Degree Project in Aeronautics

Transcription

1 DEGREE PROJECT IN VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2017 Degree Project in Aeronautics Conceptual design, flying and handling qualities of a supersonic transport aircraft. NIKOLAOS PERGAMALIS KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

2

3 Abstract The purpose of this project is the design of a supersonic aircraft that is able to meet the market s requirements, be economically viable and mitigate the current barriers. The initial requirements of the design have been set according to the understanding obtained from a brief market research, taking into account the market needs, in addition to the economical and environmental restrictions. The conceptual design proposed is a supersonic transport able to execute transatlantic flights carrying 15 passengers. The aerodynamics, propulsion data and weight of the design have been estimated using empirical relations and experimental data found in references. The design has been evaluated regarding its performance, stability, flying and handling qualities. The relevant models have been created using the software Matlab, while the flight testing has been executed at the Merlin MP521 engineering flight simulator. Finally, a discussion is made about the environmental impact of the supersonic transport, focusing on the aerodynamic noise, generated by the sonic boom, and the air pollutants emissions.

4 Contents 1 Introduction 11 2 Conceptual Design Market Research Initial Sizing Desired Requirements Initial takeoff weight estimation Mission profile and segments weight fractions Thrust-to-weight ratio Wing loading Constraint analysis Initial sizing results Wing Tail Fuselage Landing gear Propulsion Aircraft model Control surfaces Aerodynamics Airfoils Airfoil selection Subsonic aerodynamic coefficients Supersonic aerodynamic coefficients Subsonic Lift-Curve Slope Wing - Fuselage Assembly Horizontal Tail Total aircraft Supersonic Lift-Curve Slope Maximum Lift Coefficient Clean configuration High lift devices Horizontal tail Subsonic Parasite Drag Coefficient Equivalent skin-friction method

5 3.5.2 Component buildup method Supersonic Parasite Drag Coefficient Critical Mach number Drag due to Lift Miscellaneous Drag Flaps Spoilers Landing gear Weights Weights Estimation Refined Method Center of Gravity Stability and Control Subsonic Static Longitudinal Stability Aircraft Pitching Moments Subsonic Neutral Point Longitudinal Control and Trim Analysis Supersonic Static Longitudinal Stability Supersonic Neutral Point Trim Analysis Longitudinal Center of Gravity Location Directional Stability Performance Climb Performance Minimum Time to Climb Minimum Fuel to Climb Range Descent and Loiter Takeoff Landing Total Mission Test Flight Simulation Flying and Handling Qualities Modes excitation Dynamic Stability Requirements Longitudinal Dynamic Stability Lateral-Directional Dynamic Stability Environmental Impact Sonic Boom Air Pollution Air Pollutants Identification Environmental Concerns of Supersonic Flight

6 9 Discussion - Conclusions 107 4

7 List of Figures 2.1 Mission profile division Fuselage top view Fuselage side view Fuselage-wing assembly top view Fuselage-wing side view Airbus A320 main landing gear retraction and stowage Main landing gear logintudinal location [17] Diagram of nose landing gear location estimation Supersonic air inlets Three-shock external inlet Oblique shock wave Concorde rectangular ramp intakes EJ200 turbofan engine Aircraft model top view Aircraft model side view Aircraft model front view Rudder illustration NACA lift curve for Re = (XFOIL) NACA lift curve for Re = (XFOIL) Wing supersonic C Nα for taper ratio of 0.2 [13] High aspect wing and airfoil maximum lift coefficient ratio at 0.2 Mach Stall angle of attack increment at subsonic Mach numbers of Trailing and leading edge high lift devices Wing TE flaps (red), LE flaps (magenta) and ailerons (cyan) Sear-Haacks body volume distribution [9] Wing-body area rule design [9] Aircraft cross-section area distribution Wing critical Mach number in two-dimensional flow Wing control surfaces (blue) and spoilers (red) Wing-body and tail mean aerodynamic centers [28] CG position influence on C m at 0.5 Mach

8 5.3 Variation of δ t to trim with the flight speed and the static margin at SL flight Variation of δ t to trim with the flight speed and the flight altitude for the subsonic Mach number range Variation of α trim with the flight speed and the flight altitude for the subsonic Mach number range Variation of δ t to trim with the flight speed and the flight altitude for the supersonic Mach number range and static margin of Variation of δ t to trim with the flight speed and the flight altitude for the supersonic Mach number range and static margin of Variation of α trim with the flight speed and the flight altitude for the supersonic Mach number range SEP contours diagram (dry thrust) Flight path for minimum time to climb at cruise conditions Flight path for minimum fuel to climb at cruise conditions Illustration of takeoff path and distance Illustration of landing path and distance [13] Short-period mode frequency requirements [39] Elevator impulse input flight recording of the short period mode for 0.6 Mach at 30 kft Body axis pitch rate flight recording of the short period mode for 0.6 Mach at 30 kft Elevator step input flight recording of the phugoid mode for 0.6 Mach at 30 kft True airspeed flight recording of the phugoid mode for 0.6 Mach at 30 kft Euler roll angle flight recording of the spiral mode for 0.6 Mach at 30 kft Aileron input flight recording of the roll subsidence mode for 0.6 Mach at 30 kft Euler roll angle flight recording of the roll subsidence mode for 0.6 Mach at 30 kft Body axis roll rate flight recording of the roll subsidence mode for 0.6 Mach at 30 kft Rudder input flight recording of the dutch roll mode for 0.6 Mach at 30 kft Body axis roll rate flight recording of the dutch roll mode for 0.6 Mach at 30 kft Body axis yaw rate flight recording of the dutch roll mode for 0.6 Mach at 30 kft Drawing and specifications of the baseline configuration [41] Drawing and specifications of the low boom configuration [41] Three view of a low boom SBJ concept [44] Air pollutants formation [48]

9 8.5 Atmosphere ozone concentration and temperature till the altitude of 100,000 ft [54] NO x emissions index for SST design (red) and for a typical subsonic long haul airliner (blue)

10 List of Tables 2.1 Summary of aircraft requirements Summary of aircraft specifications Summary of wing basic dimensions Summary of tail basic dimensions Fuselage basic dimensions Properties of the designed 4-shock external inlet for freestream Mach number M 1 = EJ200 engine specifications Propulsion system basic dimensions Aircraft exposed and wetted areas NACA aerodynamic coefficients ( Re = ) NACA aerodynamic coefficients ( Re = ) Lift-curve slope of wing - body assembly for subsonic Mach number range Lift-curve slope of horizontal tail, downwash angle derivative and horizontal tail C Lα contribution to the aircraft, respectively, for subsonic Mach number range Aircraft lift-curve slope for subsonic Mach number range Wing-body and horizontal tail lift-curve slope for supersonic Mach number range Horizontal tail downwash angle derivative and C Lα contribution to the aircraft, respectively, for supersonic Mach number range Aircraft lift-curve slope for supersonic Mach number range Subsonic aircraft maximum lift coefficient and stall angle of attack Subsonic horizontal tail maximum lift coefficient and stall angle of attack Subsonic parasite drag coefficients for the stated Mach number and altitude flight conditions Supersonic skin-friction drag coefficient component for the stated Mach number and altitude flight conditions Supersonic parasite drag coefficient component for the stated Mach number and altitude flight conditions Supersonic drag-due-to-lift factor Drag coefficients of high lift devices during takeoff and landing

