configuration is notused in passengers aircraft for structural reasons, since the loads have to becarried across the fuselage, reducing the internal usable volume of the fuselagesignificantly. A low-wing configuration usually is accompanied with a dihedralangle. However, the high wing sweep is contributing to the dihedral effect too,creating a quite high effective dihedral angle, which diminishes the need of havinga wing geometric dihedral. For this reason, an initial zero dihedral angle will beconsidered for this design.

Wing sizing

The first step of the wing sizing is to calculate the wing area. This can besimply done using the estimation for the minimum wing loading in the followingequation

SW = m0g

(W/S)min(2.26)

Knowing the wing area, aspect ratio and taper ratio of the chosen trapezoidalwing, the expressions about some important wing properties are presented.

Wing span:

bW =√AR · S (2.27)

Chord at root:

croot = 2Sb(1 + λ) (2.28)

Chord at tip:

ctip = λcroot (2.29)

Mean aerodynamic chord (MAC):

cW = 23croot

(1 + λ+ λ2

1 + λ

)(2.30)

Spanwise location of MAC with respect to the aircraft longitudinal axis ofsymmetry:

YW = b

6

(1 + 2λ1 + λ

)(2.31)

22

Wing dimensions

In table 2.3 the basic wing dimensions are presented for the initial design.

Area 63.7487 m2

Span 14.2827 mRoot chord 7.4389 mTip chord 1.4878 m

Mean aerodynamic chord 5.1246 mSpanwise location of MAC 2.7772 m

Table 2.3 – Summary of wing basic dimensions.

2.2.9 Tail

The tail area can be calculated using the tail volume coefficients presented in[9] for the horizontal and the vertical tail. These coefficients are used to relatethe wing to the tail size, so that an initial estimation for the vertical (VT) andhorizontal (HT) tail area can be made from the following equations.

SV T = VV T bWSWLV T

(2.32)

SHT = VHT cWSWLHT

(2.33)

where VV T , VHT the volume coefficient, and LV T , LHT the moment arm for thevertical and the horizontal tail respectively. Typical values for the cV T and cHTare provided in [9]. The value selected for the horizontal tail is 0.4, which issmaller than the recommended typical value, since the choice of a whole-movingsurface has been made in order to decrease the horizontal tail volume. Decreasingthe horizontal tail volume is critical in order to achieve a area-ruled design anddecrease the wave drag. The volume coefficient for the vertical tail has been setto the typical value of 0.09 for the jet transport. The tail arm moment L , whichis initially approximated as the longitudinal distance of the quarter position ofthe wing mean chord to the quarter mean chord position of the tail, has beenset to 40% of the fuselage length for both the vertical and horizontal tail arm.

In order to model the tail geometry, typical values have to be used for itsgeometric properties. The horizontal stabilizer has been modeled as a straighttrailing edge tapered wing, with a sweep angle at the leading edge of 50 deg,which is typically 5 deg larger than the wing sweep, so that it experiences agreater critical Mach number compared to the wing. The vertical stabilizer hasbeen modeled as a trapezoidal wing having a 60 degrees leading edge sweepangle. The selected values for the aspect ratio are 2.5 for the horizontal and 1.3

23

for the vertical stabilizer, while the taper ratio is 0.15 and 0.2 for the horizontaland the vertical stabilizer respectively.

For computing the rest of the geometric properties of the horizontal andvertical stabilizer, like the mean aerodynamic chord, the span etc., the expressions,which have been presented for the wing in the previous subsection, can be used.

Tail dimensions

In table 2.4 the basic wing dimensions are presented for the initial design.

Horizontal stabilizer Vertical stabilizerArea 12.0995 m2 7.5875 m2

Span 5.4999 m 3.1407 mRoot chord 3.8386 m 4.0265 mTip chord 0.5613 m 0.8053 m

Mean aerodynamic chord 2.6068 m 2.7738 m

Table 2.4 – Summary of tail basic dimensions.

2.2.10 Fuselage

Fuselage dimensions

The fuselage has been dimensionalized taking two important factors intoconsideration. Firstly, the existence of enough usable volume to host the passengersand secondly, the area ruling design, which will be further analyzed during thewave drag calculation. Briefly the fuselage has to be squeezed at the area wherethe wing is placed (”coke-bottling” design), so that a smooth volume distributionand a smaller cross-sectional area is achieved.

An initial estimation for the fuselage length for a jet transport is given usingthe relation (2.34) based on statistical data [9].

Lfus = 0.287m0.430 (2.34)

The typical compartment properties for first class seats are seat pitch of 1m and seat width of 60 cm, where the aisle width should be about 60 cm andits height more than 193 cm [9]. Thus, the maximum diameter has been set to2.6 m, which is a value providing enough space, while keeping the cross-sectionalarea as low as possible. The length of the fuselage has been enlarged by about3 m compared to the stimation given from equation (2.34). This is done mainlyfor two reasons. While the fuselage maximum diameter is enough to host twopassengers sitting side by side, for the portion of fuselage which is squeezedthis would not be possible and just one passenger could be hosted there. The

24

need to place also a lavoratory increases the compartment’s length requirements.Additionally, the typical cabin compartment to overall length ratio for a supersonictransport is about 0.55 [16], thus the lengthened fuselage should provide enoughspace for hosting all the 15 passengers. Finally, the supersonic aircraft has asharper and longer nose in comparison to the subsonic aircraft, and a typicalvalue of its nose length to diameter ratio is about 4 [16]. The reason for that isto avoid strong bow shock waves forming at the fuselage nose, which lead to asignificant increment of the wave drag. However, having a very low nose lengthto diameter ratio would create practical problems with the cockpit housing andthe unhindered pilots’ visibility, especially during landing.

Fuselage lofting

The designed fuselage consists of three parts: the conical nose, the maincylindrical fuselage and the fuselage tail. The main cylindrical fuselage consistof three parts. The first one is a cylinder assembled with the nose till it reachesthe maximum diameter, the second part is a cylinder of the maximum diameterbut squeezed in the lateral direction (the fuselage width is manipulated whilethe height remains constant) and the final part which is a cylinder assembledwith the fuselage tail. The fuselage has been lofted in Matlab and its model canbe seen in figures 2.2 and 2.3.

Figure 2.2 – Fuselage top view.

Figure 2.3 – Fuselage side view.

As it can be seen in fig. 2.3, the tail fuselage is converging towards thehigher side, so that the empennage can be placed higher up of the wing andthus minimize the aerodynamic interactions due to the wing wake. The basicdimensions of the fuselage lofting are presented in table 2.5. The fuselage totalvolume has been computed to be 78.75 m3.

25

Nose length 4 mNose maximum diameter 1.8 mCylindrical part length 19 m

Cylindrical part maximum diameter 2.6 mSqueezed part minimum width 1.56 m

Fuselage tail length 4 mFuselage tail maximum diameter 2 m

Table 2.5 – Fuselage basic dimensions.

Fuselage-wing assembly

A low-wing configuration has been chosen for this aircraft design. Theposition of the quarter mean aerodynamic chord, which corresponds to theaerodynamic center in subsonic flight, has been placed in the longitudinal direction14.07 m rear of the fuselage nose. The fuselage-wing assembly, incorporating thearea ruled design, can be seen in figures 2.4 and 2.5.

It has to be mentioned that the wing has been placed in that position due totwo factors. The first one is to have a long enough tail arm moment (L), whichresults in a smaller tail size and demands the placement of the wing forward.However, as it will be observed in the following subsection, the placement of thewing too much forward, will have the consequence of a much longer and heavierlanding gear and perhaps an unacceptably high load acting on the nose landinggear.

Figure 2.4 – Fuselage-wing assembly top view.

26

Figure 2.5 – Fuselage-wing side view.

2.2.11 Landing gear

In order to meet the requirements for the airframe layout and to avoid anyincrement in the aerodynamic drag, the way of how the landing gear will bestowed has to be decided. First of all, the landing gear arrangement has beenchosen to be the common ”tricycle” gear, with two main landing gears aft of theaircraft center of gravity (CG) and one nose landing gear forward of the aircraftCG. The number of wheels per strut are typically dependent on the aircrafttakeoff weight. For aircraft weighing 60,000 to 175,000 lbs, such as the currentdesign, two tires per struts are recommended [17]. The usage of two tires is alsopreferable for safety reasons, like in the case of a flat tire.

One issue that is faced with the supersonic aircraft is the existence of verythin wings, which does not give the opportunity for the main landing gear to bestowed inside the wing easily, especially for configurations with two tires per strutlike the current. For this reason, the strut will be stowed inside the wing, whilethe tires will be stowed inside the fuselage, after retraction, where the availablevolume is much bigger (inward retraction). The aforementioned concept to beused is visualized in fig. 2.6 for a subsonic airliner.

Figure 2.6 – Airbus A320 main landing gear retraction and stowage.

27

The main landing gear length and location can be determined using theconceptual design method from reference [17]. The initial recommended locationfor the main landing gear is about 55 % of the wing MAC. The main landing gearlocation is then adjusted using the 15 deg angle rule in the static position shownin fig. 2.7. For the current design, the correspondent location was estimated tobe at about 15.6 m aft of the fuselage nose. The length then should be set sothat the tail does not hit the ground during landing. Using the recommended 12deg angle for fuselage tail tipping avoidance, which should not be much smallerthan the stall angle, the main landing gear length can be approximated as 2.45m.

Figure 2.7 – Main landing gear logintudinal location [17].

The nose landing gear has been selected to be a forward retracting, whichis preferred since in the case of a failure the gravity and air drag assists thegear to reach the down-and-locked position. The nose landing gear lengthis initially set to be equal to the main landing gear length for the low-wingconfiguration. The longitudinal position of the nose landing gear depends on theaircraft position of the CG. For a first approximation the most aft location ofthe CG is set just forward of the aerodynamic center (quarter-chord of MAC).Assuming its longitudinal distance from the main landing gear location to be 12m, the correspondent static loads on the main and the nose gear can be estimated[17].

Max static main gear load (per strut) % = (B −Bm)/2B (2.35)

Max static nose gear load % = (B −Bn)/2B (2.36)

28

where the relevant distances are described in fig. 2.8. For the given distances,the landing gear load is about 43.5 % per main landing gear strut and 13 % forthe nose landing gear strut, a loading contribution which is not optimal (8-10 %preferable static loading for nose landing gear considering the most aft locationof the CG) but within the acceptable range for the initial layout.

Figure 2.8 – Diagram of nose landing gear location estimation.

The main landing gear tires can be sized too, using the obtained results andthe following statistical relations for transport aircraft [9]. Their diameter andwidth are estimated from the equations (2.37) and (2.38) as 84.1 cm and 26.3cm respectively.

Dtire = 5.3m0.315tire (2.37)

wtire = 3.9m0.48tire (2.38)

where mtire is the load per tire or wheel in kg.

2.2.12 Propulsion

For the propulsion system, a similar concept to Concorde will be followed,with each engine mounted at the lower side of the wing. The engine locationis a quite complex task, mainly due to the engine intake, which especially forsupersonic flows has to be designed very carefully in order to control and providethe airflow needed for the engine operation. Other things that deteriorate theengine performance is the location of the engine inlet in a position where itingests distorted airflow, such as in the wing wake, which can cause stall tothe compressor. For supersonic fighters the most common configuration is touse fuselage side-mounted inlets. This is a location that provides short ductsand relatively clean air [9]. However, this is not possible for the low-wingconfiguration transport aircraft for practical reasons, for instance due to theneed of placing the engines outside the fuselage and the need of landing gear

29

stowage. Using a configuration like the Concorde, has the advantages of havinga quite undisturbed airflow, of avoiding interferences between the two exhaustnozzles for not being placed side by side, and for decreasing the structural stresseson the wing, due to the inertial relief effect (the wing-root shear force can be thisway significantly reduced). A disadvantage of this configuration comes from thespatial requirement of mounting the engines directly at the wing, since neitherthe engine nor the inlet can be too long. Moreover, the nozzle placement atthe wing trailing edge will reduce the usable wing area for the placement of therespective control surfaces (flaps, ailerons).

Air intake

In order to have a proper operation for the compressor blades, the airflow hasto be decelerated to about 0.4 Mach. The air intakes for supersonic aircraft aresophisticated devices, which need to decelerate the supersonic flow to subsonicthrough shock waves. The efficiency of the intake is expressed from the reductionin total pressure loss, which is mainly dependent of the shock-wave pattern [12].The air intakes used for supersonic flight are divided in two parts: the convergingsupersonic inlet and the diverging subsonic diffuser. The principles followed fora conceptual layout of the intake are presented in the following subsections.

1. Supersonic inlet

The choice of the supersonic inlet type is mainly determined from the designMach number. A ”pitot” or normal shock inlet, decelerating the supersonic flowto subsonic through a single normal shock wave, results in big total pressurelosses for higher Mach numbers, which decrease significantly the inlet efficiency.For example, for Mach number 1.7, which is the one of interest for this design,the pressure recovery is just 85.57 %. In this type of intake the maximum inletmass flow is achieved when the normal shock is located right at the cowl lipposition (fig. 2.9(a)).

(a) Pitot or normal shock inlet (b) Internal shock inlet

Figure 2.9 – Supersonic air inlets.

Another type of air inlet is the internal compression, which is a ”two -

30

dimensional ramp” inlet. When this inlet operates at optimal design condition,theflow is decelerated by two oblique shocks existing at the entrance of the facingramps, before a normal shock takes place at the minimum section position insidethe intake (fig. 2.9(b)). However, when operating at off-design conditions it ispossible the normal shock to take place outside the inlet (inlet not ”started”), asituation that can stall the engine [9]. Moreover, the boundary layer on the inletwalls can tolerate only a very modest adverse pressure gradient before separating,a fact that leads to a smooth decrease of the inlet area and consequently to alonger and heavier intake [23].

The type of supersonic inlet to be used in this design is the external compressionrectangular ramp inlet, where the weak oblique shocks are generated outside theinlet and are followed by a normal shock at the cowl lip (fig. 2.10). In order todesign an efficient intake, the number of oblique shocks and the relevant wedgeangles have to be chosen. The external shock intake length can be initiallyapproximated using the shock angles computed from the correspondent rampangles. The cowl lip is then located just aft of the shocks [9]. In this case, a 5% elongation of the computed external inlet length has been adopted as a safetymargin.

Figure 2.10 – Three-shock external inlet.

The inlet efficiency can be optimized through the appropriate selection of thewedge angles. In order to achieve very high efficiency, the inlet will incorporatethree weak oblique shocks before the normal shock. The Mach number (M ), thewedge angle (δ), the shock angle (θ) and the total pressure recovery (Pt2/Pt1 ),are related using the equations (2.39), (2.40) and (2.41) for compressible, adiabaticflow of a perfect gas (for air γ=1.4) [18]. The correspondent notation can beseen in fig. 2.11.

M2 =√

36M41 sin2 θ − 5(M2

1 sin2 θ − 1)(7M21 sin2 θ + 5)

(7M21 sin2 θ − 1)(M2

1 sin2 θ + 5)(2.39)

tan δ = 5 M21 sin 2θ − 2 cot θ

10 +M21 (7 + 5 cos 2θ)

(2.40)

31

Pt2Pt1

=(

6M21 sin2 θ

M21 sin2 θ + 5

)7/2 ( 67M2

1 sin2 θ − 1

)5/2(2.41)

Figure 2.11 – Oblique shock wave.

The above equations can be used for the final normal shock too, setting θ=90deg. In table 2.6, the wedge angles and the rest of the results of the four-shockexternal compression inlet design are presented.

Wedge angle (deg) Mach number Shock angle (deg) Pressure recovery (%)5.8960 1.5955 39 99.965.7782 1.4920 42 99.966.1309 1.2714 50 99.71

- 0.8009 90 98.40

Table 2.6 – Properties of the designed 4-shock externalinlet for freestream Mach number M1=1.7.