11 4.1 Aircraft weights estimation CG vertical location of basic aircraft components Directional stability derivatives for the subsonic Mach number range Short-period mode damping ratio limits Phugoid mode stability requirements Minimum time to double amplitude limits for spiral mode Roll subsidence mode time constant limits Dutch roll mode damping ratio and frequency limits Variation of short-period pitching mode characteristics with speed and altitude Variation of phugoid mode characteristics with speed and altitude Variation of spiral mode characteristics with speed and altitude Variation of roll subsidence mode characteristics with speed and altitude Variation of dutch roll mode characteristics with speed and altitude Carbon dioxide emissions of subsonic airliner and SST design (6050 km distance flown) Water vapor emissions of subsonic airliner and SST design (6050 km distance flown)

12 Nomenclature A Area, m 2 a Acceleration, m/s 2 AR Aspect ratio b Span, m C Thrust SFC, g/kn s c Chord. m C D Drag coefficient C f Skin-friction coefficient C L Lift coefficient C m Pitching moment coefficient C P Pressure coefficient D Drag, N D Diameter,m d Distance, m E Endurance, sec EI Emissions index e Oswald efficiency factor g Gravitational acceleration, m/s 2 h Height, m I Area moment of inertia, m 4 i Incidence angle, deg K Drag-due-to-lift factor L Lift, N L Length, m l Length, m M Mach number m Mass, kg ṁ Mass flow, kg/s n Load factor P Pressure, P a p Roll rate, deg/sec q Pitch rate, deg/sec q Dynamic pressure, P a R Range, m r Yaw rate, deg/sec r Radius, m Re Reynolds number S Area, m 2 T Thrust, N T Temperature, K T Period, sec t Time, sec t Thickness, m T R Throttle ratio V Speed, m s 1 W Weight, N x Longitudinal position, m y Span-wise (lateral) position, m z Vertical position, m α Angle of attack, deg γ Flight path angle, deg δ Control surface deflection, deg ɛ Downwash angle, deg η Elevator deflection angle, rad ζ Rudder deflection angle, rad ζ Damping ratio θ Angle, deg Λ Sweep angle, deg λ Taper ratio µ Rolling friction coefficient ξ Aileron deflection angle, rad ρ Density, kg/m 3 σ Sidewash angle, deg φ Euler roll angle, deg ω Angular frequency, rad/s 10

13 1. Introduction In recent years, the prospect for an supersonic passenger jet operation has risen again. The progress achieved in jet propulsion engines and the possibility of composite materials usage at the aircraft structure are the main reasons that the success of the supersonic flight has become much more feasible nowadays compared to the past. NASA has already began to work on the preliminary design for a low-boom supersonic passenger with the project Quiet Supersonic Technology (QueSST) [1], which has aroused its interest in the supersonic transportation, after the High Speed Research (HSR) program that phased out in Moreover, a newly founded company, named Boom Technology Inc., has started the development of a supersonic transport aircraft being able to fly at a speed of 2.2 Mach and carry up to 45 passengers [2]. The aim of the Boom Technology design is to achieve fares comparable to the subsonic airliners business class and increase the aircraft s utilization and passengers load factors through the reduced seat capacity of the aircraft, in comparison with the Concorde s economic failure in this 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 regards the relevant regulation process and the mission accomplishment limitations. In this project, an effort is made for a supersonic transport aircraft conceptual design, which could be viable in the current market, as a result of the increasing interest on this aeronautical domain. The whole conceptual design process is demonstrated and the design is evaluated regarding its performance, stability, and flying and handling qualities. Difficulties and problems that refer to the design process and the requirements satisfaction are addressed, and improvements, solutions are implemented or proposed, where possible. 11

14 2. Conceptual Design 2.1 Market Research Flying supersonic has always been a very promising and tempting idea. A flight duration could become two or three times less in comparison to the relevant ones of subsonic aircraft. After the Concorde retirement in 2003,the supersonic civil transportation is not existent any more. Although the required technology to construct supersonic aircraft exists, the economic sustainment of the concept, as the case of the Concorde, has shown is not feasible [3]. The supersonic overland flight ban has also imposed one more important constraint. For the above reasons, an excessive turn of the civil transportation from subsonic to supersonic is highly improbable at least in the upcoming two or three decades. However, the need for over-haul flights is expected to increase significantly during the next twenty years. According to the Airbus forecast about the global market for the period from 2016 to 2035 an increase of 95 % is anticipated for the long-haul traffic [6]. Moreover, Boeing s current market outlook ( ) is also forecasting a grow of 5 % annually in the long-haul traffic over the relevant time period [7]. These forecasts regarding the market growth and the increased demand in intercontinental flights set a quite promising ground for the supersonic flight involvement, where its biggest advantage of diminishing the flight time could be maximally exploited. Large supersonic transport aircraft, like the Concorde, will more likely not be successful, since the added cost will be a significant hindering factor for the common passenger to choose it. For this reason, the supersonic aircraft will probably recruit exclusively business class passengers from the regular airline flights, 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 the economic success of the concept, since the development risk and expenditure will be significantly lower, as well as the potential market share [4]. Private individuals who are keen to buy business jets could be potential customers for small supersonic aircraft too. In the upcoming ten years ( ) 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 and Europe, fast and comfort transatlantic flights with a prestigious aircraft could 12

15 be an interesting choice for some wealthy individuals, not caring so much for overall cost. Other potential customers could be government agencies, since officials could save this way valuable time, and big corporations. Regarding the overland ban, the solution of planning routes that cover long overseas distances seems the more realistic. Such routes can be for example the London New York or the Paris New York, which are now two of the most busy intercontinental routes in operation. Moreover, routes in south-east Asia 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 aircraft delivery with a global share of 38 % [7]. The growth that will be realized in this area offers also new opportunities for long-haul supersonic flights. An example is the Dubai Singapore route, which can be performed almost overseas, by just making a small detour (less than 5 % in total distance covered) compared to the direct route [4]. The possibilities given for mostly overseas long-haul flights decreases the necessity for an extreme low-boom design, which would reduce the sonic boom sound intensity level into the acceptable range for human hearing. Developing this kind of design would add extra development costs and would deteriorate in general the aerodynamic performance of the aircraft, resulting in reduced fuel efficiency, thus increasing further the cost, which has to be kept as low as possible. The environmental consequences due to increased pollutant emission to the atmosphere would be another important factor to be considered. In conclusion, using all the above observations, the most feasible supersonic transport design, considering mainly the financial and secondly the technical limitations, would be the construction of a quite small supersonic aircraft that could carry 15 passengers and have a range of 7200 km in order to execute transatlantic flights. The cruise speed would be 1.7 Mach, which is about the double of the regular cruise speed of a subsonic airliner. Although a higher Mach number is preferred as more enticing for the clients, the choice of a moderate speed would result in building an aircraft with reduced weight, having a positive effect in fuel consumption and noise generation [5]. 13