The total pressure recovery for the designed supersonic inlet reaches 98.04% for decelerating the airflow from 1.7 to about 0.8 Mach. During off-designoperation, the mass flow demand at lower speeds is reduced. This decreaseresults in the static pressure rise at the compressor inlet, which forces the flowto spill outside the compressor. Since this redundant subsonic flow has to spillout, the normal shock moves farther upstream from the lip cowl, increasing theso-called spillage drag significantly [22]. In order to avoid this effect and keep thenormal shock attached at the cowl lip, a by-pass door is opened in the diffuser,so that the excess air can be thrown away before reaching the compressor. Thistechnique has been adopted in the Concorde’s air intake, as can be seen in fig.2.12. It can be also observed in this figure the knife-edge shape of the intakesections, which is a necessary feature of the supersonic inlet, so that large shockangles and consequently increased wave drag can be avoided.

32

Figure 2.12 – Concorde rectangular ramp intakes.

Finally, a preliminary estimation can be made for the required capture areasize according to an approximation found in [9], which correlates the capture areawith the Mach number and the mass flow. For the freestream Mach number of1.9, which corresponds to a safety margin of 0.2 Mach higher than the aircraftmaximum design condition, the capture area (Ac) is approximated as 0.0054times the maximum air mass flow (m).

2. Subsonic diffuser

In the subsonic diffuser the airflow is further decelerated from the subsonicMach number obtained after the normal shock to 0.4 Mach to meet the compressoroperation conditions. This is achieved through a diverging duct, which meansthat the area inside the intake should increase. The throat area to the enginefront face area can be estimated from the relation (2.42), which is used to expressthe maximum area ratio between any two stations into the diffuser in terms ofthe Mach number, corresponding to maximum air mass flow [23].

AthroatAengine

= M1M0

(1 + 0.2M2

01 + 0.2M2

1

)3

(2.42)

In this design, the objective is to slow down the flow from 0.8009 to 0.4 Machand thus the relevant ratio between the throat and the engine area is computedas 0.6527, which means that the respective diameter ratio between the throatand the engine would be 0.8079.

The subsonic diffuser has a typical efficiency of 97 - 98 %, which will resultto a total efficiency of the supersonic air intake of about 95 % for the givendesign. In order to avoid high viscous forces on the duct walls and consequentlyseparation of the boundary layer flow, which would increase the total pressurelosses, the diffuser has to incorporate small expansion angles. The upper limitof the slope is considered to be 10 deg [23]. Therefore, a slope of 6 deg has been

33

chosen for the diffuser design to ensure high intake efficiency. Knowing the ductslope and the correspondent throat and engine diameters, an initial estimationcan be made for the subsonic diffuser length.

Engine selection

The main criteria for the engine selection is to provide enough thrust forthe aircraft operation (satisfy the maximum thrust-to-weight ratio), to have alow thrust specific consumption, so that it it satisfies the requirements, a lowweight and a small size, to avoid increased parasite drag. For satisfying thefuel consumption requirement, it is preferable to incorporate a low-bypass ratioafterburning turbofan instead of a turbojet. Another benefit of the turbofanengine is the reduced noise, which is of big interest especially during take-off.

After a research for the available engines and the relevant manufacturer data,the engine selected was the EJ200 (fig. 2.13), a turbofan engine that is usedas powerplant for the Eurofighter Typhoon. The EJ200 has been developedand produced in an international cooperation among Rolls-Royce, Avio, ITP(Industria de Turbo Propulsores) and MTU Aero Engines. The relevant enginespecifications are shown in table 2.7. The presented data have been retrievedfrom one of the engine manufacturers, particularly the MTU Aero Enginesproduct leaflet [24]. Two EJ200 engines will be incorporated in the supersonictransport design.

Maximum thrust, reheated 90 kNMaximum thrust, dry 60 kN

Bypass ratio 0.4Overall pressure ratio 26:1

Specific fuel consumption, reheated 48 g/kNsSpecific fuel consumption, dry 21 g/kNs

Air flow rate 77kg/sLength 4 m

Maximum diameter 74 cmWeight 1010 kg

Table 2.7 – EJ200 engine specifications.

Propulsion system dimensions

After having chosen the jet engine to be used for the supersonic aircraft,the dimensions for the intake and thus for the whole propulsion system can bequantitatively determined (Table 2.8). For simplicity, an initial rough estimationof a rectangular nacelle with width equal to 1.05 times the engine diameter will beincorporated in the design, for the total propulsion system length, excluding theexhaust nozzle. The relevant ratio of intake length to engine diameter is about

34

3.19. The two nacelles have been placed in distance 2.9 m from the aircraftlongitudinal axis of symmetry.

Figure 2.13 – EJ200 turbofan engine.

Intake length 2.36 mCapture area 0.4158 m2

Throat diameter 59.8 cmNacelle length 5.36 mNacelle width 77.7 cm

Table 2.8 – Propulsion system basic dimensions.

2.2.13 Aircraft model

The aircraft model has been created in Matlab, using the aforementioneddimensions. The airfoils used for the wing and the tail modeling are discussedin the following chapter. The relevant views of the model can be observed infigures 2.14, 2.15 and 2.16.

Figure 2.14 – Aircraft model top view.

35

Figure 2.15 – Aircraft model side view.

Figure 2.16 – Aircraft model front view.

In table 2.9, some important geometric properties of the aircraft are presented,in particular its computed exposed and wetted areas.

Wing exposed area (Sexp) 48.2012 m2

Wing wetted area (Swwet ) 88.9441 m2

Fuselage wetted area (Sfwet ) 164.1938 m2

Horizontal tail wetted area (SHTwet ) 11.2816 m2

Vertical tail wetted area (SVTwet ) 15.5985 m2

Nacelles wetted area (Snacwet ) 26.8351 m2

Table 2.9 – Aircraft exposed and wetted areas.

36

2.2.14 Control surfaces

The primary control surfaces for this design are the aileron and the rudder.The model will not incorporate an elevator, because the horizontal tail has beenmodeled as a whole moving surface. A guidance for their initial geometry isprovided in reference [25].

The aileron spans the 28% of the wing, and in particular from 63 till 91%of the semi-span. The outer 9% of the wing semi-span is excluded, since it isplaced at the wing tip vortex flow region and thus provides little effectiveness.The aileron chord is modeled to include the aft 20% of the wing chord. Theaileron geometry and location is illustrated in the figure 3.8 of the upcomingchapter.

The rudder spans the 90% of the vertical stabilizer, except for the outer 10%near the vertical tail tip. The rudder chord is modeled as 35% of the verticalstabilizer chord. The rudder geometry is depicted in figure 2.17.

The total aileron surface is 2.27 m2, or 3.56% of the wing reference area. Therudder surface is 2.55 m2 or 33.6% of the vertical stabilizer area.

Figure 2.17 – Rudder illustration.

37

3. Aerodynamics

3.1 Airfoils

3.1.1 Airfoil selection

The main feature of the aircraft to be designed is the efficient supersonicflight. The dominant characteristic of the supersonic flow is the presence ofshock waves. In the case of a sharp-nosed wing section, oblique waves will beformed on the nose with the flow remaining supersonic. On the other hand, ifa nose which is blunt is incorporated, the flow would detach from the nose tipand would form a bow shock creating a region of subsonic flow behind the wave.That is a very important factor to avoid the blunt wing section nose in orderto keep the wave drag low. Consequently, in the supersonic aircraft thin airfoilsare being used with typical thickness ratio 4 - 6 %.

Typical wing sections that are used for supersonic aircraft are the NACA64-series. For instance, the fighters F-15 and F-16 are using 64A modified airfoils.These airfoils are designed for maximizing laminar flow, decreasing drag andincreasing the critical Mach number.

For the wing, the NACA 64−006 section has been chosen. This is a symmetricairfoil with 6 % thickness ratio.

For the horizontal stabilizer, the same symmetrical airfoil used for the winghas been installed. Since the horizontal tail is swept back more than the wing,using the same airfoil, ensures that it will have a greater critical Mach number,as well as greater stall angle, which is necessary for recovery.The particular airfoiloffers a a low drag coefficient (Cd) too.

For the vertical stabilizer, the symmetric airfoil NACA 64 - 009 has beenchosen. This airfoil offers a quite high Cla, which is an important factor forhaving satisfying directional stability, while minimizing the weight, due to itsrelative low thickness. The low drag coefficient (Cd) of the airfoil is also anotherreason for its selection.

The chosen airfoils and their coordinates, according to NACA, can be foundin Appendix A.

38

3.1.2 Subsonic aerodynamic coefficients

The aerodynamic coefficients for the selected airfoils in subsonic flow has beencalculated with the XFOIL airfoil design/analysis system, which is a viscous,panel method program with boundary layer analysis. According to the programcreator, XFOIL is a tool that is particularly applicable to low Reynolds numbersand works better for subcritical airfoils [26]. Thus, the calculated aerodynamiccoefficients have been compared to published experimental data for the particularairfoils found in reference [15] and presented in Appendix B.

The zero angle of attack lift (Cl0 ) and pitch moment (Cm0 ) coefficients equalzero for the used symmetrical airfoils.

NACA 64 - 006

In figure 3.1, the lift curve obtained with the XFOIL simulation is presented.The resulting aerodynamic coefficients obtained from both aforementioned sourcesare presented in table 3.1. A significant difference can be observed for theClmax and the stall angle. The data to be used for the ongoing analysis arethe experimental data, since for the angles of attack near stall the simulationwith XFOIL failed to achieve convergence of the solution.

Figure 3.1 – NACA 64-006 lift curve for Re = 9·106 (XFOIL).

XFOIL simulation Experimental dataLift curve slope (Cla), deg−1 0.1077 0.1040

Maximum lift coefficient (Clmax) 0.73 0.83Minimum drag coefficient (Cd) 0.0049 0.0038

Stall angle (deg) 10 8.5

Table 3.1 – NACA 64-006 aerodynamic coefficients ( Re = 9·106).

39

NACA 64 - 009

In table 3.2 are presented both the simulation and the experimental data thathave been obtained. Significant differences for the Clmax and the stall angle canbe observed for this airfoil as well. Knowing the weakness of the supercriticalairfoil simulation, the experimental data will be used for the further analysis inthis case too.

Figure 3.2 – NACA 64-009 lift curve for Re = 9·106 (XFOIL).

XFOIL simulation Experimental dataLift curve slope (Cla), deg−1 0.1092 0.1080

Maximum lift coefficient (Clmax) 1.62 1.17Minimum drag coefficient (Cd) 0.0040 0.0041

Stall angle (deg) 17 11

Table 3.2 – NACA 64-009 aerodynamic coefficients ( Re = 9·106).

3.1.3 Supersonic aerodynamic coefficients

For an airfoil in supersonic flow, an analytical expression is given from theequations (3.1) and (3.2). These equations have been derived disregarding theviscous terms and solving the relevant linearized velocity potential equation ??.The results are valid for thin airfoils, which are typical for supersonic flight,and for small angles of attack, where the linearization can be considered quiteaccurate. Deriving the aforementioned equations, it can be observed that the clis independent of the airfoil shape and thickness, in contrast with the cd .

cl = 4α√M2 − 1

(3.1)

40

cd = 4(α2 + g2c + g2

t )√M2 − 1

(3.2)

In equation (3.2), gc and gt are functions of the camber and the thicknessalong the chord, respectively. For a symmetric airfoil the camber term gc equalsto zero and for a double-wedge airfoil the thickness term gt equals the square ofthe thickness ratio ( (t/c)2 ).

3.2 Subsonic Lift-Curve Slope

3.2.1 Wing - Fuselage Assembly

Reference [27] provides with an empirical equation for the wing’s subsonicCLα estimation. This equation takes into account the compressibility effects, theaspect ratio and the wing sweep. The effect of taper ratio is not directly includedin the relation, but it has been proved by the author that it can be diminishedby using the half-chord (Λc/2 ), instead of the quarter-chord (Λc/4 ) wing sweep.The relevant equation is expressed as

(CLαw)M = clα ·ARclαπ +

√(AR

cos Λc/2

)2+( clαπ

)2 − (AR ·M)2in radians (3.3)

In order to account for the fuselage contribution, the CLα obtained from theabove relation, is multiplied with the factor (Sexp/Sref ) · (F ), where the fuselagelift factor F is defined as [9]

F = 1.07 (1 +Dfus/b)2 (3.4)

If the F obtained from relation (3.4) is greater than one, the result is physicallywrong, since it assumes that the fuselage produces more lift than the coveredportion of the wing. For that reason, the factor F is set to 0.98 [9]. Sinceequation (3.3) can be considered valid for all subsonic values of Mach numbertill the critical one, the results for a freestream Mach number range of 0.2 till0.8 are presented in table 3.3.

41

Mach number CLαwb (deg−1)0.2 0.05430.3 0.05480.4 0.05570.5 0.05680.6 0.05840.7 0.06030.8 0.0630

Table 3.3 – Lift-curve slope of wing - body assembly forsubsonic Mach number range.

3.2.2 Horizontal Tail

The lift coefficient of the horizontal tail (CLt ) with respect to the horizontaltail angle of attack (αt) for the linear part of the curve is given from the followingrelation

CLt = CLatαt (3.5)

The term CLt can be computed using the equation (3.3) and introducing thecorrespondent properties of the horizontal stabilizer. In order to define a totallift coefficient for the aircraft, the relevant coefficient of the horizontal stabilizershould be written in terms of the wing-body angle of attack. The relation thatcorrelates the wing-body and the horizontal tail angle of attack is [28]

at = awb − it − ε (3.6)

The horizontal tail incidence (it) has been set to one degree. The downwashangle ((ε)) which is created by the wing wake and changes the effective angle ofthe horizontal tail can be approximated by [28]

ε = ε0 + ∂ε

∂ααwb (3.7)

The downwash angle ε0 at αwb = 0, is mainly dependent on the wing twist.Since wing twist has been set to zero for the initial layout, the ε0 can approximatedas zero. The downwash angle derivative can be approximated using the empiricalequation (3.8), based on wind-tunnel experimental data [29].

∂ε

∂α= 21oCLαw

AR0.5

(cWLHT

)(10− 3λw7

)(1− zHT

bw

)(3.8)

42

where the term zHT is the vertical distance of the horizontal stabilizer above ofthe main wing plane equal to 2.2 m for this design. Therefore, the horizontaltail contribution to the aircraft CLα can be written as

∆CLαt = CLαt

(1− ∂ε

∂α

)SHTSW

(3.9)

In table 3.5, the calculated values of interest for the horizontal tail can beobserved.

Mach number CLαt (deg−1) ∂ε/∂α ∆CLαt (deg−1)0.2 0.0487 0.6104 0.00360.3 0.0492 0.6168 0.00360.4 0.0498 0.6262 0.00350.5 0.0506 0.6391 0.00350.6 0.0517 0.6562 0.00340.7 0.0531 0.6787 0.00320.8 0.0549 0.7083 0.0030

Table 3.4 – Lift-curve slope of horizontal tail, downwash angle derivative andhorizontal tail CLα contribution to the aircraft, respectively, for subsonic Mach

number range.

3.2.3 Total aircraft

The lift-curve slope for the total aircraft can be obtained by summing thewing-fuselage and the horizontal tail contribution. The final results are presentedin table 3.5.

Mach number CLα (deg−1)0.2 0.05790.3 0.05840.4 0.05920.5 0.06030.6 0.06170.7 0.06360.8 0.0660

Table 3.5 – Aircraft lift-curve slope for subsonic Mach number range.

43

3.3 Supersonic Lift-Curve SlopeThe wing is considered to be in purely supersonic flow when the Mach cone

angle is greater than the leading edge sweep. For the wing leading edge sweepof 45 deg, that holds for Mach numbers greater than 1.4. The lift-slope curve atsupersonic speeds is quite hard to estimate without experimental measurementsor usage of a sophisticated fluid dynamics simulation model. An estimationabout the wing normal force curve-slope coefficient (CNα) is given in figure 3.3.

Figure 3.3 – Wing supersonic CNα for taper ratio of 0.2 [13].

From the figure 3.3, the CNα can be approximated, taking into account theleading edge wing sweep, the taper ratio and the aspect ratio.For small anglesof attack CNα can be considered equal to the supersonic wing CLα. In orderto account for the fuselage contribution the obatined coefficients are multipliedwith the factor (Sexp/Sref ) · (F ), like in the case of the subsonic flow.

Mach number CLαwb (deg−1) CLαt (deg−1)1.4 0.0663 0.06231.5 0.0597 0.05701.6 0.0545 0.05241.7 0.0499 0.0482

Table 3.6 – Wing-body and horizontal tail lift-curve slope forsupersonic Mach number range.

For the horizontal stabilizer, the supersonic lift curve slope is obtained applying

44

the same methodology with the aircraft wing. The correspondent values of CLαwbfor the wing-fuselage assembly and CLαt for the horizontal tail are presented intable 3.6.

The relation (3.9) can be used to calculate the horizontal stabilizer contributionto the CLα of the total aircraft. The downwash angle derivative can be roughlyapproximated using the relation (3.10), provided in [9], with the relevant resultspresented in table 3.7. In table 3.8, the supersonic lift-curve slope for the totalaircraft is included.

∂ε

∂α= 1.62CLαw

πARin radians (3.10)

Mach number ∂ε/∂α ∆CLαt (deg−1)1.4 0.6250 0.00441.5 0.5621 0.00471.6 0.5135 0.00481.7 0.4700 0.0049

Table 3.7 – Horizontal tail downwash angle derivative and CLα contribution tothe aircraft, respectively, for supersonic Mach number range.

Mach number CLα (deg−1)1.4 0.07081.5 0.06441.6 0.05931.7 0.0547

Table 3.8 – Aircraft lift-curve slope for supersonic Mach number range.

3.4 Maximum Lift Coefficient

3.4.1 Clean configuration

The aircraft maximum lift coefficient CLmax is very important for low flightspeeds and especially for the landing and the take-off flight phase. The estimationof the CLmax in this section is for the stall speed at sea-level, which has been setto 0.2 Mach and for a range till 0.6 Mach.

For the CLmax , the method from the USAF DATCOM has been used. Firstly,the aspect ratio condition of the method has to be considered. The relations 3.11and 3.12 are presenting the low and high aspect ratio condition, according toUSAF DATCOM, respectively [9], [21].

45

AR ≤ 3(C1 + 1)cos(ΛLE) (3.11)

AR >4

(C1 + 1)cos(ΛLE) (3.12)

where C1 is the taper ratio correction coefficient that can be calculated usingthe following relation [21].

C1 = 0.5 sin(π(1− λ)1.5+0.8 sin0.4(π(1−λ)2)

)(3.13)

Figure 3.4 – High aspect wing and airfoil maximum lift coefficientratio at 0.2 Mach.

The wing used for this design does not satisfy neither of the conditions, sinceit falls between the above calculated values. For that reason, both conditionshave been implemented and the results have been compared in the end. Animportant parameter that is used for this method is the leading edge parameter(∆y) of the wing section, defined as 21.3 times the thickness ratio (t/c) for aNACA 64-series airfoil. Then the CLmax can be obtained from the followingrelation in the case of high aspect ratio condition.

CLmax = Clmax

(CLmaxClmax

)+ ∆CLmax (3.14)

where Clmax is the wing section maximum lift coefficient, the ratio CLmax/Clmax

is obtained from figure 3.4 for Mach 0.2, while ∆CLmax is the correction forMach numbers up to 0.6 and can be found using the relevant chart provided inreference [9].

The correspondent stall angle of attack (αstall) can be approximated fromthe relation

46

αstall = CLmaxCαw

+ α0L + ∆αCLmax (3.15)

where the zero lift angle of attack (α0L) is equal to zero for the initially assumedzero wing incidence and the angle of attack increment (∆αCLmax ) can be obtainedfrom figure 3.5.

Figure 3.5 – Stall angle of attack increment at subsonic Machnumbers of 0.2 - 0.6.

The CLmax and αstall , in the case of the low aspect ratio condition, can beobtained from the equations 3.16 and 3.17, where the correspondent parameterscan be found from the USAF DATCOM charts provided in reference [9].

CLmax = (CLrmmax)base + ∆CLmax (3.16)

αstall = (αCLmax)base + ∆αCLmax (3.17)

Mach number CLmax αstallHigh AR Low AR Final High AR Low AR Final

0.2 095 0.91 0.93 25.6 22 23.80.3 0.93 0.89 0.91 25.1 21 23.00.4 0.90 0.88 0.89 24.3 21 22.60.5 0.87 0.85 0.86 23.5 20 21.70.6 0.86 0.83 0.85 22.9 20 21.4

Table 3.9 – Subsonic aircraft maximum lift coefficient and stall angle of attack.

47

The relevant values of CLmax and αstall obtained from both conditions arepresented in table 3.9. Since the values obtained are not very far, the meanvalue of them has been computed and are implemented as values for this model.

It can be seen that the values obtained for the aircraft maximum lift coefficientand stall angle of attack are greater than the relevant ones for the airfoil thatwas implemented. This happens due to the fact that the low aspect ratio, sweptwing incorporates a sharp leading edge, which results in the leading-edge vorticesformation that enhances the maximum aircraft lift.

3.4.2 High lift devices

In order to achieve a CLmax high enough for landing and take-off, both trailingedge (TE) and leading edge (LE) high lift devices have been incorporated to thedesign. At the trailing edge the single slotted Fowler flap has been used, whileat the leading edge the slotted LE flap or so-called slat. Both devices aim atthe wing camber and wing area increment, with the slots being incorporated toassist the avoidance of flow separation, with high pressure air being able movethrough the slots from the lower to the upper side of the wing.

Figure 3.6 – Trailing and leading edge high lift devices.

The ∆Clmax increase of the wing section incorporating a TE slotted flap isapproximated as 1.3 times the airfoil chord ratio (c′/c) after and before the flaprearward movement [9], as can be observed in figure 3.6. For this design a typicalvalue of 1.1 or 10 % chord increment, has been chosen.

Both TE flaps and slats are hinged having a chord 20% of the local wingsection chord. The TE flaps span the 35% of the wing span, while the slats its62%. Due to the engines existence, the TE flaps and the slats are not continuous,as can be seen in figure 3.7.

The maximum total aircraft ∆CLmax increment due to TE flap deflectionduring landing can be estimated using the following equation [30]

∆CLmax = ∆ClmaxSwfSw

K∆ (3.18)

where the empirical sweep correction K∆ is given from the relation

K∆ = (1− 0.08 cos2 (Λc/4)) cos0.75 (Λc/4) (3.19)

48

The area Swf corresponds to the wing area that are incorporating flaps andthe area Sw to the total wing area. The ratio (Swf /Sw) equals to 39.7% and therelevant ∆CLmax increment equals to 0.45.

Figure 3.7 – Wing TE flaps (red), LE flaps (magenta) and ailerons (cyan).

The ∆CLmax increment due to the LE device extension has been crudelyapproximated as 0.4 [9], since there is no analytical method for its prediction.The total ∆CLmax increment can be estimated as 0.85, meaning that the aircraftCLmax using the designed high lift devices will be 1.78 at 0.2 Mach.

3.4.3 Horizontal tail

A requirement during the horizontal tail design is that it should stall laterthan the wing for recovery reasons. Following the USAF DATCOM method fora low aspect ratio wing, the CLmax and αstall for the horizontal stabilizer can beestimated from equations (3.16) and (3.17). The obtained results are presentedin table 3.10.

Mach number CLmax αstall0.2 0.89 240.3 0.88 240.4 0.87 230.5 0.85 230.6 0.83 22

Table 3.10 – Subsonic horizontal tail maximum lift coefficient and stallangle of attack.

The values for the horizontal tail αstall are slightly higher than the relevantvalues calculated for the aircraft previously. Taking into account that due tothe tail incidence and the downwash angle, which cause the horizontal tail to

49

experience an angle of attack lower than the wing, the horizontal tail will haveindeed a quite higher actual stall angle.

3.5 Subsonic Parasite Drag Coefficient

3.5.1 Equivalent skin-friction method

The equivalent skin-friction method is an approximative method, which usesa equivalent skin-friction coefficient Cfe that is relevant to the aircraft class. Thiscoefficient includes both skin-friction and separation drag and for a supersonicaircraft equals to 0.0025 [9]. This method is very generic and is presented herejust to get an initial estimate to use for comparison with the more accurateresults obtained later on.

The relevant equation for the parasite (zero-lift) drag coefficient CD0 estimationis

CD0 = CfeSwetSref

(3.20)

The total aircraft wetted area (Swet) can be obtained from table 2.9 by justsumming the relevant wetted areas of each aircraft component. The resultingCD0 is 0.0120.

3.5.2 Component buildup method

The component buildup method estimates the CD0 for each aircraft component.Every component that has direct contact with air flow, is producing drag. Thebasic contributing components of an aircraft in cruise are the wing, the fuselage,the tail and the engine nacelles. The CD0 of each component is approximatedby computing a flat-plate skin-friction coefficient (Cf ) and multiplying it witha component form factor (FF), which is used in order to include the separationdrag. For the additional drag related to the components interference effects,because of the thicker boundary layer formation at components intersections,the interference factor (Q) is introduced. Therefore, the relation to calculate thesubsonic CD0 is expressed as [9]

CD0 =∑

(CfcFFcQcSwetc)Sref

+ CDmisc + CDL&P (3.21)

The factor CDL&P is related to drag created due to leakages and protuberances.A carefully designed aircraft of this type can almost eliminate the specific dragcontribution, so that it can be considered negligible. The factor CDL&P correspondsto miscellaneous drags, such as the flaps extension or the landing gear deployment.This factor for the cruise condition can be set equal to zero. During differentflight phases, like for instance during landing, these drag contributions have tobe estimates and added to the total drag.

50

In order to compute the friction coefficient Cf , it has to be examined in whatextend the flow is laminar or turbulent. That was achieved through the Reynoldsnumber (Re) calculation for all the components for Mach number range of 0.2till 0.8, which is just below the critical Mach number (see subsection 3.7), andfor the altitudes of 0, 5 and 10 km, respectively. It has to be mentioned thatthe flight at the lowest Mach numbers and higher altitudes is not possible, thusnot of interest, but the relevant coefficients will be presented just for reasons ofcompleteness.

The characteristic length for the Reynolds number calculation has beenfor the wing, the horizontal and the vertical stabilizer the respective meanaerodynamic chord of each surface, while for the fuselage and the nacelle-engineassembly their longitudinal total length. The Reynolds number has been computedto be grater than 5 ·105 for the aforementioned flight conditions, so that the flowcan be considered fully turbulent in every case.

In order to account for the skin surface roughness, which can possibly increasethe viscous forces on the components’ surface, a fictitious Reynolds number, theso-called cutoff Re, has been used. This Re can be computed from the equation(3.22), using the characteristic length (l) of each component, as defined before,and the skin roughness value k of polished metal, which is equal to 0.152·10−5

m. Therefore, in the case of an actual Re being higher than the relevant cutoffRe, its actual value has to be replaced by the cutoff one in the equation (3.23)for the Cf calculation.

Recutoff = 38.21(l

k

)1.053(3.22)

The skin-friction coefficient (Cf ) can then be estimated for every componentusing the relation

Cfc = 0.455(log10Rec)2.58(1 + 0.144M2)0.65 (3.23)

The form factor (FF) for the wing, the horizontal and the vertical tail can becalculated from the equation (3.24). The parameter (x/c)m corresponds to thechordwise position of the airfoil maximum thickness, which is 0.4 for the selectedairfoils, while Λm is the sweep angle of the maximum thickness line.

The form factors (FF) of the fuselage and the nacelle assembly can becomputed from the equations (3.25) and (3.26), respectively. The factor f inboth equations is equal to the length over the maximum diameter ratio.

FF =(

1 + 0.6(x/c)m

(t

c

)+ 100

(t

c

)4)(

1.34M0.18(cos Λm)0.28)

(3.24)

FF =(

1 + 60f3 + f

400

)(3.25)

51

FF = 1 + (0.35/f) (3.26)

The interference factor (Q) for a well-filleted wing design and the fuselage isnegligible and can be set to unity. For a conventional tail, it can be assumedas 1.04 for the horizontal and vertical stabilizer surfaces, while for the directlymounted to wing nacelles is about 1.5 [9].

Making all the necessary calculations presented previously, the ”clean” subsonicparasite drag coefficient (i.e. cruise condition configuration) can finally be computedusing the aforementioned relation (3.21). The obtained results are presented intable 3.11.

Mach number CD0

0 km 5 km 10 km0.2 0.0125 0.0132 0.01410.3 0.0121 0.0128 0.01360.4 0.0118 0.0125 0.01330.5 0.0115 0.0122 0.01300.6 0.0113 0.0119 0.01270.7 0.0111 0.0117 0.01240.8 0.0109 0.0115 0.0122

Table 3.11 – Subsonic parasite drag coefficients for the stated Machnumber and altitude flight conditions.

These results are close to the expected value of parasite drag coefficient, asit has been obtained with the equivalent-skin-friction method. The respectivecoefficient is also increasing at higher flight altitudes as it can be observed.However, that does not mean a higher drag force, since the relevant dynamicpressure at higher altitude is much smaller.

3.6 Supersonic Parasite Drag Coefficient

The supersonic parasite drag includes the skin-friction drag, the miscellaneousdrag and the drag due to leakages and protuberances, like in the case of thesubsonic flight. In addition to these contributions, it includes the so-called wavedrag, which is a drag increment resulting from the shock waves formation intransonic and supersonic speed. The total drag coefficient using the componentsbuildup method, following the same principle like in the subsonic flow case, isgiven from

CD0 =∑

(CfcSwetc)Sref

+ CDmisc + CDL&P + CDwave (3.27)

52

Since external stores are not incorporated in the SST aircraft design, theCDmisc is zero. Moreover, the drag due to leakages and protuberances can beassumed negligible, like in the case of the subsonic drag coefficient.

From the equation (3.27), it can be seen that for the supersonic skin-frictiondrag component, the form (FF) and the interference factor (Q) are not included.The skin friction coefficient (Cf ) is calculated using the equation (3.23), since theflow is fully turbulent for the supersonic flight conditions. The flight conditionsthat are evaluated here are flight at 10, 12 and 15 km altitude, with the supersonicMach number range to be from 1.4 to 1.7. Furthermore, in order to accountfor the skin roughness, a cutoff Mach number is introduced and used in theexactly same manner for the Cf calculation, such as for the subsonic flight. Theexpression for the supersonic cutoff Mach number is

Recutoff = 44.62(l

k

)1.053M1.16 (3.28)

The total skin-friction drag coefficient (CDf ) can then be estimated by summingthe respective coefficients of every aircraft component for the aforementionedflight conditions. The results are presented in table 3.12.

Mach number CDf

10 km 12 km 15 km1.4 0.0084 0.0087 0.00931.5 0.0081 0.0084 0.00901.6 0.0079 0.0082 0.00881.7 0.0077 0.0079 0.0085

Table 3.12 – Supersonic skin-friction drag coefficient component for thestated Mach number and altitude flight conditions.

The wave drag is the biggest drag contributor during supersonic flight. Thewave drag is dependent on the way the aircraft volume is distributed along itslongitudinal axis. The minimum wave drag appears for a so-called Sears-Haackbody, having an ideal volume distribution, like the one illustrate in figure 3.8.The cross-section radius (r) of a Sears-Haack body can be given from the relation

r(x) = rmax (4x(1− x))0.75 (3.29)

where x is the ratio of the longitudinal distance from the aircraft nose over thetonal length, having thus values between 0 and 1.

53

Figure 3.8 – Sear-Haacks body volume distribution [9].

Figure 3.9 – Wing-body area rule design [9].