16 2.2 Initial Sizing The initial design process includes the specification of the desired requirements according to the aircraft mission and role. Then, the mission profile sections have to be defined. According to this mission profile, an initial estimation will be done for the maximum take-off weight Desired Requirements The desired requirements for the supersonic transport to be designed are presented in Table 2.1. Cruise speed Maximum speed Minimum payload mass Cruise altitude Range Loiter time Landing distance Takeoff distance (SL) Thrust specific fuel consumption (cruise) 1.7 Mach 1.7 Mach 1900 kg 15 km 7200 km 20 min 3500 m 3500 m 26.9 g/kn s Table 2.1 Summary of aircraft requirements. The payload mass corresponds to the 15 passengers plus the pilot, the co-pilot and two crew members. An average of 100 kg is assigned for each person on-board including the luggages Initial takeoff weight estimation The first step is to make an initial estimation of the takeoff weight (W 0 ). The takeoff weight consists of the empty weight (W e ), the payload weight (W p ) and the fuel weight (W f ) as shown in equation (2.1). The payload weight is defined by the requirements, when the fraction of empty weight over the takeoff weight is given by the empirical relation (2.2) found in reference [9]. W 0 = W p + W f + W e W 0 W 0 (2.1) ( ) W e T 0.06 ( ) 0.05 = m AR 0.3 W0 Mmax 0.05 in fps units (2.2) W 0 W 0 S The fuel weight is computed after calculating the weight fractions for the different mission segments, since the total aircraft weight drop corresponds only to consumed fuel weight. The final fuel weight is then increased for safety reasons 14

17 by 6 %. The relevant weight fractions are calculated according to estimations derived from historical data or with approximating relations. For each mission segment i, the weight of the burned fuel is given by the relation W fi = ( 1 W ) i W i 1 (2.3) W i 1 while the total amount of fuel for all n segments of the mission is estimated as n W f = 1.06 W fi (2.4) i=1 Finally, the take-off weight can be computed using an iterative method for solving the equations (2.1), (2.2) and (2.4), making an initial estimation for W 0, which will then converge to the actual value. In order to estimate the empty weight faction (W e /W 0 ), the aspect ratio (AR,), the wing loading (W 0 /S) and the thrust-to-weight ratio (T/W 0 ) have to 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 is not feasible to construct a light wing which could be structurally strong enough to resist the relevant bending and torsional stresses in such high airspeeds and to be free of the aeroelastic phenomena effects. The thrust-to-weight ratio and the wing loading will be defined in the relevant following subsections. It should be stated here that the selection of the appropriate values for the two aforementioned parameters is a compromise. A large wing loading is more preferred for the supersonic aircraft, which results in smaller values of thrust-to weight ratio and thus lower thrust requirements. However, the wing loading is limited from a reasonably low stall speed requirement and consequently from the landing and takeoff distance restrictions Mission profile and segments weight fractions In Figure 2.1 the different segments of the mission profile for the transport aircraft 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

18 Figure 2.1 Mission profile division. The weight fractions for the different mission segments are calculated using the following relations [9] W 1 W 0 = 0.97 (2.5) W 2 W 1 = M cruise 0.01M 2 cruise (2.6) W 3 W 2 = e W 4 W 3 = e RC V (L/D) cruise (2.7) EC V (L/D) max (2.8) W 5 W 4 = 0.99 (2.9) W 6 W 5 = (2.10) For the weight fraction estimation (eq. 2.7) of the cruise phase, the Breguet range equation is used. The specific fuel consumption C for the cruise is the one defined from the requirements before, while for the loiter the typical value of the 22.7 g/kns has been used [9]. The maximum lift to drag ratio (L/D max ) is equal to the relevant value of the loiter phase for a jet aircraft. The correspondent value for the condition of the most efficient cruise is 86.6% of the L/D max for a jet aircraft [9] and is approximated using the relation [11] ( L D ) cruise = 11M 0.5 (2.11) 16

19 2.2.4 Thrust-to-weight ratio Cruise The required T/W during cruise can be simply approximated using the rigid equations of motion for steady flight. In this case, the thrust should equal the drag and the lift should equal the weight, assuming that the thrust installation angle is zero (thrust vector aligned with the velocity vector) and disregarding the angle of attack influence. Thus ( T W ) cruise ( ) L 1 = D cruise (2.12) The above equation is a good initial approximation, although it underestimates the drag, since during the level and unaccelerated flight the angles of attack experienced 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 where ( T W ) T O ( ) T = W ( ) Wcruise W T O cruise = ( ) ( Wcruise TT O W T O ( ) ( ) W2 W1 W 1 W 0 T cruise ) (2.13) = β c (2.14) The fraction (T TO /T cruise ) can be computed using the installed engine thrust lapse equations for maximum thrust presented in [10], for cruise at the desired altitude and for sea level flight. These equations apply to the expected performance of the advanced engines in the 2000 era and beyond. The flight altitude in these relations are introduced as the ratio between the static temperature (θ) and the static pressure (δ), respectively, at the flight altitude to the corresponding values at sea level, as shown in equations (2.15) and (2.16). θ = T alt /T SL (2.15) δ = P alt /P SL (2.16) The nondimensional temperature (θ 0 ) and pressure (δ 0 ) are defined using the correspondent total temperatures and pressures at flight altitude, respectively, as ( θ 0 = T t alt /T SL = θ 1 + γ 1 ) M (2.17)

20 ( δ 0 = P t alt /P SL = δ 1 + γ 1 2 M 2 ) γ γ 1 (2.18) The specific heat ratio (γ is equal to 1.4 for atmospheric air. The thrust lapse (α) is defined as the maximum thrust at flight altitude over the maximum thrust 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 α dry = { 0.6δ0 for θ 0 T R 0.6δ 0 (1 3.8(θ 0 T R)/θ 0 ) for θ 0 > T R (2.19) and the so-called wet thrust lapse, using the afterburner, is estimated as α wet = { δ0 for θ 0 T R δ 0 (1 3.5(θ 0 T R)/θ 0 ) for θ 0 > T R (2.20) The term TR appeared in the above equations is the throttle ratio, which is equal to the so-called value θ 0,break [10]. These equations are valid for values of the theta break greater than one. The theta break relates two important constraints of the turbine engine, the compressor pressure ratio and the turbine inlet temperature, being actually the point where the engine control system must switch from limiting the compressor pressure ratio to limiting the turbine inlet temperature. The θ 0,break should be chosen by the designer so that it provides the best balance of engine performance over the expected range of flight conditions. In this case of the supersonic transport, the throttle ratio should be greater than one in order to fulfill the supercruise requirement. For this reason, it is set to 1.2, so that it operates closer to the optimal value of θ 0, as given by the cruise condition, thus sustaining thrust to higher values of Mach number Wing loading Having estimated the thrust-to-weight ratio at takeoff, the wing loading will be estimated for the most critical conditions of the mission, which are the takeoff, stall and landing. After computing the relevant values, the minimum wing loading obtained will be used to calculate the wing reference area. Stall For the calculation of the wing loading for the stall condition, an initial maximum lift coefficient (C Lmax ) has to be estimated. For a supersonic aircraft having a low aspect ratio wing and a large leading edge sweep, the value for C Lmax would be quite small. In this case, a C Lmax of 1.6 will be assumed, which is a typical value for supersonic wings. Since a moderate value for C Lmax can only be obtained for the supersonic aircraft configuration, in order to avoid a 18