The Sears-Haack body distribution cannot be achieved for a real aircraft,since the wing, the tail and the nacelles installation, are resulting in distortionof this smooth cross-section area distribution. However, in order to make thedistribution smoother and as close to the ideal one as possible, the area ruledfuselage is implemented. The area ruling of the fuselage has been firstly proposedby Whitcomb, who presented this principle for the wing-body combination [31].In order to achieve a smoother distribution and reduce the wave drag, thefuselage has been squeezed at the location of the wing installation (see figure3.9).

54

Figure 3.10 – Aircraft cross-section area distribution.

The area rule has been applied in this design, like it was stated in thefuselage lofting section. In figure 3.10, the cross-section area of the designedaircraft can be compared with the Sears-Haack ideal distribution. The presentedcross-section area of the aircraft corresponds to intersection with perpendicularto the longitudinal axis and at zero roll angle. The nose location of the aircraftcorresponds to the zero longitudinal dimension. The inlet capture area has beensubtracted from the cross-section area distribution graph.

The most credible way to measure the wave drag, so that to test the designand optimize it, is to conduct experiments on a wind tunnel. However, thereare also some analytical methods that can be used in order to make an initialestimation during the conceptual aircraft design. Here two of them will beillustrated, provided from references [9] and [29]. Both of them relate the aircraftwave drag with the Sears-Haack body wave drag, through the relevant coefficientgiven from relation (3.30), and an efficiency factor EWD. The typical value forthe EWD factor of a supersonic fighter and SST is about 1.8 [9]. However, a factorof 1.4 is selected for this area-ruled design, since a very high wave drag woulddeteriorate the aerodynamic efficiency significantly. The wave drag minimizationand optimization of the aircraft shape is a necessary procedure and one of themost important challenges that has to be met for an efficient SST design, andusually demands a lot of experimental testing of the model as well.

CDwS−H = 9π2Sref

(Amaxl

)2(3.30)

In the above equation, the Amax is the maximum cross-section area, whichis about 6.42 m2 for this design, and l the aircraft’s overall length. The aircraftwave drag coefficient can then be analytically estimated using the equations(3.31) and (3.32). The final wave drag coefficient to be used is the arithmeticmean of the values obtained from the two analytical relations. These value are

55

then added to the computed ones for the skin-friction drag, as presented before,with the final supersonic parasite drag coefficients to be displayed in table 3.13.

CDwave = CDwS−HEWD

(1− 0.386(M − 1.2)0.57

(1−

πΛ0.77LE−deg100

))(3.31)

CDwave = CDwS−HEWD (0.74 + 0.37 cos ΛLE) (1− 0.3√M − cos−0.2 ΛLE)

(3.32)

Mach number CD0

10 km 12 km 15 km1.4 0.0216 0.0219 0.02261.5 0.0211 0.0214 0.02201.6 0.0205 0.0209 0.02141.7 0.0201 0.0204 0.0209

Table 3.13 – Supersonic parasite drag coefficient component for thestated Mach number and altitude flight conditions.

3.7 Critical Mach numberA method for determining the critical Mach number of an infinite swept

wing is illustrated in reference [32]. The equation (3.33) relates the criticalMach number (Mcrit) for an infinite swept wing at zero angle of attack with thecritical pressure coefficient (CPcrit ).

CPcrit = 2γMcrit2

(1 + γ−12 M2

crit cos2 Λc/4γ+1

2

) γγ−1

− 1

(3.33)

The pressure coefficient (CP) at freestream Mach number M is then obtainedusing the relation (3.34), where β is the compressibility correction factor. TheCP at M=0 is approximated as the minimum airfoil pressure coefficient. Forincompressible, inviscid flow using the Bernoulli equation the CP can be obtainedfrom relation (3.35).

CPM = CPM=0

β= CPM=0√

1−M2(cos2 Λc/4 − CPM=0)(3.34)

CP = 1− (V/V∞)2 (3.35)

The ratio (V /V∞) of the local velocity along the chord over the freestreamvelocity can be obtained for the symmetrical airfoils NACA 64-006 and NACA

56

64-009 at zero angle of attack from reference [15]. Therefore, the minimumairfoil pressure coefficient for the aforementioned airfoils is -0.171 and -0.267,respectively.

Figure 3.11 – Wing critical Mach number in two-dimensional flow.

At the critical Mach number, the CP from the two equations (3.33) and (3.34)is equal. Thus, the Mcrit can be found graphically by plotting the CP obtainedfrom both equation for a Mach number range of 0.6 to 1.0. The Mcrit is the onewhere the two curves intersect. From figure 3.11, the Mcrit corresponding to thewing can be obtained.

Using the same procedure the Mcrit for the horizontal and vertical stabilizercan been computed too. The relevant values of the Mcrit are 0.92 for the wingand the vertical stabilizer, and 0.94 for the horizontal stabilizer. It has to bementioned that these values for Mcrit correspond to two-dimensional linearizedflow based on the Weber’s compressibility correction [32] of equation (3.34). Themain reason for illustrating this method is to ensure that the Mcrit of the wingdoes not exceed the Mcrit of the tail, for the selected wing sections and sweepangles.

The aircraft Mcrit can be estimated through the relation [29]

Mcrit = 1− 0.065(

100 cos Λc/4(t

c

)max

)0.6(3.36)

For this SST aircraft design the Mcrit has been calculated as 0.84. Anotherimportant Mach number related with the transonic flow, is the drag divergenceMach number Mdd . The Mdd is the Mach number at which the formation ofshock waves begins to affect the aircraft drag significantly. As a rule of thumbthe Mdd is 0.08 Mach higher than the Mcrit [9], or 0.92 in this case.

57

3.8 Drag due to Lift

In order to calculate the total aircraft drag the drag produced due to lift hasto be added to the parasite drag. The total drag coefficient (CD) is related tothe lift coefficient (CL) through the following equation known as the drag polar.

CD = CD0 +KC2L (3.37)

The so-called drag-due-to-lift factor K, in this case of a symmetric airfoil,includes both the induced drag term and the viscous separation drag term. Thefactor K for subsonic flight can be estimated through the equation

K = 1πARe

(3.38)

The coefficient e is the Oswald efficiency factor, which accounts for thenon-elliptical lift distribution over the wing. For a swept-wing aircraft, withleading edge sweep over 30 deg, it can be estimated as [9]

e = 4.61(1− 0.045AR0.68)(cos ΛLE)0.15 − 3.1 (3.39)

Therefore, K for the subsonic flight range for this design is equal to 0.1181.

For the supersonic flight range, the factor K can be obtained from the relation(3.40) [9]. The obtained values are presented in table 3.14.

K = AR(M2 − 1) cos ΛLE(4AR

√M2 − 1)− 2

(3.40)

Mach number K

1.4 0.20611.5 0.22981.6 0.25241.7 0.2742

Table 3.14 – Supersonic drag-due-to-lift factor.

3.9 Miscellaneous Drag

3.9.1 Flaps

The flaps and slats are contributing to both the parasite and induced drag.The relations (3.41) and (3.42) are giving a first estimation for the relevant dragcoefficients calculation [9].

58

∆CD0flap= Fflap

(CfC

)(SwfSw

)(δflap − 10) (3.41)

∆CDi = k2f (∆CLflap)

2 cos Λc/4 (3.42)

In the above equations, the factor Fflap equals 0.0074 for slotted flaps andthe factor kf about 0.28. The Cf /C is the flap over wing chord ratio and theδflap is the flap deflection in deg. Typical values for a Fowler TE flap is 40 degat landing and 20 deg at takeoff, while for a slat is 25 deg at landing and 15 attakeoff. As a rule of thumb, the lift coefficient increment at take-off is about 65% of the relevant value at landing. The approximated values for the flap dragcoefficients during takeoff and landing are presented in table 3.15.

Takeoff LandingCD0 CDi CD0 CDi

TE Flaps 0.0059 0.0053 0.0176 0.0124Slats 0.0041 0.0042 0.0123 0.0098

Table 3.15 – Drag coefficients of high lift devices during takeoff and landing.

3.9.2 Spoilers

The spoilers are secondary control surfaces that are used as speed brakesduring flight, as lift dumpers during ground roll and takeoff abortion and asroll control surfaces, mainly for higher speed, where the aileron effectiveness isreduced.

Figure 3.12 – Wing control surfaces (blue) and spoilers (red).

59

The initial layout of the spoilers was based on guidance from [33]. The spoileris put just ahead of the flaps with a chord equal to 15% of the local wing chord.The spoiler spans the 42% of the wing, and in particular from 19.6 till 61.6 % ofthe semispan, as it can be seen in figure 3.12. The total spoilers surface (Ss) isabout 4.52 m2 or 7.1% of the reference wing area.

The spoilers drag coefficient with respect to the spoiler deflection angle (δs)can be roughly approximated through the relation [33]

∆CDspoiler = 1.9 sin (δs)SsSref

(3.43)

Using the above relation for a spoilers deflection of 45 deg, the increment ofthe aircraft CD is estimated as 0.0952.

3.9.3 Landing gear

A quick estimation for the drag coefficient of a retractable landing gear can bemade from the empirical relation 3.44 [21]. This equation is valid for commercialjet aircraft having with deployed flaps, which is the case during takeoff andlanding, when the landing gear is deployed too. The value obtained using thefollowing relation for the CD increment due to deployed landing gear is 0.0152.

∆CDLG = 3.099 · 10−4m0.7850

Sref(3.44)

60

4. Weights

4.1 Weights Estimation Refined MethodThere are several approximative methods for estimating the weights of the

aircraft components. For a quick estimation, they can be computed as percentageof the total aircraft weight. These methods are good for giving some initialestimates for the basic aircraft components, which can be used as a guide.

Aircraft Component Weight (kg)Wing 2360.2

Horizontal tail 244.4Vertical tail 329.1

Fuselage 3340.3Main landing gear 459.6Nose landing gear 97.7

Engines 2590.3Nacelle group 510.1

Engine controls 21.2Starter (pneumatic) 88.3

Fuel system 207.7Flight controls 285.3APU installed 104.8Instruments 69.3Hydraulics 60.3Electrical 329.3Avionics 697.8

Furnishings 253.9Seats 394.0

Air conditioning 176.2Anti-ice 59.0

Handling gear 8.8

Table 4.1 – Aircraft weights estimation.

In this chapter, a more refined method, developed in reference [9], has beenimplemented. The relevant weights are estimated using statistical equations

61

based on the aircraft geometric characteristics and initial layout. The analysis isbased on the equations correspondent to transport aircraft, which can be foundin [9] and will not be reproduced here. The results obtained from the weightsestimation analysis are registered in table 4.1.

One important parameter, used in the aforementioned equations and notdefined before, is the maximum load factor (nmax), which has been set equal to3.5 for the SST aircraft design.

The total aircraft empty weight after the sum of all the weights of the aircraftcomponents is calculated to be 12,541 kg. The initial estimated aircraft emptyweight has been 13,908 kg. Since the weight obtained is lower than the initialestimation with the difference to be not very high, the aircraft dimensions willnot be refined. The initial takeoff weight will be considered the same for therest of analysis and they weight savings of the aircraft structure can be utilizedas payload increment. That means that the refined empty weight fraction isdropping to 0.4251 from 0.4715 for this SST design. The relevant value ofthe empty weight fraction for the Concorde has been calculated to be about0.417, which means that the value obtained from this refined method is indeeda reasonable estimate.

4.2 Center of Gravity

The center of gravity of the aircraft cannot be estimated so accurately duringthe conceptual design, since the aircraft is susceptible of many changes till thefinal actual design is obtained. For the symmetric aircraft design, the lateralCG location is found on the aircraft longitudinal axis of symmetry. Moreover,the location of the longitudinal CG has to be carefully placed from the designer,since it strongly affects the aircraft longitudinal stability. An analysis, madein the next chapter, makes an initial recommendation for the longitudinal CGplacement.

The vertical CG location can be calculated from the equation (4.1), whereall the N aircraft components have to be included.

zCG =

N∑i=1

mczc

N∑i=1

mc

(4.1)

An initial approximation of the vertical CG location has been made usingjust the basic aircraft components, i.e. the wing, the fuselage, the horizontal andvertical tail and the engine-nacelle groups. The estimations of the aforementionedcomponents’ vertical locations (zc) are given in table 4.2. The aircraft CGvertical location has been found to be at about 0.75 m with respect to thefuselage centerline and defining the positive z direction as downwards.

62

Component zc (m)Wing 1.1

Fuselage 0Horizontal tail -1.1

Vertical tail -2.42Engine - Nacelle assembly 1.69

Table 4.2 – CG vertical location of basic aircraft components.

63

5. Stability and Control

5.1 Subsonic Static Longitudinal Stability

The two criteria that have to be met to achieve static longitudinal conditionare that the aircraft pitching moment at zero angle of attack is positive (Cm0 > 0)and that the slope of the pitching moment coefficient is negative (Cmα < 0). Thepitching moment (Cm) is about the aircraft’s center of gravity (CG). Meetingthis two criteria is meaning that the aircraft can fly in stable equilibrium.

The assumptions that have been used for the analysis are presented here. Thewing aerodynamic center is modeled to be at 25 % of the wing mean aerodynamicchord and the same holds for the horizontal tail. Moreover, the wing-bodyassembly aerodynamic center has been assumed to be in the same location asfor the wing. The fuselage pitching moment about the wing-body aerodynamiccenter has been set equal to zero and the propulsive system contribution hasbeen neglected.

5.1.1 Aircraft Pitching Moments

The pitching moment of the wing-body can be calculated from the followingequation [28]

Cmwb = Cmacwb + CLαwbαwb(h− hnwb) (5.1)

In the above equation αwb is the wing-body angle of attack, hn and hnwb thenon-dimensional longitudinal distance of the center of gravity and aerodynamiccenter from the fuselage nose divided with the wing’s mean aerodynamic chord,respectively. Moreover, all the longitudinal locations presented in this chapterare measured as distances from the aircraft nose.

The pitching moment Cmacw of the wing about the aerodynamic center isstrongly dependent on the airfoil pitching moment and it can be estimatedthrough the relation [9]

Cmacw = Cm0airfoil

(AR cos2 ΛAR+ 2 cos Λ

)(5.2)

The airfoil that has been used for the wing is a symmetrical one with Cm0 = 0.Thus, the resulting Cmacw is equals to zero too.

64

The tail pitching moment coefficient can be expressed as [28]

Cmt = −VHCLt + CLtShtSref

(h− hnwb) (5.3)

where VH = (ltSHT )/(cSref ) with lt to be the distance between the wing bodyand the horizontal tail mean aerodynamic center (see figure 5.1).

Figure 5.1 – Wing-body and tail mean aerodynamic centers [28].

The total aircraft Cm can then be written as

Cm = Cm0 + Cmαα (5.4)

where

Cm0 = Cmacwb + CLαt VH (ε0 + it)(

1−CLαtCLα

SHTSref

(1− ∂ε

∂α

))(5.5)

Cmα = CLα(h− hnwb)− CLαt VH(

1− ∂ε

∂α

)(5.6)

The parameter Cm0 corresponds to the pitching moment coefficient at zerolift and is independent of the CG location.

5.1.2 Subsonic Neutral Point

The neutral point (NP) location of the aircraft can be found from the relation

hn = hnwb +CLαtCLα

VH

(1− ∂ε

∂α

)(5.7)

The aircraft has a positive stiffness (Cmα < 0) when the center of gravity isforward of the neutral point. This means that it should hold

Static margin (SM) = hn − h > 0 (5.8)

65

From the equation (5.7) the aircraft’s neutral point location for the subsonicaircraft range has been calculated to be 14.6 m, which determines the limit forthe center of gravity aft position.

The influence of the CG location on the aircraft Cm can be observed in thefigure 5.2. For positive pitch stiffness (h < hn) the aircraft can fly in equilibrium,when for zero (h = hn) or negative pitch stiffness (h > hn) the aircraft is unbalanced,since the pitching moment cannot be zero for any angle of attack.

Figure 5.2 – CG position influence on Cm at 0.5 Mach.

5.1.3 Longitudinal Control and Trim Analysis

The longitudinal control of the designed aircraft can accomplished throughthe all moving horizontal tail surface. The change in the tail angle δt results inthe change of the tail incidence. The tail incidence has been defined as positive,when it incorporates a negative angle of attack with respect to the wing-bodyzero angle of attack reference axis, with the tail thus to create negative lift and apositive (nose up) pitching moment. The tail deflection angle δt is then, in fact,the tail incidence for the given condition, but with the opposite sign convection.

In order to present the δt as a change of tail incidence with respect to thezero wing-body angle of attack line, the initial tail incidence (it) for the trimanalysis has been set equal to zero. The results then for the δt are the oppositesigned it that are required for stable equilibrium. This has been done in orderto avoid conversions of the obtained from the trim analysis angles, which wouldbe with respect to the it , and keep the δt definition simpler.

The derivatives of the lift and the pitching moment with respect to the δtcan be expressed, respectively, as

CLδt = CLαtSHTSref

(5.9)

66

Cmδt = −CLαt VH + CLαt (h− hnwb) (5.10)

So for the case of linear lift and linear pitching moment the set of equationsobtained is

CL = CL0 + CLαα+ CLδt δt (5.11)

Cm = Cm0 + Cmαα+ Cmδt δt (5.12)

where

CL0 = −CLαtSHTSref

(it + ε0) (5.13)

The conditions for the aircraft trim are given in (5.14). Solving this systemof equations (3.11) and (5.12), the set of angle of attack and tail deflection anglethat trims the aircraft for each flight condition can be obtained.

It can be observed from the CLtrim condition that the relevant set of anglesis dependent on the flight speed V , flight altitude (through density ρ) and theinstant aircraft mass m. The variation of the δt with the flight speed and theCG location can be seen in figures 5.3, for m = 27000 kg, which is a valuecorresponding to the aircraft mass at the beginning of the cruise phase.

CLtrim = 2WρV 2Sref

Cmtrim = 0(5.14)

Figure 5.3 – Variation of δt to trim with the flight speed and the staticmargin at SL flight.

67

The δt and α variation with the flight speed for different flight altitudes ispresented in figures 5.4 and 5.5, respectively. The given results correspond to astatic margin of 0.1. The flight speed range of the presented results and of thetrim analysis in general, is restricted from the critical Mach number, which setsthe upper limit, and from the aircraft CLmax for each flight condition, which setsthe relevant lower limit.

Figure 5.4 – Variation of δt to trim with the flight speed and the flightaltitude for the subsonic Mach number range.

Figure 5.5 – Variation of αtrim with the flight speed and the flightaltitude for the subsonic Mach number range.

68

5.2 Supersonic Static Longitudinal Stability

The criteria for static longitudinal stability remain the same for the supersonicflight, although the relevant aerodynamic coefficients are changing. The mostimportant change, during the supersonic flight compared to subsonic speed,is the aft movement of the wing’s aerodynamic center. For this analysis, theaerodynamic center of the wing-body has been assumed to be at 45% of themean aerodynamic chord, which corresponds to an aft movement of 20%. Theaerodynamic center of the horizontal tail has been place to the 45% location ofits mean aerodynamic chord as well [9].

5.2.1 Supersonic Neutral Point

The aforementioned change of the aerodynamic center position for supersonicflight affects the aircraft neutral point, which moves aft too. From the equation(5.7), the NP longitudinal location for supersonic flight has been computed tobe at about 15.9 m, which is 1.3 m aft in comparison with the subsonic NP,which corresponds to 0.25 the wing’s aerodynamic chord, which is the value ofincrement of the static margin for this design.

5.2.2 Trim Analysis

The aircraft total CL and Cm , like for case of the subsonic flight, are givenfrom the equations (5.11) and (5.12). These equations hold for angles of attacklower than 5 deg, since for larger angles of attack, the linearized supersonic theorythat was used to obtain the relevant aerodynamic coefficients is not valid. Thetrim conditions are given in (5.14) as well.

Figure 5.6 – Variation of δt to trim with the flight speed and the flight altitudefor the supersonic Mach number range and static margin of 0.1.

69

Similarly to the subsonic trim analysis, the mass of aircraft at trim is considered27000 kg. In figures 5.6 and 5.7, the variation of the δt with the flight speed andaltitude is illustrated, for static margin 0.1 and 0.35, respectively. The relevantvariation of the angle of attack for static margin of 0.1 is illustrated in figure 5.8.

Figure 5.7 – Variation of δt to trim with the flight speed and the flight altitudefor the supersonic Mach number range and static margin of 0.35.

Figure 5.8 – Variation of αtrim with the flight speed and the flight altitude forthe supersonic Mach number range.

5.3 Longitudinal Center of Gravity Location

The longitudinal center of gravity location, like it has been explained before,should be forward of the neutral point. The typical values for the static marginare 0.05 - 0.15, since a CG shift of 10% that can take place during flight is

70

considered tolerable. Thus, setting a static margin of 0.1 the CG has to beplaced at 14.1 m for subsonic flight.

During the supersonic flight due to the neutral point aft movement, the staticmargin will increase to 0.35. Comparing the values for δt from figures (5.6) and(5.7), it can be seen that the tail deflection angle increases substantially due tothe relevant static margin increment at supersonic flight. This is an undesiredsituation, since the larger δt is a factor that leads to increased drag duringcruise. For that reason, the aircraft CG has to be moved aft too, so that thestatic margin is kept inside the desired range. This can be achieved through fuelshifting, like in the case of Concorde. Therefore, having a static margin of 0.1after the fuel shift, means that the location of the CG during supersonic flighthas to be at 15.4 m.

5.4 Directional StabilityAn analysis for the directional or weathercock stability, for subsonic speeds

and fixed-rudder, has been accomplished in order to evaluate the vertical stabilizerdesign. The requirement for static directional stability is that the directionalstability derivative, or so-called yaw stiffness, is positive (Cnβ > 0). That meansthat on the aircraft will act restoring moments that will tend to decrease apositive sideslip angle (β). For the normal case that both engines are operating,the yaw stiffness contributions come from the wing, the fuselage and the verticalstabilizer. The Cnβ can then be expressed as

Cnβ = Cnβfus + Cnβw + CnβV T (5.15)

The fuselage, the wing and the vertical tail contributions, for the subsonicrange of Mach numbers, can be estimated using the equations (5.16), (5.17) and(5.18) [30]. In equation (5.16) Volf is the fuselage volume, df is the fuselagemean depth and wf is the fuselage mean width.

Cnβfus = −1.3 V olfSrefb

dfwf

in radians (5.16)

Cnβw = C2L

(1

4πAR −tan Λc/4

πAR(AR+ 4 cos Λc/4) ·(cos Λc/4 −

AR

2 − AR2

8 cosλc/4+ 6(hn − h)

sin Λc/4AR

))in radians

(5.17)

CnβV T = VV TCFβV T

(1 + ∂σ

∂β

)qV Tq

(5.18)

where(1 + ∂σ

∂β

)qV Tq

= 0.724 + 3.06(S′V T /Sref )1 + cos Λc/4

+ 0.4zwfdf

+ 0.009AR (5.19)

71

The wing-fuselage combination at a sideslip angle creates a sidewash σ, whichchanges the effective angle of the vertical tail. The sidewash that comes fromthe fuselage is the dominant factor, in comparison with the wing, and gives astabilizing air above the fuselage wake [34]. Hence, the effect of the sidewash isstabilizing for a low-wing aircraft. The ratio (qVT/q) is actually equal to thesquare of the velocity ratio (VVT/V ), and accounts for the propeller slipstreameffect [28]. For the case of the propeller absence this ratio equals to one.The contribution of the two aforementioned parameters to the CnβVT

can beestimated analytically from the relation (5.19), where S ′VT is the vertical tailarea including the area extended to the fuselage centerline and zwf is the verticaldistance of the root chord to the fuselage centerline, being positive for wing rootvertical location below it. For this design, the S ′VT equals to 11.47 m2 and thezwf to 1.1 m.

The VVT is the vertical tail volume coefficient, which can be obtained fromequation (2.32), where LVT is the distance of the vertical tail aerodynamic centerto the aircraft center of gravity. Finally, the CFβVT

is the lift-curve slope of thevertical tail. This can be computed from the equation (3.3), like in the case ofthe wing, introducing the relevant properties of the vertical tail. However, inthis equation it has to be introduced the effective and not the geometric aspectratio of the vertical tail. The effective aspect ratio of the vertical tail is 1.55times greater than the geometric one, and this increment comes from the endplate effect of the horizontal tail mounted below the vertical stabilizer [34].

The calculated subsonic directional stability derivatives (Cnβ ) are presentedin table 5.1. These values are greater than the suggested values of NASA TND-423, as presented in reference [9], meaning that the aircraft will be directionallystable enough.

Mach number Cnβ (deg−1)0.2 0.0025 + 0.00094·C2

L

0.3 0.0025 + 0.00094·C2L

0.4 0.0026 + 0.00094·C2L

0.5 0.0026 + 0.00094·C2L

0.6 0.0027 + 0.00094·C2L

0.7 0.0028 + 0.00094·C2L

0.8 0.0029 + 0.00094·C2L

Table 5.1 – Directional stability derivatives for the subsonic Machnumber range.

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6. Performance

6.1 Climb PerformanceFor the climb performance analysis, the equations of motion for the rigid and

mass point geometry body have been utilized. The thrust model has been createdaccording to the thrust lapse expression from the equation (2.19), which givesthe variation of the thrust with the Mach number and the flight altitude. Therelation of the dry thrust has been used for this analysis, since the aim is the totalavoidance of using the afterburner for reasons of increased fuel consumption andnoise. However, the afterburner could be installed and used for safety reasons,for instance in the case of an emergency, like the loss of one of the engines.The aerodynamic model of the aircraft has been based on the aerodynamiccoefficients computed in previous chapter. The trim drag has been neglectedfor the performance analysis of this section as well as for the following ones.The aircraft center of gravity has also been assumed not to be influenced fromthe fuel mass burned during flight. The equations describing this model, for theengine installation angle of zero degrees, can be written as

mV = T cosα−D −mg sin γ (6.1)

0 = T sinα+ L−mg cos γ (6.2)

h = V sin γ (6.3)

xE = V cos γ (6.4)

m = −C · T (6.5)

With the assumption that the acceleration perpendicular to the flight pathis negligible, made in equation (3.2), the nonlinear equation can then be solvedto obtain the trim angle of attack. The thrust specific fuels consumption (C ),in the absence of the engine data for the altitude and Mach range of interest,can be approximated using the relations provided from reference [10], for the dryand wet thrust of a low-bypass ratio turbofan engine, respectively.

Cdry = (0.9 + 0.3M)√θ (6.6)

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Cwet = (1.6 + 0.27M)√θ (6.7)

The C in the above equations is given in fps units, i.e. 1/hr , with theparameter θ to have been already defined in equation (2.15).

6.1.1 Minimum Time to Climb

In order to find the optimal path that corresponds to the minimum time forthe climb and the acceleration phase, the flight envelope including the specificexcess power (SEP) contours for different altitudes has to be created. The SEPis given from the formula

SEP = (T cosα−D)VW

(6.8)

The SEP is defined as the excess power divided by the weight, where theexcess power is just the excess thrust, (T cosα−D), times the velocity, V. Thisexcess power can be used for altitude gain or for acceleration. For load factorequal to one and considering steady and level flight, which means that the flightpath angle γ = 0 , the relevant flight envelope can be created for a specific aircraftweight. The SEP contours of this SST design for maximum payload and 85 %fuel mass (i.e. aircraft total mass of 27240 kg) are presented in figure 6.1. Inthis figure, the stall angle of attack and maximum dynamic pressure limitationshave also been included. The stall angle of attack can be computed by dividingthe clean configuration CLmax with the aircraft CLα , with the relevant value tobe computed as 16 deg. The maximum dynamic pressure has been set to 85.82KPa, which is the dynamic pressure corresponding to 1.1 Mach at sea level.

Figure 6.1 – SEP contours diagram (dry thrust).

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The SEP contours of figure 6.1 are actually corresponding to the aircraftclimb rate. In order to obtain the minimum time to climb, the path to beplanned has to follow the maximum aircraft climb rates. For that reason theaircraft has to accelerate at the same altitude till Mach 0.9, where the climbwith maximum climb rate will take place. The aircraft is climbing till about thedesired cruise height and then it dives, so that it accelerates and passes throughthe transonic region, where the drag is too high that does not allow the aircraftto accelerate any more, due to thrust deficiency. After the aircraft acceleration,the altitude is regained, since the drag becomes lower in supersonic speeds. Thedive follows the relevant constant energy height curves, for which the dynamicenergy is purely converted to kinetic energy. The final part of the trajectoryincludes the climb to the final cruise altitude and the acceleration to the cruiseMach number.

In figure 6.2, the minimum time to climb trajectory is presented. The flightpath angle γ as a function of time has been defined as the control variable thathas been used to solve the set of differential equations (6.1) - (6.5), with theinitial conditions to be 0.1 km flight altitude and 0.3 Mach flight speed. Thefuel mass at the start of the climb has been set to 97 % of the total fuel capacity,since a 3 % or 452 kg of the fuel has been assumed to be used during the taxiingand takeoff. The time needed for this climb at 14.55 km and Mach 1.7, is about1430 sec, where the fuel that has been burned has been estimated as 3399 kgor 22.6 % of the total fuel capacity. It has to be mentioned that the initialcruise altitude that can be reached is 450 m lower than the specified from therequirements altitude of the 15 km.

Figure 6.2 – Flight path for minimum time to climb at cruise conditions.

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6.1.2 Minimum Fuel to Climb

The flight path giving the minimum fuel consumption to climb is a bitdifferent in comparison with the minimum time to climb one. The minimumfuel to climb trajectory follows the path that maximizes the fuel specific energy(FSE) for each energy height. The fuel specific energy is defined as the changein specific energy per change in fuel weight [9]. The FSE is defined as

FSE = SEP

C · T(6.9)

The FSE contours and the relevant flight path is presented in figure 6.3. Theγ(t) is the control variable in this case as well, while the same set of equationshas been solved, like for the minimum time to climb trajectory. The initial flightand weight conditions have been considered the same too. The time needed toreach the cruise flight conditions of 14.55 km and 1.7 Mach has been computedas 1580 sec. For this climb, the mass of the burned fuel is 3205 kg or 21.3 %of the total fuel capacity. The fuel savings following this trajectory comparedto the minimum time to climb one are about 1.3 % of the total fuel capacity.The horizontal range covered during the climb and acceleration phase has beencalculated as 517.5 km.

Figure 6.3 – Flight path for minimum fuel to climb at cruise conditions.

6.2 RangeThe horizontal range of aircraft during cruise can be calculated from the

Breguet range equation (6.10). During the cruise the aircraft is flying at constantCL and speed. However, keeping these two parameters constant means that theaircraft due to the fuel burn, which is reducing its weight during the cruise, willgradually climb to higher altitudes. Moreover, the aircraft is possible to fly at

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constant speed and Mach number, since the speed of sound for cruise altitudesin stratosphere remains unchanged.

R = V

C

L

Dln

(Winit

Wfinal

)(6.10)

Since the target is the range maximization, the minimum fuel to climb flightpath is the desired one to be followed before the cruise. Knowing the relevantfuel that has been burned during the climb the Winit can be easily obtained. Atthe end of the cruise, it is assumed that the aircraft has a remaining 12% of thetotal fuel capacity or Wfinal equal to 16248 kg.

For the cruise flight conditions of 1.7 Mach at the height of 14.55 km, thelift-to drag ratio (L/D) has been calculated as 5.764. Therefore, the horizontalrange to be covered during cruise is estimated as 5068.9 km, while the flightaltitude at the end of the cruise as 17.49 km.