21 low wing loading resulting in a large wing area, a very low stalling speed cannot be achieved. However, it should be kept as low as possible so that the landing distance requirement can be fulfilled too. For this reason, a stalling speed of 68 m/s has been selected at sea-level flight. Therefore the wing loading at stall can be calculated as ( W S ) stall = 1 2 ρ SLV 2 stallc Lmax (2.21) Takeoff The wing loading at takeoff is given from the relation [9] ( W S ) T O = (T OP )σc LT O ( T W ) T O in fps units (2.22) where σ is the air density ratio (density at takeoff altitude over density at sea-level), set in this case equal to one, assuming operation from airports at almost zero altitude, like the Heathrow in London and the John F. Kennedy in New York. The takeoff speed is specified from the FAR Part 25 regulations for civil aircraft as 1.1 times the stall speed. Hence, the takeoff lift coefficient (C LTO ) is obtained by dividing the maximum lift coefficient (C Lmax ) with The takeoff parameter (TOP) can be obtained solving equation (2.22), where increasing the TOP results in a requirement for increased takeoff distance. In this case, the TOP should be chosen so that the aircraft fulfills the takeoff distance requirement, while keeping the wing loading as high as possible. Landing The maximum wing loading at landing will be estimated using the maximum landing distance requirement. A relation that connects the two parameters is the following [9] ( W S ) land = 1 80 ( ) dland 1.67 d a σc Lmax in fps units (2.23) where the landing distance (d land ) is divided by 1.67 to provide the required safety margin set by regulations (FAR 25) and d a is the obstacle-clearance distance, which is equal to 1000 ft for an airliner-type aircraft Constraint analysis After estimating the thrust-to-weight ratio and the wing loading of the aircraft for the aforementioned conditions, two important constraints, which relate the two parameters, will be evaluated so that the final values for both parameters are specified. These parameters are the takeoff distance and the supercruise 19

22 requirements. The two conditions will be evaluated using the relevant relations from reference [10]. Takeoff distance An initial approximation for takeoff distance, consisting of the ground roll and the rotation distance, can be made with relation (2.24) assuming that the thrust force is much larger than the resistance forces in the ground roll ( k 2 ) (W ) T O d T O = gρ SL C LT O α dry (T SL /W T O ) S T O ) (W ) 2 + (t r k T O in fps units ρ SL C LT O S T O (2.24) where k TO is the ratio of takeoff speed over stall speed (1.1 as defined in the previous subsection) and t R the total rotation time needed for the aircraft to move 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 cruise at 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 achieve economically 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 ( ) TSL W T O = β ( c K β ( ) c W + α dry q S T O qc D0 β c (W/S) T O ) in fps units (2.25) where α dry and β c are given from the equations (2.19) and (2.14) respectively and q is the dynamic pressure for the given cruise flight speed and altitude. The zero lift drag coefficient (C D0 ) and the K coefficient of the lift-drag polar equation (these two coefficients will be analyzed in more detail later on) are initially approximated using typical values for the specific cruise conditions as 0.03 and 0.3 respectively Initial sizing results The results obtained from the initial sizing analysis are presented in Table 2.2. The thrust-to-weight ratio corresponds to the maximum value obtained, which is the one satisfying the supercruise condition. 20

23 Empty weight fraction Fuel weight fraction Takeoff mass kg Wing loading (takeoff) 5110 N/m 2 Wing loading (stall) 4539 N/m 2 Wing loading (landing) 5629 N/m 2 Maximum thrust-to-weight ratio Takeoff distance (SL) 2283 m Table 2.2 Summary of aircraft specifications Wing Wing geometry In this section, the geometry of the wing will be defined. The choice for the wing is the trapezoidal with aspect ratio of 3.2, as stated previously. Other parameters to be defined are the leading edge wing sweep (Λ LE ) and the taper ratio (λ). The wing sweep is being used in transonic flow in order to increase the critical Mach number (the freestream Mach number at which the local Mach number on the aircraft first reaches the sonic speed) and in supersonic flow in order to decrease the loss of lift, associated with supersonic flight. Another important feature for using swept wings at supersonic flows is the delay of the appearance of aeroelastic divergence, which is critical for a light weight design for such high values of dynamic pressure. For this aircraft configuration a LE wing sweep angle of 45 deg has been chosen, which is although a bit larger compared to the Mach cone angle (arcsin(1 /M )), so that the wing is capable of creating the necessary lift for satisfying the takeoff and landing distance requirements. The usage of a swept wing results in the requirement of having a highly tapered wing in order to preserve the desired elliptical lift contribution over the wing. Producing a lift distribution over the wing that resembles the ideal elliptical 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 the ailerons placement. Recommended values for highly swept wings in supersonic flow are [9][16]. For practical and structural reasons, the lower value of 0.2 is chosen, since results in a larger chord near wing root, which is needed for engines placement, as well as grater internal volume due to increased maximum thickness, making it possible to house the landing gear and fuel tanks. The aircraft will have a low-wing configuration mainly for the practical reason of placing the landing gear. A high-wing configuration is not feasible, since for low aspect ratio supersonic wings where thin airfoils are used, there is not 21

24 enough space for their housing. An external blister would be unacceptable, since it would increase the drag significantly. A mid-wing configuration is not used in passengers aircraft for structural reasons, since the loads have to be carried across the fuselage, reducing the internal usable volume of the fuselage significantly. A low-wing configuration usually is accompanied with a dihedral angle. However, the high wing sweep is contributing to the dihedral effect too, creating a quite high effective dihedral angle, which diminishes the need of having a wing geometric dihedral. For this reason, an initial zero dihedral angle will be considered for this design. Wing sizing The first step of the wing sizing is to calculate the wing area. This can be simply done using the estimation for the minimum wing loading in the following equation S W = m 0 g (W/S) min (2.26) Knowing the wing area, aspect ratio and taper ratio of the chosen trapezoidal wing, the expressions about some important wing properties are presented. Wing span: Chord at root: b W = AR S (2.27) c root = 2S b(1 + λ) (2.28) Chord at tip: Mean aerodynamic chord (MAC): c tip = λc root (2.29) c W = 2 ( ) 1 + λ + λ 2 3 c root 1 + λ (2.30) Spanwise location of MAC with respect to the aircraft longitudinal axis of symmetry: Ȳ W = b 6 ( ) 1 + 2λ 1 + λ (2.31) 22

25 Wing dimensions In table 2.3 the basic wing dimensions are presented for the initial design. Area m 2 Span m Root chord m Tip chord m Mean aerodynamic chord m Spanwise location of MAC m Table 2.3 Summary of wing basic dimensions 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 relate the wing to the tail size, so that an initial estimation for the vertical (VT) and horizontal (HT) tail area can be made from the following equations. S V T = V V T b W S W L V T (2.32) S HT = V HT c W S W L HT (2.33) where V V T, V HT the volume coefficient, and L V T, L HT the moment arm for the vertical and the horizontal tail respectively. Typical values for the c V T and c HT are provided in [9]. The value selected for the horizontal tail is 0.4, which is smaller than the recommended typical value, since the choice of a whole-moving surface has been made in order to decrease the horizontal tail volume. Decreasing the horizontal tail volume is critical in order to achieve a area-ruled design and decrease the wave drag. The volume coefficient for the vertical tail has been set to the typical value of 0.09 for the jet transport. The tail arm moment L, which is initially approximated as the longitudinal distance of the quarter position of the wing mean chord to the quarter mean chord position of the tail, has been set 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 its geometric properties. The horizontal stabilizer has been modeled as a straight trailing 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 a greater critical Mach number compared to the wing. The vertical stabilizer has been modeled as a trapezoidal wing having a 60 degrees leading edge sweep angle. The selected values for the aspect ratio are 2.5 for the horizontal and