6.3 Descent and Loiter

After the end of the cruise phase, the aircraft needs to decelerate and descendto a lower altitude, where the loiter before the final descent to land will take place.For the descent the same model has been used, like in the case of the climb,with the difference that the thrust provided from the engine is decreased. Thatmeans that the excess power becomes negative and the aircraft decelerates, whilea negative γ initiates the dive. As it can be seen from the endurance equation(6.11), the loiter should take place at the flight conditions where the product ofthe (L/D)max with the C is maximum. Thus, the chosen conditions for the loiterhave been the 6.8 km altitude and the 0.4 Mach. The thrust has been reducedto 20% of the maximum thrust for this descent. When the loiter phase ends,the aircraft has to descend again to land. The final flight conditions before theapproach have been modeled to be the 0.2 km height and the 0.3 Mach speed,using in this case the 10% of the engines maximum thrust.

E = 1C

L

Dln

(Winit

Wfinal

)(6.11)

During the first descent the fuel burned and the horizontal range covered are207 kg and 253.5 km, respectively. During the loiter, a total 441 kg of fuel hasbeen burned, corresponding to an endurance of 24 min and 14 sec. The finaldescent has consumed 179 kg of fuel, covering an additional horizontal range of159.4 km. The aircraft weight before the final approach has then been computedto be 15421 kg, with 6.51% of the total fuel to be left for usage during the landingand taxiing phases.

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6.4 Takeoff

The takeoff distance, as can be seen from figure 6.4, consists of two basiccomponents, the ground run distance and the airborne distance.

Figure 6.4 – Illustration of takeoff path and distance.

The ground run distance includes the ground roll distance (dg) and therotation distance (dr). During the ground roll, the aircraft accelerates fromthe zero velocity till the takeoff velocity (VTO), which should be 1.1 times thestall speed (Vstall) [9]. The Vstall can be simply calculated setting the lift equalto weight and using the CLmax for flaps in the takeoff position (about 80% ofthe landing CLmax). The relevant value obtained is 71 m/s. The dg can then becalculated from the integral

dg =∫ VTO

0

Vα

dV (6.12)

where the acceleration α is given from the relation

α = g

((T

W− µ

)+ ρ

2W/S(−CD0 −KC2

L + µCL)V 2)

(6.13)

For the rolling friction coefficient µ, the typical value of 0.05 for brakes offhas been used [13]. The total CD0 at the takeoff has been estimated as 0.0472,including the flaps, slats and landing gear contributions. The lift coefficient CLbeing based on the wing angle of attack during the ground roll is typically small.The conservative assumption that is negligible has been made for this analysis.Moreover, the trust provided during the ground run is not constant. For thatreason, in order to obtain more accurate results, the integral has been brokeninto smaller segments for which average thrust has been used.

The rotation distance dr can be simply obtained multiplying the VTO withthe typical rotation time tr of 3 sec. The total distance during the ground runhas then been calculated as 1927 m.

In order to obtain the total takeoff distance, the dab has to be estimatedas well. During this airborne phase the aircraft is accelerating from the takeoffspeed (1.1Vstall) to the climb speed (1.2Vstall) [9]. Moreover, the aircraft gains

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altitude, in order to achieve the 35 ft obstacle clearance (hob), defined from theFAR regulations.

The load factor (n) during the pull-up can be calculated from the equation(6.14), where the 90% of the takeoff CLmax is used as a safety margin [13]. Then,the correspondent turn radius (R) can be calculated from the equation (6.15).Since the speed is not constant, the load factor and thus the relevant turn radiusis changing. For that reason, they have been computed for the given range ofspeeds, and then the mean value of the turn radius has been used.

n =12ρS(0.9CLmax)V 2

W(6.14)

R = V 2

g(n− 1) (6.15)

Having estimated the pull-up R, the airborne distance can be calculated as

dab =√R2 − (R− hob)2 (6.16)

The relevant value obtained for the dab is 289.2 m, which means that thetotal takeoff distance is estimated as 2216.2 m.

6.5 Landing

The landing distance includes the approach distance (da), the flare distance(df ), the free roll distance (dfr) and the ground roll distance (dg). The landingphases can be observed in figure 6.5.

The approach angle θa is usually small, and for a transport aircraft shouldbe θa≤ 3 deg [9]. The θa can then approximated from the equation (6.17). Inorder to satisfy the aforementioned constraint for the approach angle, the 63%of the thrust has been used during landing, resulting in a θa equal to 2.79 deg.

sin θa = 1L/D

− T

W(6.17)

During the approach and flare phase, the aircraft should decelerating fromthe approach speed (Va = 1.3Vstall) to the touchdown speed (Va = 1.15Vstall).The Vstall is the one obtained using the CLmax corresponding to flaps in landingposition and is equal to 64.5 m/s. The approach turn radius (R) can then becomputed using the relations (6.14) and (6.15), like in the takeoff case, for thepreviously stated variation of velocities. The approach distance, taking then intoaccount a clearance distance of 50 ft [13], is approximated as

da = 15.24−R(1− cos θa)tan θa

(6.18)

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Figure 6.5 – Illustration of landing path and distance [13].

The flare and the free roll distance can be approximated using the relations(6.19) and (6.20), respectively [13].

df = R sin θa (6.19)

dfr = trVTD (6.20)

Finally, the ground roll distance can be computed using from the integral

dg =∫ 0

VTD

Vα

dV (6.21)

where α is given again from the equation (6.13). The integral has been computedusing the same method, as for the takeoff. The total CD0 at the landing hasbeen estimated as 0.175, including the flap, slats, landing gear and spoilerscontribution. A spoilers deflection of 45 deg has been assumed. The value ofrolling friction coefficient used is the one corresponding to brakes usage. Thetypical value of 0.5 has been used for the µ [13].

The total landing distance can be estimated by just summing all the relevantcontributions. The obtained value is then increased, so that the FAA requirementsthat allow for pilot technique are met [9]. Hence, the final landing distance canbe estimated from the equation (6.22) as 2147.3 m .

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dland = 53(da + df + dfr + dg) (6.22)

6.6 Total MissionThe evaluation of the above results shows that the aircraft is meeting the

requirements regarding the takeoff and landing distances. The total horizontalrange is 6053 km and the maximum endurance about 24 min. The maximumrange without any loiter can reach the 6354 km.

The obtained range is lower than the desired one, but yet enough to executetransatlantic flights. The main focus for getting a bigger range should be theimprovement of the lift-to-drag ratio during cruise. A slight increment of the(L/D)cruise to 6.2 from 5.764 would result to a total horizontal range of 6437km or an increment of 384 km. This value assigned for the (L/D)cruise is quitereasonable and feasible to be obtained, when compared with the relevant valueof the Concorde. According to reference [36], the Concorde had a (L/D)max of7.5 for cruise at Mach 2, which corresponds to a (L/D)cruise of about 6.5. The(L/D)cruise of the aircraft could be increased even more through camber andwing twist optimization.

For a flight between London and New York, the total time of the climb, cruiseand descent is 3 hrs and 35 min. Assuming that no loiter is needed, which is thecase most of the times and including the time for taxiing, take-off and landing,the time needed for the whole mission is 4 hrs maximum. Given that the normaltime of a subsonic airliner for that route is 7 hrs and 40 min to 8 hrs, the timesaving is very significant. Although the SST cannot follow the minimum fuel toclimb flight path for practical reasons, like the overland sonic boom ban, whichmight impose an initial small subsonic cruise part on the mission, the time savedremains still substantial and would be about 3 hrs and 30 min for the whole trip.

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7. Test Flight

7.1 Simulation

The flying and handling qualities of the design have been flight tested usingthe Merlin MP521 Engineering Flight Simulator. The MP521 Simulator comprisesa capsule with a six axis motion system, visual and instrument displays, touchcontrol panels, and hardware flight controls [37]. The software of the flightsimulator that has been run is the Excalibur II, while the design has been createdat the Excalibur Data Editor.

The model in the editor has utilized the geometrical data and mass propertiesof the design, in addition to the aerodynamics and propulsion data, acquiredduring the conceptual design. The mass moments of inertia are calculated bythe editor, using empirical relations, from the inserted values that correspond tothe aircraft mass parameters, center of mass and wing span, assuming one planeof symmetry, i.e. Ixy = Iyz = 0.

The wing is split into panels for which the relevant data are inserted to theeditor. The wing is divided according to its control surfaces, particularly thereis a change when a control surface is met, so that there can be lifting surfaceswith or without control surface. In this case, the wing semi-span has been splitin a total six panels, where the other half includes six more panels, which areautomatically mirrored due to symmetry. For the horizontal tail, just one panelhas been used, since it has been modeled as a whole moving surface, while twomore panels have been considered for the vertical tail. For each panel the controlsurfaces data, and the wing geometrical characteristics, in addition to the usedairfoil aerodynamic data, have been specified. The aerodynamic center of eachpanel has to be independently calculated and set in the model editor too.

The model includes excessive data for the undercarriage as well, such as thenose-wheel steering and the brakes, determining the aircraft ground performance.These data have been specified using typical values recommended from thesoftware’s user guide manual, the Excalibur II Flight Model Editor Data Definitions.

The software of the flight simulator is based on the six degrees-of-freedomequations of motion of a rigid body, and thus does not take into account anyaeroelastic effects. The translational positions are integrated in earth (NED)axes and the angular positions (aircraft attitudes) are represented in the standardfour-parameter Quaternion format, in order to allow the attitudes be integrated

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through the 90 degrees pitch attitude singularity.

The simulator includes a flight data recorder (FDR) with a recording frequencythat can be set to 1, 5 or 25 Hz. The flight data are held in an ASCII text file,including speed and flight path variables, aircraft control deflections, rigid bodyvariables and atmosphere parameters. The recorded data have then been readand processed using Matlab.

7.2 Flying and Handling Qualities

Aircraft handling is related with the aircraft response to the control inputs,as for instance the elevator deflection, which can be discerned in short-term andlong-term response [38]. The short-term characteristics of the aircraft are veryessential, since poor behavior can make the aircraft very hard or even impossiblefor the pilot to handle. Thus, the primary goal when evaluating the flight andhandling qualities of the design is to achieve satisfactory short-term response,which are related to its short period dynamic modes. The long-term response issubstantial in maintaining steady flight of the aircraft and is determined fromthe static stability and its long period dynamic modes [38]. However, thesemodes having a long period, can be handled a lot easier by the pilot, so thateven marginally unstable modes can be considered satisfactory.

Taking the above into consideration, the flight test of the design aimed to thedynamic modes evaluation, in terms of both longitudinal and lateral-directionaldynamic stability. The aircraft has been trimmed by determining the necessarythrottle setting and horizontal tail deflection for each flight condition beingconsidered. Then each mode has been excited and the results have been recordedusing the simulator’s FDR. For the executed measurements, the highest recordingfrequency of 25 Hz has been implemented. Finally the obtained results havebeen rated using the relevant guidelines and margins as specified in the MilitarySpecification MIL-F-8785C.

The aircraft flying and handling qualities have been evaluated for threedifferent altitudes, in particular at 10, 20 and 30 kft, and for subsonic Machnumbers. The design was tried to be assessed for the supersonic cruise conditionsas well, however the results obtained from the simulation have been consideredas inaccurate and hence will not be presented.

7.2.1 Modes excitation

The dynamic stability modes of the aircraft can be discerned in two categories,the longitudinal and the lateral-directional dynamic modes, which are uncoupled.Detailed guidance about the procedure of the excitation for both types of dynamicstability modes during flight is given in reference [38], which is briefly describedin this subsection. These procedures help to measure and quantify the relevantmodes properties during test flight in a way that they can be comparable withthe analytical values.

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The longitudinal dynamic stability modes consist of the short-period pitchingmode and the long-period or phugoid mode, which are both related to oscillatorymotion. The two modes have a significant difference as regards their frequency,which makes possible their independent excitation. The short-period oscillationcan be excited by applying a short duration disturbance in pitch to the trimmedaircraft. In order to achieve this a unit impulse is applied to the elevatorfor about one sec. This impulse will more likely excite the phugoid modetoo. However, due to its low frequency, which requires significantly more timein comparison with the short-period mode to develop the phugoid oscillatorymotion, the short-period measurements will not get affected.

In order to excite the phugoid mode, a small step input is applied to theelevator, which causes the aircraft to accelerate, when descending, while thethrust level setting is kept constant. The elevator is returned to its initialposition, when the aircraft speed has increased by about 5% compared to relevantspeed at the trimmed condition. It has to be mentioned that it is essential thisspeed disturbance to be small for the results to be accurate, since the modesare being evaluated using the small-perturbation model, which should not beviolated.

In contrast with the longitudinal dynamic modes, the lateral-directional onesare more difficult to excite independently, due to mode coupling. For that reason,the aileron or rudder input to excite these modes should be applied more carefullyand accurately for the relevant measurements to be taken. The lateral-directionalstability modes consist of the spiral, the roll subsidence and the dutch roll mode.The first two are related to real eigenvalues, thus no oscillation is observed,while the dutch roll mode is related to an imaginary eigenvalue, such as theshort-period and the phugoid mode, which includes oscillatory motion as well.

The spiral mode is excited when a small step input is applied to the rudder.The aircraft then begins to turn and the inner wing of the turn side drops.When the roll attitude is about 20 deg, the rudder returns to its initial position.If the mode is stable, the aircraft will converge to its zero roll attitude angle,and recover wings level. Differently, for the case of an unstable mode, the rollattitude angle of the aircraft would contrarily increase and thus diverge fromthe initial balance condition. The spiral mode is a weak mode with a big timeconstant, and thus does not affect substantially the flying and handling qualitiesof the aircraft, so that unstable modes can be acceptable too.

The roll subsidence mode can be excited when a square pulse is applied to theaileron. In order to specify this dynamic mode during flight test, the roll attitudeangle is set initially at about -30 deg. Then the relevant aileron deflection isapplied, so that the aircraft rolls steadily to the +30 deg roll attitude, when theaileron has returned to the neutral position. The roll subsidence mode is the onethat governs the transient exit of the steady part of the rolling motion. Its timeconstant is short and its effect is visible just in the roll attitude response.

The dutch roll mode can be excited by applying a doublet to the rudderpedals. The period of the rudder deflection should approximately match the

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period of the mode for it to be excited. During this cyclical rudder deflection,the aircraft is compelled to a forced oscillation. After returning the rudderto the neutral position, the aircraft will continue to execute a free oscillation,which corresponds to the oscillatory motion related to the dutch roll mode. Thedutch roll mode having short period should be stable and demonstrate adequatedamping, so that the aircraft flying qualities can be considered satisfactory.

7.2.2 Dynamic Stability Requirements

A common method for the flying and handling qualities evaluation of theaircraft is the so-called Cooper-Harper rating scale. This is a qualitative ratingscale that expresses the pilot opinion. The pilot rates the aircraft behavior,respective with the different flying phases that are needed to be tested, usingan 1 to 10 scale, where the lower the grade the better the flying and handlingqualities the aircraft exhibits.

However, in order for the results to be impartial, the modes obtained fromthe flight test will be quantified, following the guidelines given in the previoussubsection. Then the calculated modes will be compared to the requirementspresented in reference [39], which correspond to specific values that determinethe margins for the aircraft’s flying and handling qualities assessment.

Before presenting the relevant requirements, the aircraft has to be classifiedand categorized, according to instructions given in [39]. The classification isrelated with the aircraft’s role, while its category with its flight mission profile.For this case, the SST that needs to be evaluated is a medium weight andlow-to-medium maneuverability aircraft, which means that it belongs in ClassII. The mission profile of the SST is in accordance with the flight phases definedfor a category B aircraft, for which accurate flight-path control is required andgradual, without precision tracking, maneuvers accomplishment.

The dynamic stability requirements, for both the longitudinal and lateral-directional modes of an Class II and Category B aircraft, are presented in thetables 7.1 - 7.5 and in figure 7.1. The time to double or half is the time requiredfor the initial perturbation of the trimmed condition to be doubled or halvedand is defined, for the case of an oscillatory motion, in equation 7.1, where thesymbol n corresponds to the real part of the relevant eigenvalue. The dampingratio ζ is defined in relation 7.2, and the ωn is the undamped angular frequencygiven from the relation 7.3 [28]. Therefore, obtaining the period (T ) of theoscillation and the thalf or tdouble after processing the recorded flight data, bothζ and ωn can be estimated using the aforementioned equations.

tdouble or thalf = ln2| n |

= ln2| ζ | ωn

(7.1)

ζ = −n/ωn (7.2)

ωn =(ω2 + n2

)0.5(7.3)

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Level Min ζ Max ζ1 0.30 2.002 0.20 2.003 0.15 -

Table 7.1 – Short-period mode damping ratio limits.

Figure 7.1 – Short-period mode frequency requirements [39].

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In figure 7.1, the parameter n/α correspond to the normal load factor perunit angle of attack α.

Level Requirement1 ζ > 0.042 ζ > 03 T > 55 sec

Table 7.2 – Phugoid mode stability requirements.

Level tdouble1 < 20 sec2 < 8 sec3 < 4 sec

Table 7.3 – Minimum time to double amplitude limits for spiral mode.

Level Time constant1 < 1.4 sec2 < 3.0 sec3 < 10 sec

Table 7.4 – Roll subsidence mode time constant limits.

Level Min ζ Min ζ · ωn (rad/sec) Min ωn (rad/sec)1 0.08 0.15 0.42 0.02 0.05 0.43 0 0 0.4

Table 7.5 – Dutch roll mode damping ratio and frequency limits.

7.2.3 Longitudinal Dynamic Stability

Short-period pitching mode

The short period pitching mode has been measured for the aforementionedflight altitudes and for the Mach numbers of 0.5 and 0.8, except for the altitudeof 30 kft, where due to the aircraft stall restriction, the lower Mach number hasbeen set to 0.6. The same flight conditions have been used for the other modesmeasurements too.

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In figures 7.2 and 7.3, the elevator impulse for the short period mode excitationand the resulting oscillation as depicted in the body axis pitch rate are presentedfor the stated flight conditions.

Figure 7.2 – Elevator impulse input flight recording of the shortperiod mode for 0.6 Mach at 30 kft.

Figure 7.3 – Body axis pitch rate flight recording of the shortperiod mode for 0.6 Mach at 30 kft.

The obtained values corresponding to the short-period pitching mode, afterprocessing the data of the flight recorder for all the tested flight conditions, aswell as their evaluation regarding the aircraft’s flying and handling qualities, canbe seen in table 7.6.

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Mach Altitude (kft) T (sec) thalf (sec) ωn (rad/sec) ζ Level0.5 10 1.74 0.73 3.74 0.254 20.8 10 1.06 0.46 6.12 0.249 20.5 20 2.09 0.92 3.10 0.242 20.8 20 1.35 0.60 4.80 0.242 20.6 30 2.02 1.03 3.18 0.212 20.8 30 1.68 0.76 3.85 0.236 2

Table 7.6 – Variation of short-period pitching mode characteristics withspeed and altitude.

Phugoid mode

Similarly to the short-period mode, the relevant values of the phugoid modecharacteristics are presented in table 7.7, while in figure 7.5, the oscillatorymotion of the mode as regards the aircraft’s true airspeed is illustrated.

Mach Altitude (kft) T (sec) thalf (sec) ωn (rad/sec) ζ Level0.5 10 84.9 88.49 0.074 0.105 10.8 10 145.8 60.05 0.045 0.258 10.5 20 79.7 99.26 0.079 0.088 10.8 20 127.4 73.34 0.050 0.188 10.6 30 83.2 113.69 0.076 0.080 10.8 30 115.6 110.23 0.055 0.115 1

Table 7.7 – Variation of phugoid mode characteristics with speed andaltitude.

Figure 7.4 – Elevator step input flight recording of the phugoidmode for 0.6 Mach at 30 kft.

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Figure 7.5 – True airspeed flight recording of the phugoid mode for0.6 Mach at 30 kft.

7.2.4 Lateral-Directional Dynamic Stability

Spiral mode

In figure 7.6, the flight recording for the roll attitude angle can be observedfor the stated flight conditions. It can be seen from the graph that the spiralmode for this case is convergent to zero roll angle attitude, and thus stable.In table 7.8, the spiral mode characteristics for the flight tested conditions arepresented.

Figure 7.6 – Euler roll angle flight recording of the spiral mode for0.6 Mach at 30 kft.

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Mach Altitude (kft) thalf (sec) Level0.5 10 26.60 10.8 10 43.05 10.5 20 27.51 10.8 20 47.92 10.6 30 32.44 10.8 30 52.95 1

Table 7.8 – Variation of spiral mode characteristics with speed andaltitude.

Roll subsidence mode

In figures 7.7 - 7.9 are presented the graphs obtained for the roll subsidencemode from the flight test at the stated flight conditions, regarding the aileroninput, the roll attitude angle and the roll rate. In table 7.9, the roll convergencetime constant and evaluation regarding the previously specified flying and handlingqualities requirements are presented.

It can be observed in figure 7.9, that the the roll response stabilizes whenthe moment due to damping in roll is the opposite to the disturbing moment inroll caused by the aileron deflection [38]. Moreover, from figure 7.8 can be seenthat after the roll angle becomes steady, it starts decreasing. This is an effect ofthe spiral mode, which tends to recover the aircraft’s wings level, after returningthe aileron to its zero deflection position.

Figure 7.7 – Aileron input flight recording of the roll subsidencemode for 0.6 Mach at 30 kft.

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Figure 7.8 – Euler roll angle flight recording of the roll subsidencemode for 0.6 Mach at 30 kft.

Figure 7.9 – Body axis roll rate flight recording of the roll subsidencemode for 0.6 Mach at 30 kft.

Mach Altitude (kft) Time constant (sec) Level0.5 10 1.81 20.8 10 1.53 20.5 20 2.17 20.8 20 1.92 20.6 30 2.92 20.8 30 2.36 2

Table 7.9 – Variation of roll subsidence mode characteristics withspeed and altitude.

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Dutch roll mode

In figure 7.10, the rudder doublet for the dutch roll excitation can be seen.In figures 7.11 and 7.12, the dutch roll oscillation is depicted in the roll and yawrate graphs, for the stated flight conditions. From these two graphs, it is visiblethe expected phase shift between the roll and the yaw rate too. It can be seenfrom the graphs that the dutch roll oscillation is the motion starting for thiscase after the first 4 sec. In the first 4 sec, the observed oscillation is the oneenforced from the rudder input. In table 7.10, the dutch roll characteristics forthe tested flight conditions are presented.

Figure 7.10 – Rudder input flight recording of the dutch roll modefor 0.6 Mach at 30 kft.

Figure 7.11 – Body axis roll rate flight recording of the dutch rollmode for 0.6 Mach at 30 kft.

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Figure 7.12 – Body axis yaw rate flight recording of the dutch rollmode for 0.6 Mach at 30 kft.

Mach Altitude (kft) T (sec) thalf (sec) ωn (rad/sec) ζ Level0.5 10 1.35 1.04 4.702 0.142 10.8 10 0.84 0.76 7.535 0.120 10.5 20 1.65 1.53 3.835 0.118 10.8 20 1.04 1.21 6.069 0.094 10.6 30 1.74 2.00 3.628 0.095 10.8 30 1.28 1.66 4.927 0.085 1

Table 7.10 – Variation of dutch roll mode characteristics with speed andaltitude.

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8. Environmental Impact

8.1 Sonic Boom

One of the most important environmental impacts of the SST operation is theaerodynamic noise generated by the shock waves. The so-called sonic boom hasimposed a ban on the overland supersonic flight, which can now be performedonly overseas. NASA is conducting research in this field in order to create a lowboom design, which could be quiet enough to overcome the applied restrictions.

The early sonic boom research was conducted according to modified linearmethods, based on Whitham’ s theory for the sonic boom prediction. Accordingto the linear theory, the pressure signatures reaching the ground are N-waves,which are typical for aircraft with high wing loading. However, later work hasshown that generation of non-N-waves on the ground was possible [40]. Moreover,some important deficiencies has been recognized regarding the linear methods,respective with the account for the three-dimensional nonlinear aerodynamics,the propagation of the sonic boom waveforms through a real atmosphere, havingthus variable ambient conditions, and the atmospheric turbulence modeling,which made necessary the development of more accurate methods and theirexperimental validation through flight testing. Therefore, the later studies focusedon creating aircraft concepts with lift and volume distributions that would shapenon-N-waveforms at the ground, rather than trying to reduce the noise generatedby the N-waves, which created substantial limitations.

The focus of the High-Speed Research (HSR) program of NASA was thecreation of a big SST, which could carry more than 250 passengers. The ideabehind that concept was that the opening of more supersonic corridors overlanddue to a low boom design, would result in a more excessive usage of supersonictransports. Therefore, the development cost of the aircraft would be smallerdue to increased demand for its purchase. The SST design proposed in thisproject refers to a small aircraft carrying 15 passengers. However, some sonicboom minimization design guidelines could be implemented to smaller aircraftand evaluated too.

In reference [41], several concepts are examined based on a reference designas regards the sonic boom loudness. The delta baseline design wing has beenchanged into a wing arrow design, having about the same aerodynamic efficiencyThe relevant baseline and the low boom design and specifications are presentedin figures 8.1 and 8.2.

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Figure 8.1 – Drawing and specifications of the baseline configuration [41].

It can be seen from the two drawings that the low boom design incorporatesa bigger wing. It has been found that a bigger wing is beneficial since thelower wing loading results in reduced pressure levels to sonic boom for thelift contribution [41]. The result is a reduction of about 7 PLdB betweenthe two designs. However, this sonic boom loudness reduction comes with asignificant price, which is an increase of about 12 % on the maximum takeoffweight per passenger. The modified wing planform with the larger area andthe higher wing sweep demands higher structural weight, which makes the lowboom configuration heavier. Thus, it has been become clear that the low boomdesign is related with a performance penalty, as an effect of the increased aircraftstructural weight. Moreover, the high wing sweep, in addition to the low aspectratio, makes the low speed performance of the aircraft very challenging. Theabove observations conclude that there is a trade-off between the aircraft performanceand the sonic boom loudness, which has to be balanced [42].

Furthermore, the low boom design usually leads to the aircraft wave dragincrement. The sonic boom minimization concepts adopt blunt nose, which isfar from the optimal configuration for minimal wave drag. A blunt nose createsa strong bow shock, so that the secondary shocks are weak and do not overtake

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and enhance the front shock. The far field pressure signature produced in thisway, thus, comes to be much weaker than in the case of a sharp nose, wherethe front bow shock coalesces with the stronger secondary shock waves [43]. Inthis case, the nose shape is a trade-off between the sonic boom loudness and thewave drag magnitude as well.

Figure 8.2 – Drawing and specifications of the low boom configuration [41].

The examination of low boom concepts for aircraft with high payload hasshown that it was very difficult to achieve theoritical ground overpressure substantiallyless than 1 psf [44]. For that reason a lighter and smaller aircraft would beperhaps a better candidate for decreasing the sonic boom loudness. A lighteraircraft demands a lower amount of lift to sustain level flight, which is a factorthat decreases the sonic boom intensity [45]. It has to be mentioned here thatthe sonic boom is measured in psf or Pa of overpressure. For shaped pressuresignatures, reference [46] provides with a method to obtain the relevant perceivedlevel of noise loudness (PLdB).

As it has been stated before, the wing planform is an important factor forachieving reduced sonic boom. In the case of the small SST design, still reduced

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wing loading is needed and thus a large wing. It is important too that the wingincorporates a long wing root, which will result in the gradual development ofthe area and lift. Moreover, the span cannot be decreased too much, in orderto maintain an acceptable performance during the low-speed flight. Normally,the wing in a low boom design is usually placed well aft in comparison with theconventional one, so that its interaction with the aircraft nose shock is reduced.However, this creates serious problems with the aircraft stability. The center ofgravity of the fuel placed in the wing can be at a long distance with respect tothe empty aircraft center of gravity, which can result in large shifts of the totalaircraft center of gravity location [47]. For that reason as much fuel as possiblehas to be placed in the front portion of the wing, which due to its increased sizeand thus volume will perhaps offer this opportunity. Finally, this fact would notallow the wing to incorporate very thin airfoils, in order to achieve the desiredvolume for the fuel storage, which would subsequently increase the drag.

The fuselage design of a small SST design has also the disadvantage ofthe decreased fineness ratio, since the length of the body is smaller but themaximum diameter cannot be decreased too much in order to be able to housethe passengers and of course the aircraft systems. That has anyway an importantwave drag penalty on the design. Furthermore, the optimal position of theengines, according to [44], would be the aft fuselage behind the wing trailingedge. This wing-nacelle interference would be in this way avoided and the flowfield disturbances of the nacelles would correspond just to volume and not tolift contribution effects. Another advantage would be increased space for thetrailing edge devices placement on the wing. However, the engines support inthis location would add on structural weight as well.

Figure 8.3 – Three view of a low boom SBJ concept [44].

In figure 8.3, a concept for a low boom supersonic business jet (SBJ), capableof carrying 8-10 passengers, is illustrated. This SBJ design incorporates acanard, instead of a horizontal tail, and all the relevant specifications of theconcept can be found in reference [44]. Due to its decreased size and weight

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compared to the bigger SST concepts, which is also a result of flying at Machnumbers below 2, this design was able to generate significant lower groundoverpressure of about 0.5 psf at cruise start. However, the drag and weightpenalties that are accompanied with the low boom design are becoming evenmore apparent. The consequence is an aircraft with lower performance, whichalthough makes the design environmentally viable, its economical viability isquestioned. Furthermore, the increased weight of the low boom design createssome difficulties regarding the incorporation of engines with reasonable size andweight, that would be capable of producing the necessary thrust for satisfyingthe aircraft supercruise requirement. The development of engines with improvedperformance and the usage of composite materials would be substantial factorsin achieving an economic viable concept as well.

8.2 Air Pollution

8.2.1 Air Pollutants Identification

During the flight, various pollutants substances are being emitted into theatmosphere and are primarily due to the combustion gases from the propulsionsystem. During the combustion process in general the most important pollutantemissions that can be identified are the carbon dioxide (CO2), the nitrogen oxides(NOx), the water vapor (H2O), the carbon monoxide (CO), the hydrocarbons(HC ), the sulfur oxides (SOx) and the soot particles (C ). In reference [48], adetailed analysis is presented regarding the chemical mechanisms of the pollutantscreation. Here only a brief description of them and their environmental impactwill be made.

Carbon dioxide is the product of complete combustion of hydrocarbon fuels,like kerosene in this case. Carbon in fuel combines with oxygen in the air toproduce CO2. It is the most significant gas that contributes to the greenhouseeffect. Carbon dioxide emissions from aircraft can be calculated from a knowledgeof the amount of fuel consumed during the flight. Fuel consumption does notscale linearly with distance traveled due to the extra fuel burn required to liftthe plane up to cruising altitude, and the necessity to carry large quantities offuel for long distance flights. The highest fuel burn rate, thus the highest rateemission of gases, occurs during the take-off and climb section, because of theincreased thrust needed to climb to cruise altitude and the heavier configurationof the aircraft comparing to the other stages of the flight. The cruise is the mostfuel-efficient stage of the flight because the air is less dense and the aircraft isflying at its most efficient operating speed, so the emissions are less than the firststage of the flight. However, for the intercontinental flight that will be executedin this case, the cruise time and distance is a lot longer than the correspondingones of the take-off and climb part. Thus the biggest part of the CO2 emissionsare carried out at the cruise altitude. These emissions from an individual flightdepend mainly on the distance traveled, the weather conditions (head or tailwind), the flight altitude, the cargo and passengers load.

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Nitrogen oxides are produced when air passes through high temperature/highpressure combustion, where nitrogen and oxygen present in the air combine toform NOx. The nitrogen oxides are one of the most dangerous and toxic airpollutant of aviation activity. They contribute to various environmental effectsand have significant impact throughout the whole flight, on both higher and loweraltitudes. The NOx are produced in higher engine power settings in contrast tothe CO and the HC, and its emissions are maximum near the stoichiometriccondition. In figure 8.4, the various air pollutants emissions dependence on theequivalence ratio (Φ), can be observed. The Φ is defined as the fuel-to-air ratioof the mixture over the relevant air-to-fuel ratio for stoichiometric combustion.Therefore, for Φ <1 the mixture is characterized as lean, and for Φ >1 as rich.