26 for the vertical stabilizer, while the taper ratio is 0.15 and 0.2 for the horizontal and the vertical stabilizer respectively. For computing the rest of the geometric properties of the horizontal and vertical 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 stabilizer Area m m 2 Span m m Root chord m m Tip chord m m Mean aerodynamic chord m m Table 2.4 Summary of tail basic dimensions Fuselage Fuselage dimensions The fuselage has been dimensionalized taking two important factors into consideration. Firstly, the existence of enough usable volume to host the passengers and secondly, the area ruling design, which will be further analyzed during the wave drag calculation. Briefly the fuselage has to be squeezed at the area where the wing is placed ( coke-bottling design), so that a smooth volume distribution and a smaller cross-sectional area is achieved. An initial estimation for the fuselage length for a jet transport is given using the relation (2.34) based on statistical data [9]. L fus = 0.287m (2.34) The typical compartment properties for first class seats are seat pitch of 1 m and seat width of 60 cm, where the aisle width should be about 60 cm and its height more than 193 cm [9]. Thus, the maximum diameter has been set to 2.6 m, which is a value providing enough space, while keeping the cross-sectional area as low as possible. The length of the fuselage has been enlarged by about 3 m compared to the stimation given from equation (2.34). This is done mainly for two reasons. While the fuselage maximum diameter is enough to host two passengers sitting side by side, for the portion of fuselage which is squeezed this would not be possible and just one passenger could be hosted there. The 24

27 need to place also a lavoratory increases the compartment s length requirements. Additionally, the typical cabin compartment to overall length ratio for a supersonic transport is about 0.55 [16], thus the lengthened fuselage should provide enough space for hosting all the 15 passengers. Finally, the supersonic aircraft has a sharper and longer nose in comparison to the subsonic aircraft, and a typical value of its nose length to diameter ratio is about 4 [16]. The reason for that is to avoid strong bow shock waves forming at the fuselage nose, which lead to a significant increment of the wave drag. However, having a very low nose length to diameter ratio would create practical problems with the cockpit housing and the unhindered pilots visibility, especially during landing. Fuselage lofting The designed fuselage consists of three parts: the conical nose, the main cylindrical fuselage and the fuselage tail. The main cylindrical fuselage consist of three parts. The first one is a cylinder assembled with the nose till it reaches the maximum diameter, the second part is a cylinder of the maximum diameter but squeezed in the lateral direction (the fuselage width is manipulated while the height remains constant) and the final part which is a cylinder assembled with the fuselage tail. The fuselage has been lofted in Matlab and its model can be 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 the higher side, so that the empennage can be placed higher up of the wing and thus minimize the aerodynamic interactions due to the wing wake. The basic dimensions of the fuselage lofting are presented in table 2.5. The fuselage total volume has been computed to be m 3. 25

28 Nose length Nose maximum diameter Cylindrical part length Cylindrical part maximum diameter Squeezed part minimum width Fuselage tail length Fuselage tail maximum diameter 4 m 1.8 m 19 m 2.6 m 1.56 m 4 m 2 m Table 2.5 Fuselage basic dimensions. Fuselage-wing assembly A low-wing configuration has been chosen for this aircraft design. The position of the quarter mean aerodynamic chord, which corresponds to the aerodynamic center in subsonic flight, has been placed in the longitudinal direction m rear of the fuselage nose. The fuselage-wing assembly, incorporating the area 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 to two factors. The first one is to have a long enough tail arm moment (L), which results 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 the wing too much forward, will have the consequence of a much longer and heavier landing gear and perhaps an unacceptably high load acting on the nose landing gear. Figure 2.4 Fuselage-wing assembly top view. 26

29 Figure 2.5 Fuselage-wing side view Landing gear In order to meet the requirements for the airframe layout and to avoid any increment in the aerodynamic drag, the way of how the landing gear will be stowed has to be decided. First of all, the landing gear arrangement has been chosen to be the common tricycle gear, with two main landing gears aft of the aircraft center of gravity (CG) and one nose landing gear forward of the aircraft CG. The number of wheels per strut are typically dependent on the aircraft takeoff weight. For aircraft weighing 60,000 to 175,000 lbs, such as the current design, two tires per struts are recommended [17]. The usage of two tires is also preferable for safety reasons, like in the case of a flat tire. One issue that is faced with the supersonic aircraft is the existence of very thin wings, which does not give the opportunity for the main landing gear to be stowed inside the wing easily, especially for configurations with two tires per strut like the current. For this reason, the strut will be stowed inside the wing, while the tires will be stowed inside the fuselage, after retraction, where the available volume is much bigger (inward retraction). The aforementioned concept to be used is visualized in fig. 2.6 for a subsonic airliner. Figure 2.6 Airbus A320 main landing gear retraction and stowage. 27

30 The main landing gear length and location can be determined using the conceptual design method from reference [17]. The initial recommended location for the main landing gear is about 55 % of the wing MAC. The main landing gear location is then adjusted using the 15 deg angle rule in the static position shown in fig For the current design, the correspondent location was estimated to be at about 15.6 m aft of the fuselage nose. The length then should be set so that the tail does not hit the ground during landing. Using the recommended 12 deg angle for fuselage tail tipping avoidance, which should not be much smaller than the stall angle, the main landing gear length can be approximated as 2.45 m. Figure 2.7 Main landing gear logintudinal location [17]. The nose landing gear has been selected to be a forward retracting, which is preferred since in the case of a failure the gravity and air drag assists the gear to reach the down-and-locked position. The nose landing gear length is initially set to be equal to the main landing gear length for the low-wing configuration. The longitudinal position of the nose landing gear depends on the aircraft position of the CG. For a first approximation the most aft location of the 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 12 m, the correspondent static loads on the main and the nose gear can be estimated [17]. Max static main gear load (per strut) % = (B B m )/2B (2.35) Max static nose gear load % = (B B n )/2B (2.36) 28

31 where the relevant distances are described in fig For the given distances, the landing gear load is about 43.5 % per main landing gear strut and 13 % for the nose landing gear strut, a loading contribution which is not optimal (8-10 % preferable static loading for nose landing gear considering the most aft location of 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 and the following statistical relations for transport aircraft [9]. Their diameter and width are estimated from the equations (2.37) and (2.38) as 84.1 cm and 26.3 cm respectively. D tire = 5.3m tire (2.37) where m tire is the load per tire or wheel in kg. w tire = 3.9m 0.48 tire (2.38) 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 location is a quite complex task, mainly due to the engine intake, which especially for supersonic flows has to be designed very carefully in order to control and provide the airflow needed for the engine operation. Other things that deteriorate the engine performance is the location of the engine inlet in a position where it ingests distorted airflow, such as in the wing wake, which can cause stall to the compressor. For supersonic fighters the most common configuration is to use fuselage side-mounted inlets. This is a location that provides short ducts and relatively clean air [9]. However, this is not possible for the low-wing configuration transport aircraft for practical reasons, for instance due to the need of placing the engines outside the fuselage and the need of landing gear 29

32 stowage. Using a configuration like the Concorde, has the advantages of having a quite undisturbed airflow, of avoiding interferences between the two exhaust nozzles for not being placed side by side, and for decreasing the structural stresses on the wing, due to the inertial relief effect (the wing-root shear force can be this way significantly reduced). A disadvantage of this configuration comes from the spatial requirement of mounting the engines directly at the wing, since neither the engine nor the inlet can be too long. Moreover, the nozzle placement at the wing trailing edge will reduce the usable wing area for the placement of the respective control surfaces (flaps, ailerons). Air intake In order to have a proper operation for the compressor blades, the airflow has to be decelerated to about 0.4 Mach. The air intakes for supersonic aircraft are sophisticated devices, which need to decelerate the supersonic flow to subsonic through shock waves. The efficiency of the intake is expressed from the reduction in 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 converging supersonic inlet and the diverging subsonic diffuser. The principles followed for a 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 design Mach number. A pitot or normal shock inlet, decelerating the supersonic flow to subsonic through a single normal shock wave, results in big total pressure losses 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 %. In this type of intake the maximum inlet mass flow is achieved when the normal shock is located right at the cowl lip position (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

33 dimensional ramp inlet. When this inlet operates at optimal design condition,the flow is decelerated by two oblique shocks existing at the entrance of the facing ramps, before a normal shock takes place at the minimum section position inside the intake (fig. 2.9(b)). However, when operating at off-design conditions it is possible the normal shock to take place outside the inlet (inlet not started ), a situation that can stall the engine [9]. Moreover, the boundary layer on the inlet walls 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 a longer and heavier intake [23]. The type of supersonic inlet to be used in this design is the external compression rectangular ramp inlet, where the weak oblique shocks are generated outside the inlet and are followed by a normal shock at the cowl lip (fig. 2.10). In order to design an efficient intake, the number of oblique shocks and the relevant wedge angles have to be chosen. The external shock intake length can be initially approximated using the shock angles computed from the correspondent ramp angles. 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 safety margin. Figure 2.10 Three-shock external inlet. The inlet efficiency can be optimized through the appropriate selection of the wedge angles. In order to achieve very high efficiency, the inlet will incorporate three weak oblique shocks before the normal shock. The Mach number (M ), the wedge angle (δ), the shock angle (θ) and the total pressure recovery (P t2 /P t1 ), are related using the equations (2.39), (2.40) and (2.41) for compressible, adiabatic flow of a perfect gas (for air γ=1.4) [18]. The correspondent notation can be seen in fig M 2 = 36M 4 1 sin2 θ 5(M 2 1 sin2 θ 1)(7M 2 1 sin2 θ + 5) (7M 2 1 sin2 θ 1)(M 2 1 sin2 θ + 5) (2.39) tan δ = 5 M 1 2 sin 2θ 2 cot θ 10 + M1 2(7 + 5 cos 2θ) (2.40) 31

34 ( P t2 6M 2 = 1 sin 2 ) 7/2 ( ) θ 6 5/2 P t1 M1 2 sin2 θ + 5 7M1 2 (2.41) sin2 θ 1 Figure 2.11 Oblique shock wave. The above equations can be used for the final normal shock too, setting θ=90 deg. In table 2.6, the wedge angles and the rest of the results of the four-shock external compression inlet design are presented. Wedge angle (deg) Mach number Shock angle (deg) Pressure recovery (%) Table 2.6 Properties of the designed 4-shock external inlet for freestream Mach number M 1 =1.7. The total pressure recovery for the designed supersonic inlet reaches % for decelerating the airflow from 1.7 to about 0.8 Mach. During off-design operation, the mass flow demand at lower speeds is reduced. This decrease results in the static pressure rise at the compressor inlet, which forces the flow to spill outside the compressor. Since this redundant subsonic flow has to spill out, the normal shock moves farther upstream from the lip cowl, increasing the so-called spillage drag significantly [22]. In order to avoid this effect and keep the normal 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. This technique has been adopted in the Concorde s air intake, as can be seen in fig It can be also observed in this figure the knife-edge shape of the intake sections, which is a necessary feature of the supersonic inlet, so that large shock angles and consequently increased wave drag can be avoided. 32

35 Figure 2.12 Concorde rectangular ramp intakes. Finally, a preliminary estimation can be made for the required capture area size according to an approximation found in [9], which correlates the capture area with the Mach number and the mass flow. For the freestream Mach number of 1.9, which corresponds to a safety margin of 0.2 Mach higher than the aircraft maximum design condition, the capture area (Ac ) is approximated as times the maximum air mass flow (m ). 2. Subsonic diffuser In the subsonic diffuser the airflow is further decelerated from the subsonic Mach number obtained after the normal shock to 0.4 Mach to meet the compressor operation conditions. This is achieved through a diverging duct, which means that the area inside the intake should increase. The throat area to the engine front face area can be estimated from the relation (2.42), which is used to express the maximum area ratio between any two stations into the diffuser in terms of the Mach number, corresponding to maximum air mass flow [23]. Athroat M1 = Aengine M M M12!3 (2.42) In this design, the objective is to slow down the flow from to 0.4 Mach and thus the relevant ratio between the throat and the engine area is computed as , which means that the respective diameter ratio between the throat and the engine would be The subsonic diffuser has a typical efficiency of %, which will result to a total efficiency of the supersonic air intake of about 95 % for the given design. In order to avoid high viscous forces on the duct walls and consequently separation of the boundary layer flow, which would increase the total pressure losses, the diffuser has to incorporate small expansion angles. The upper limit of the slope is considered to be 10 deg [23]. Therefore, a slope of 6 deg has been 33

36 chosen for the diffuser design to ensure high intake efficiency. Knowing the duct slope and the correspondent throat and engine diameters, an initial estimation can be made for the subsonic diffuser length. Engine selection The main criteria for the engine selection is to provide enough thrust for the aircraft operation (satisfy the maximum thrust-to-weight ratio), to have a low thrust specific consumption, so that it it satisfies the requirements, a low weight and a small size, to avoid increased parasite drag. For satisfying the fuel consumption requirement, it is preferable to incorporate a low-bypass ratio afterburning turbofan instead of a turbojet. Another benefit of the turbofan engine 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 used as powerplant for the Eurofighter Typhoon. The EJ200 has been developed and produced in an international cooperation among Rolls-Royce, Avio, ITP (Industria de Turbo Propulsores) and MTU Aero Engines. The relevant engine specifications are shown in table 2.7. The presented data have been retrieved from one of the engine manufacturers, particularly the MTU Aero Engines product leaflet [24]. Two EJ200 engines will be incorporated in the supersonic transport design. Maximum thrust, reheated 90 kn Maximum thrust, dry 60 kn Bypass ratio 0.4 Overall pressure ratio 26:1 Specific fuel consumption, reheated 48 g/kn s Specific fuel consumption, dry 21 g/kn s Air flow rate 77kg/s Length 4 m Maximum diameter 74 cm Weight 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 be quantitatively determined (Table 2.8). For simplicity, an initial rough estimation of a rectangular nacelle with width equal to 1.05 times the engine diameter will be incorporated in the design, for the total propulsion system length, excluding the exhaust nozzle. The relevant ratio of intake length to engine diameter is about 34

37 3.19. The two nacelles have been placed in distance 2.9 m from the aircraft longitudinal axis of symmetry. Figure 2.13 EJ200 turbofan engine. Intake length 2.36 m Capture area m 2 Throat diameter 59.8 cm Nacelle length 5.36 m Nacelle width 77.7 cm Table 2.8 Propulsion system basic dimensions Aircraft model The aircraft model has been created in Matlab, using the aforementioned dimensions. The airfoils used for the wing and the tail modeling are discussed in the following chapter. The relevant views of the model can be observed in figures 2.14, 2.15 and Figure 2.14 Aircraft model top view. 35

38 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 (S exp ) m 2 Wing wetted area (S wwet ) m 2 Fuselage wetted area (S fwet ) m 2 Horizontal tail wetted area (S HTwet ) m 2 Vertical tail wetted area (S VTwet ) m 2 Nacelles wetted area (S nacwet ) m 2 Table 2.9 Aircraft exposed and wetted areas. 36