Figure 8.4 – Air pollutants formation [48].

Water vapor is the other product of complete combustion as hydrogen inthe fuel combines with oxygen in the air to produce H2O and is released by thepropulsion system into the atmosphere after the combustion process. For thelow layers of the atmosphere these emissions can be neglected, since they aretoo low compared to the natural emissions. However, at high altitude, undercertain atmospheric conditions, because of the very low temperature of the air,the vapor condenses into droplets to form contrails and cirrus clouds. So, theimpact of this pollutant should be taken into account only on the cruise part ofthe flight. It is considered to have an effect to global warming and possibly toprecipitation inducement.

Carbon monoxide is formed due to the incomplete combustion of the carbonin the fuel. It is a short-lived greenhouse gas (2 months) and its concentration isextremely variable. In the atmosphere it is eventually oxidized to carbon dioxide.It is very toxic and poisonous in the ground level, and in the higher layers of theatmosphere can contribute to the increase of the tropospheric ozone, through its

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photochemical oxidation. The CO is a result of the incomplete combustion ofthe fuel and is mainly formed because of the absence of sufficient O2 during thecombustion. Thus, the emissions of CO are maximized at lean mixture operationat low power settings, such as during idle. The presence of carbon monoxide canbe detected and measured with CO detectors, in order to prevent poisoning.

Hydrocarbons are emitted due to incomplete fuel combustion. They arealso referred to as volatile organic compounds (VOCs). Many VOCs are alsohazardous air pollutants. The formation of unburned hydrocarbons (UHC) area result of engines with low pressure increase in the compressor and relatively lowtemperatures in the combustor. Hence, the largest amount of UHC are producedduring the lean mixture operation, i.e. during idle, like in the case of the CO.

Sulfur oxides are produced when small quantities of sulfur, present in essentiallyall hydrocarbon fuels, combine with oxygen from the air during combustion.SOx emissions are directly related to the sulfur content of the fuel, so it canbe estimated from the burned fuel and the relevant sulfur content of kerosene.These oxides are corrosive and responsible for the formation of acid rain.

Soot particles that form as a result of incomplete combustion, and are smallenough to be inhaled, are referred to as particulate matters. They can be solidor liquid. Particulate emissions were a problem on the earlier jet engines whenoperating on high thrust settings. For normal operating conditions of the modernengines, the production of smoke in every stage of the flight has been radicallyreduced, so that the amount of particulate emissions can be considered negligible.

8.2.2 Environmental Concerns of Supersonic Flight

The major environmental impacts of aviation include primarily the climatechange and the ozone layer depletion. The two more prominent differencesbetween supersonic and subsonic cruise are the increased fuel consumption,which leads to an increase in combustion products, and the higher cruise altitudeof the supersonic compared to the subsonic aircraft. The relevant influence of thesupersonic transport on the aforementioned environmental impacts is examinedin the following subsections.

Climate Change

The climate change, which is particularly being referred as enhanced greenhouseeffect or global warming, is one of the most important environmental concerns.The uniqueness of the aircraft operation, compared to the other human activitiesaffecting the climate change, is the direct emission of air pollutants into thehigher levels of the atmosphere. The gases, which are being emitted from thejet engines and contribute to the greenhouse effect, are the carbon dioxide,the nitrogen oxides and the water vapor. The greenhouse effect increases thetemperature of the Earth by trapping heat in the atmosphere. This heat isa result of the sun radiation absorption from the greenhouse gases, which are

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hindering the heat absorbed from the ground to bounce back to space. Theglobal average surface temperature of the earth has increased by 0.6◦C duringthe 20th century, while a increment of at least 1.8◦C is expected for the nextone [49]. Apart from the global temperature rise, this trapping of heat in theatmosphere can also affect the weather conditions on the planet, such as theappearance of heavier rainfall, floods, tornadoes, thunderstorms. Investigationshave also shown that the oceans are possible to expand, the ice on the poles tomelt and the surface of the sea level to rise covering parts of the existing land.

Although the contribution of the aviation emissions is only a small portionof the total greenhouse gases emissions, the increment of the air traffic over thelast years and the forecasts for the upcoming ones, show that can develop in arather serious factor as regards the climate change. According to the EuropeanEnvironmental Agency [51], the emissions of CO2 have increased about 80 %between 1990 and 2014, while the prediction is for a further grow of 45 % between2014 and 2035. There are currently no requirements for the engine certificationrespective with the greenhouse gases. However, the recent trend of the aviationemissions increment, make their influence on the enhanced greenhouse effectmore substantial.

From the emitted gases the most problematic for the greenhouse effect isconsidered to be the CO2, which among else has a long life cycle. The H2Ocan be considered a significant emission too, especially for flying vehicles in thestratosphere, like the supersonic transport. Flying in such high altitudes, withvery low temperatures, the water vapor produced is converted into persistentcontrails, which evaporate very slowly. These contrails may be very long (dozensof kilometers), forming the so-called cirrus cloud fields, which can potentiallyhave a strong influence in the climate change. The water is produced as a fixedratio to fuel which is consumed for complete combustion of kerosene, like inthe case of the carbon dioxide. In particular, the combustion of 1 kg keroseneproduces 3.16 kg CO2 and 1.24 kg H2O [48].

In tables 8.1 and 8.2, the emissions of CO2 and H2O of the supersonictransport design are compared to the relevant emissions of a commercial subsonicairliner. The results correspond to a transatlantic flight of 6050 km with a 100%passenger load factor. The emissions of the SST design per km are lower, whichis a consequence of its smaller payload (just 15 passengers instead of the 416of the Boeing 747) and thus size. However, the emissions of CO2 and H2Oper km per seat of the SST are about 5.85 times greater than the subsonicairliner’s. That comes from the fact that the SST cruises at a significantlysmaller drag-to-lift ratio and with a larger thrust specific fuel consumption. Inparticular, the specific fuel consumption of the RB211-524H installed in Boeing747 during cruise is 16.14 g/KN/s [52], which is a value considerably lower.

From the obtained results, it can be inferred that the influence of smallsupersonic aircraft flight would not be so environmentally problematic concerningthe greenhouse effect. However, an excessive growth of the supersonic transportation,especially in the case of large supersonic transports replacing part of the current

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subsonic flee, could essentially affect the total aviation emissions. Moreover,the phenomenon of the persistent contrails and cirrus clouds formation at thestratosphere and its consequences on the environment would need to be furtherinvestigated.

Aircraft CO2 (kg/km) CO2 (kg/km/seat)Boeing 747 33.6960 0.0810 [53]

SST 7.1191 0.4746

Table 8.1 – Carbon dioxide emissions of subsonic airliner and SST design(6050 km distance flown).

Aircraft H2O (kg/km) H2O (kg/km/seat)Boeing 747 13.2225 0.0318

SST 2.7936 0.1862

Table 8.2 – Water vapor emissions of subsonic airliner and SST design(6050 km distance flown).

Ozone Layer Depletion

The influence of the supersonic flight on the ozone layer constitutes thebiggest environmental concern. Nearly 90% of the ozone exists in the stratosphere,forming the ozone layer. Since the SST cruises at high altitudes from 47,700 toabout 57,300 ft, it is obvious that the aircraft will directly emit the producedNOx in the stratosphere and thus in the ozone layer. The subsonic airlinersexecuting long haul flights at a cruise altitude of around 35,000 ft are emittingNOx in the low level of the stratosphere as well. The NOx in the stratosphereare participating in a catalytic chemical reaction, which leads to the ozonedestruction. The ozone layer breakdown could allow the ultraviolet B radiationfrom the sun to pass through this ozone shield and reach the Earth, whichcould cause among else skin cancer and cataract in humans, but could harm theanimals too. However, both the subsonic and supersonic aircraft emit NOx inthe stratosphere, the impact of the SST flying at higher flight altitudes is moresignificant due to the increased ozone concentration. It is shown in figure 8.5that the highest ozone concentrations are observed between 60,000 and 80,000 ft,which comprise the typical flight altitudes of supersonic aircraft at speeds equalto Mach 2 and higher. Thus, the excessive flight of large supersonic transportswith speeds greater than Mach 2, cruising at altitudes near the maximum ozoneconcentration while burning big amount of fuel, could potentially be the mostproblematic SST concept regarding the ozone depletion environmental impact.

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Figure 8.5 – Atmosphere ozone concentration and temperature till thealtitude of 100,000 ft [54].

The NOx are produced during the combustion of the kerosene. In reference[55], it is shown a simple correlation between the NOx emission index (EINOx )and the combustor inlet total temperature (Ttc). The equation (8.1) is anempirical relation for the prediction of the NOx emissions based on the so-calledLipfert correlation, stated previously [48], where δ is defined in equation (2.16).

EINOx = 10(1+0.0032(Ttc−581.25))√δ (8.1)

The above equation demonstrates that for high combustor inlet temperaturesand thus high engine pressure ratios, the NOx emissions of the engine aresignificantly increased. The pressure ratio, determining the total temperatureat the compressor exit, influences the actual primary zone temperature in thecombustion chamber [48], and thus the NOx production as well. In figure 8.6, theNOx emissions index variation is presented with respect to the overall pressureratio for a subsonic airliner and the SST design. The example of the subsonicaircraft that was used is the Boeing 747-400, and the relevant cruise conditionsare 0.85 Mach at a flight altitude of 11 km. For the SST the cruise speed is1.7 Mach at an average flight altitude of 16 km. The upper limit of the overallpressure ratio, including the fan, of the RB211-524H engine of the Boeing 747-400is set to 33 [52], while for the EJ200 is set to 22, so that the total temperatureat the compressor exit does not exceed 900 K, which is a practical limit of thecompressor materials and its cooling requirements [50]. For the RB211-524H a

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diffuser isentropic efficiency of 0.97 has been assumed, while the intake isentropicefficiency for the SST would be 0.95 as estimated in Chapter 2. For both engines,the compression isentropic efficiency has been set to the typical value of 0.85.

Figure 8.6 – NOx emissions index for SST design (red) and for a typicalsubsonic long haul airliner (blue).

From the calculated values illustrated on figure 8.6, the maximum EINOx ofthe subsonic aircraft is about 16.2 g/kg fuel at its maximum compression ratio of33, which is a value that agrees with the relevant ones stated in reference [56] forlong range subsonic transports. On the contrary, the pressure ratio effect on theEINOx of the SST is much more prominent with an emissions index of 36.58 g/kgfuel at the maximum set pressure ratio of 22. The increased fuel consumptionof the SST is also a parameter that contributes to even higher NOx emissions,creating great concerns about the environmental viability of an excessive turnin supersonic transportation in the near future.

In order to keep NOx emissions within acceptable limits, an emissions indexas low as 5 during cruise, which corresponds to about a 80% reduction of theabove calculated values, would be necessary, which has been the goal set tobe investigated during the NASA’s High Speed Research Program as well [54].In order to achieve such low NOx emissions, new engine concepts have to bedeveloped emphasizing on this reduction, while maintaining the other enginerequirements of low thrust specific fuel consumption, high thrust-to-weight ratioand reliability. Moreover, the economic viability of the undertaking to build anew engine capable to be incorporated at supersonic aircraft has to be examinedas well.

In order to reduce the NOx emissions, the equivalence ratio Φ has to becontrolled, so that the engine operates in the low emissions region of Φ, accordingto figure 8.4. Moreover, it is important to reduce the time of the gases remainingin high temperatures. There are different types of combustor concepts, referred

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to as dry low NOx combustors, which focus on more efficient, as regards therelevant emissions, combustion process. Three types of them are the lean premixedpre vaporized combustor, the staged combustor type and the rich burn quickquench lean combustor. The concepts behind the aforementioned combustionchambers operation, in addition to their pros and cons, are more thoroughlydescribed in reference [48].

Finally, the water emissions in the stratosphere is believed to have someinfluence on the ozone destruction too, since it can affect the affect the composition,growth and aerosol reactions and provide a source of HOx radicals that enhanceozone loss [54]. However, this is an effect that has to be further investigated, sothat the consequences of the water vapor emissions in the ozone layer becomemore certain.

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9. Discussion - Conclusions

Since the Concorde retirement, there is no supersonic transport aircraft inoperation, but the possibility of a new SST development is becoming a realityonce again. Efforts are being made in both the development of a low-boomdesign and a SST able to fly supersonically just overseas.

The design proposed in this project is a supersonic transport aircraft able tocarry 15 passengers and 4 crew members, having a maximum payload of 1900kg. The aircraft is being able to fly at supersonic speeds just overseas, since ithas not be designed for reduced aerodynamic noise generation. The cruise flightconditions are 1.7 Mach at an initial altitude of 14.55 km. The aircraft’s take offmass is estimated as 24499 kg, while the wing area is about 63.75 m2. The totaldry thrust at SL is 120 kN , provided by two low-bypass ratio turbofan EJ200engines. In order to surpass the sound barrier, the aircraft has to incorporatea carefully area-ruled design, with a parasite drag coefficient at the given cruiseconditions that should not exceed 0.021.

The aircraft, in order to exhibit satisfactory static longitudinal stability inboth subsonic and supersonic speeds, keeping the static margin to 0.1 for everyflight condition, uses fuel shifting for the aft movement of the aircraft centerof gravity during supersonic flight. The design incorporates a whole movinghorizontal tail is used instead of an elevator. During the supersonic cruise, theaircraft is estimated to fly at about 3 deg angle of attack in trimmed condition.Hence, a wing incidence of 3 deg would be chosen to minimize the fuselage dragduring cruise.

During the mission a total horizontal range of 6053 km can be covered, inaddition to a maximum loiter of 24 min. This range is rather smaller thanthe desired requirement of 7200 km. However, it could be increased throughcamber and wing twist optimization, so that the estimated drag-to-lift ratio of5.764 reaches a more efficient value. The estimated time of a transatlantic flightbetween London and New York is estimated at about 4 hrs.

The aircraft exhibits adequate flying and handling qualities in subsonic speeds,like the dynamic stability modes evaluation has shown, from the obtained flighttest measurements. However, these qualities was not possible to be assessed forthe supersonic speeds as well, since the flight test failed to give reasonable resultsusing the simulation model created.

The two most important environmental concerns about the supersonic flight

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are the noise generated by the shock waves, the so-called sonic boom, and the airpollutants emissions. A discussion made about low-boom design shows that thesonic boom is quite hard to be reduced in larger and heavier aircraft. Moreover,the low-boom design and the aircraft performance optimization contradict eachother, so that this trade-off between them questions the economic viability of thereduced sonic boom loudness designs. As regards the air pollution, the excessiveturn in supersonic flight could lead to two significant environmental impacts,named the climate change and the ozone layer depletion. It has been shown thatthe emissions of greenhouse gases, like the carbon dioxide, are bigger comparedto subsonic airliners, as a result of the higher fuel consumption. The highernitrogen oxide emissions, resulting from the supersonic flight, at the stratosphere,especially in altitudes where the ozone concentration is maximum, constitute aneven more significant problem to be tackled.

During the conceptual design and the flight test, the aeroelastic effects havebeen disregarded. Moreover, the aerodynamic coefficients referring to transonicflights have been just interpolated following charts and theoretical guidelinesgiven from Raymer in reference [9], due to lack of valid empirical relations.CFD simulation would be a more accurate way for obtaining the transonicaerodynamic coefficients. Finally, CFD simulations could be used for the evaluationand validation of the used subsonic and supersonic wing aerodynamic coefficientsas well.

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Appendices

A. Airfoils Coordinates

NACA 64-006 coordinates [15].

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NACA 64-009 coordinates [15].

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B. Airfoils Aerodynamic Characteristics

NACA 64-006 lift and pitching moment coefficient [15].

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NACA 64-006 drag polar [15].

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NACA 64-009 lift and pitching moment coefficient [15].

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NACA 64-009 drag polar [15].

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