39 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 been modeled as a whole moving surface. A guidance for their initial geometry is provided 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 is placed 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. The aileron geometry and location is illustrated in the figure 3.8 of the upcoming chapter. 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 vertical stabilizer chord. The rudder geometry is depicted in figure The total aileron surface is 2.27 m 2, or 3.56% of the wing reference area. The rudder surface is 2.55 m 2 or 33.6% of the vertical stabilizer area. Figure 2.17 Rudder illustration. 37

40 3. Aerodynamics 3.1 Airfoils Airfoil selection The main feature of the aircraft to be designed is the efficient supersonic flight. The dominant characteristic of the supersonic flow is the presence of shock waves. In the case of a sharp-nosed wing section, oblique waves will be formed on the nose with the flow remaining supersonic. On the other hand, if a nose which is blunt is incorporated, the flow would detach from the nose tip and 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 order to keep the wave drag low. Consequently, in the supersonic aircraft thin airfoils are being used with typical thickness ratio 4-6 %. Typical wing sections that are used for supersonic aircraft are the NACA 64-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 and increasing the critical Mach number. For the wing, the NACA section has been chosen. This is a symmetric airfoil with 6 % thickness ratio. For the horizontal stabilizer, the same symmetrical airfoil used for the wing has 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 airfoil offers a a low drag coefficient (C d ) too. For the vertical stabilizer, the symmetric airfoil NACA has been chosen. This airfoil offers a quite high C la, which is an important factor for having satisfying directional stability, while minimizing the weight, due to its relative low thickness. The low drag coefficient (C d ) of the airfoil is also another reason for its selection. The chosen airfoils and their coordinates, according to NACA, can be found in Appendix A. 38

41 3.1.2 Subsonic aerodynamic coefficients The aerodynamic coefficients for the selected airfoils in subsonic flow has been calculated with the XFOIL airfoil design/analysis system, which is a viscous, panel method program with boundary layer analysis. According to the program creator, XFOIL is a tool that is particularly applicable to low Reynolds numbers and works better for subcritical airfoils [26]. Thus, the calculated aerodynamic coefficients have been compared to published experimental data for the particular airfoils found in reference [15] and presented in Appendix B. The zero angle of attack lift (C l0 ) and pitch moment (C m0 ) coefficients equal zero for the used symmetrical airfoils. NACA In figure 3.1, the lift curve obtained with the XFOIL simulation is presented. The resulting aerodynamic coefficients obtained from both aforementioned sources are presented in table 3.1. A significant difference can be observed for the C lmax and the stall angle. The data to be used for the ongoing analysis are the experimental data, since for the angles of attack near stall the simulation with XFOIL failed to achieve convergence of the solution. Figure 3.1 NACA lift curve for Re = (XFOIL). XFOIL simulation Experimental data Lift curve slope (C la ), deg Maximum lift coefficient (C lmax ) Minimum drag coefficient (C d ) Stall angle (deg) Table 3.1 NACA aerodynamic coefficients ( Re = ). 39

42 NACA In table 3.2 are presented both the simulation and the experimental data that have been obtained. Significant differences for the C lmax and the stall angle can be observed for this airfoil as well. Knowing the weakness of the supercritical airfoil simulation, the experimental data will be used for the further analysis in this case too. Figure 3.2 NACA lift curve for Re = (XFOIL). XFOIL simulation Experimental data Lift curve slope (C la ), deg Maximum lift coefficient (C lmax ) Minimum drag coefficient (C d ) Stall angle (deg) Table 3.2 NACA aerodynamic coefficients ( Re = ) Supersonic aerodynamic coefficients For an airfoil in supersonic flow, an analytical expression is given from the equations (3.1) and (3.2). These equations have been derived disregarding the viscous 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 quite accurate. Deriving the aforementioned equations, it can be observed that the c l is independent of the airfoil shape and thickness, in contrast with the c d. c l = 4α M 2 1 (3.1) 40

43 c d = 4(α2 + g 2 c + g 2 t ) M 2 1 (3.2) In equation (3.2), g c and g t are functions of the camber and the thickness along the chord, respectively. For a symmetric airfoil the camber term g c equals to zero and for a double-wedge airfoil the thickness term g t equals the square of the thickness ratio ( (t/c) 2 ). 3.2 Subsonic Lift-Curve Slope Wing - Fuselage Assembly Reference [27] provides with an empirical equation for the wing s subsonic C Lα estimation. This equation takes into account the compressibility effects, the aspect ratio and the wing sweep. The effect of taper ratio is not directly included in the relation, but it has been proved by the author that it can be diminished by using the half-chord (Λ c/2 ), instead of the quarter-chord (Λ c/4 ) wing sweep. The relevant equation is expressed as (C Lαw ) M = c lα AR ( ) in radians (3.3) c 2 lα π + AR ( cos Λ + clα ) 2 c/2 π (AR M) 2 In order to account for the fuselage contribution, the C Lα obtained from the above relation, is multiplied with the factor (S exp /S ref ) (F ), where the fuselage lift factor F is defined as [9] F = 1.07 (1 + D fus /b) 2 (3.4) If the F obtained from relation (3.4) is greater than one, the result is physically wrong, since it assumes that the fuselage produces more lift than the covered portion of the wing. For that reason, the factor F is set to 0.98 [9]. Since equation (3.3) can be considered valid for all subsonic values of Mach number till the critical one, the results for a freestream Mach number range of 0.2 till 0.8 are presented in table

44 Mach number C Lαwb (deg 1 ) Table 3.3 Lift-curve slope of wing - body assembly for subsonic Mach number range Horizontal Tail The lift coefficient of the horizontal tail (C Lt ) with respect to the horizontal tail angle of attack (α t ) for the linear part of the curve is given from the following relation C Lt = C Lat α t (3.5) The term C Lt can be computed using the equation (3.3) and introducing the correspondent properties of the horizontal stabilizer. In order to define a total lift coefficient for the aircraft, the relevant coefficient of the horizontal stabilizer should be written in terms of the wing-body angle of attack. The relation that correlates the wing-body and the horizontal tail angle of attack is [28] a t = a wb i t ɛ (3.6) The horizontal tail incidence (i t ) has been set to one degree. The downwash angle ((ɛ)) which is created by the wing wake and changes the effective angle of the horizontal tail can be approximated by [28] ɛ = ɛ 0 + ɛ α α wb (3.7) The downwash angle ɛ 0 at α wb = 0, is mainly dependent on the wing twist. Since wing twist has been set to zero for the initial layout, the ɛ 0 can approximated as zero. The downwash angle derivative can be approximated using the empirical equation (3.8), based on wind-tunnel experimental data [29]. ( ɛ α = 21o C Lαw cw AR 0.5 L HT ) ( 10 3λw 7 ) ( 1 z ) HT b w (3.8) 42

45 where the term z HT is the vertical distance of the horizontal stabilizer above of the main wing plane equal to 2.2 m for this design. Therefore, the horizontal tail contribution to the aircraft C Lα can be written as ( C Lαt = C Lαt 1 ɛ ) SHT (3.9) α S W In table 3.5, the calculated values of interest for the horizontal tail can be observed. Mach number C Lαt (deg 1 ) ɛ/ α C Lαt (deg 1 ) Table 3.4 Lift-curve slope of horizontal tail, downwash angle derivative and horizontal tail C Lα contribution to the aircraft, respectively, for subsonic Mach number range Total aircraft The lift-curve slope for the total aircraft can be obtained by summing the wing-fuselage and the horizontal tail contribution. The final results are presented in table 3.5. Mach number C Lα (deg 1 ) Table 3.5 Aircraft lift-curve slope for subsonic Mach number range. 43

46 3.3 Supersonic Lift-Curve Slope The 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 sweep of 45 deg, that holds for Mach numbers greater than 1.4. The lift-slope curve at supersonic speeds is quite hard to estimate without experimental measurements or usage of a sophisticated fluid dynamics simulation model. An estimation about the wing normal force curve-slope coefficient (C Nα ) is given in figure 3.3. Figure 3.3 Wing supersonic C Nα for taper ratio of 0.2 [13]. From the figure 3.3, the C Nα can be approximated, taking into account the leading edge wing sweep, the taper ratio and the aspect ratio.for small angles of attack C Nα can be considered equal to the supersonic wing C Lα. In order to account for the fuselage contribution the obatined coefficients are multiplied with the factor (S exp /S ref ) (F ), like in the case of the subsonic flow. Mach number C Lαwb (deg 1 ) C Lαt (deg 1 ) Table 3.6 Wing-body and horizontal tail lift-curve slope for supersonic Mach number range. For the horizontal stabilizer, the supersonic lift curve slope is obtained applying 44

47 the same methodology with the aircraft wing. The correspondent values of C Lαwb for the wing-fuselage assembly and C Lαt for the horizontal tail are presented in table 3.6. The relation (3.9) can be used to calculate the horizontal stabilizer contribution to the C Lα of the total aircraft. The downwash angle derivative can be roughly approximated using the relation (3.10), provided in [9], with the relevant results presented in table 3.7. In table 3.8, the supersonic lift-curve slope for the total aircraft is included. ɛ α = 1.62C Lα w πar in radians (3.10) Mach number ɛ/ α C Lαt (deg 1 ) Table 3.7 Horizontal tail downwash angle derivative and C Lα contribution to the aircraft, respectively, for supersonic Mach number range. Mach number C Lα (deg 1 ) Table 3.8 Aircraft lift-curve slope for supersonic Mach number range. 3.4 Maximum Lift Coefficient Clean configuration The aircraft maximum lift coefficient C Lmax is very important for low flight speeds and especially for the landing and the take-off flight phase. The estimation of the C Lmax in this section is for the stall speed at sea-level, which has been set to 0.2 Mach and for a range till 0.6 Mach. For the C Lmax, the method from the USAF DATCOM has been used. Firstly, the aspect ratio condition of the method has to be considered. The relations 3.11 and 3.12 are presenting the low and high aspect ratio condition, according to USAF DATCOM, respectively [9], [21]. 45

48 AR 3 (C 1 + 1)cos(Λ LE ) (3.11) AR > 4 (C 1 + 1)cos(Λ LE ) (3.12) where C 1 is the taper ratio correction coefficient that can be calculated using the following relation [21]. ( ) C 1 = 0.5 sin π(1 λ) sin0.4 (π(1 λ) 2 ) (3.13) Figure 3.4 High aspect wing and airfoil maximum lift coefficient ratio at 0.2 Mach. The wing used for this design does not satisfy neither of the conditions, since it falls between the above calculated values. For that reason, both conditions have been implemented and the results have been compared in the end. An important 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 a NACA 64-series airfoil. Then the C Lmax can be obtained from the following relation in the case of high aspect ratio condition. ( ) CLmax C Lmax = C lmax + C Lmax (3.14) C lmax where C lmax is the wing section maximum lift coefficient, the ratio C Lmax /C lmax is obtained from figure 3.4 for Mach 0.2, while C Lmax is the correction for Mach numbers up to 0.6 and can be found using the relevant chart provided in reference [9]. The correspondent stall angle of attack (α stall ) can be approximated from the relation 46

49 α stall = C Lmax C αw + α 0L + α CLmax (3.15) where the zero lift angle of attack (α 0L ) is equal to zero for the initially assumed zero wing incidence and the angle of attack increment ( α CLmax ) can be obtained from figure 3.5. Figure 3.5 Stall angle of attack increment at subsonic Mach numbers of The C Lmax and α stall, in the case of the low aspect ratio condition, can be obtained from the equations 3.16 and 3.17, where the correspondent parameters can be found from the USAF DATCOM charts provided in reference [9]. C Lmax = (C Lrmmax ) base + C Lmax (3.16) α stall = (α CLmax ) base + α CLmax (3.17) Mach number C Lmax α stall High AR Low AR Final High AR Low AR Final Table 3.9 Subsonic aircraft maximum lift coefficient and stall angle of attack. 47

50 The relevant values of C Lmax and α stall obtained from both conditions are presented in table 3.9. Since the values obtained are not very far, the mean value 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 coefficient and stall angle of attack are greater than the relevant ones for the airfoil that was implemented. This happens due to the fact that the low aspect ratio, swept wing incorporates a sharp leading edge, which results in the leading-edge vortices formation that enhances the maximum aircraft lift High lift devices In order to achieve a C Lmax high enough for landing and take-off, both trailing edge (TE) and leading edge (LE) high lift devices have been incorporated to the design. At the trailing edge the single slotted Fowler flap has been used, while at the leading edge the slotted LE flap or so-called slat. Both devices aim at the wing camber and wing area increment, with the slots being incorporated to assist the avoidance of flow separation, with high pressure air being able move through the slots from the lower to the upper side of the wing. Figure 3.6 Trailing and leading edge high lift devices. The C lmax increase of the wing section incorporating a TE slotted flap is approximated as 1.3 times the airfoil chord ratio (c /c) after and before the flap rearward movement [9], as can be observed in figure 3.6. For this design a typical value of 1.1 or 10 % chord increment, has been chosen. Both TE flaps and slats are hinged having a chord 20% of the local wing section chord. The TE flaps span the 35% of the wing span, while the slats its 62%. 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 C Lmax increment due to TE flap deflection during landing can be estimated using the following equation [30] C Lmax = C lmax S wf S w K (3.18) where the empirical sweep correction K is given from the relation K = ( cos 2 (Λ c/4 )) cos 0.75 (Λ c/4 ) (3.19) 48

51 The area S wf corresponds to the wing area that are incorporating flaps and the area S w to the total wing area. The ratio (S wf /S w ) equals to 39.7% and the relevant C Lmax increment equals to Figure 3.7 Wing TE flaps (red), LE flaps (magenta) and ailerons (cyan). The C Lmax increment due to the LE device extension has been crudely approximated as 0.4 [9], since there is no analytical method for its prediction. The total C Lmax increment can be estimated as 0.85, meaning that the aircraft C Lmax using the designed high lift devices will be 1.78 at 0.2 Mach Horizontal tail A requirement during the horizontal tail design is that it should stall later than the wing for recovery reasons. Following the USAF DATCOM method for a low aspect ratio wing, the C Lmax and α stall for the horizontal stabilizer can be estimated from equations (3.16) and (3.17). The obtained results are presented in table Mach number C Lmax α stall Table 3.10 Subsonic horizontal tail maximum lift coefficient and stall angle of attack. The values for the horizontal tail α stall are slightly higher than the relevant values calculated for the aircraft previously. Taking into account that due to the tail incidence and the downwash angle, which cause the horizontal tail to 49

52 experience an angle of attack lower than the wing, the horizontal tail will have indeed a quite higher actual stall angle. 3.5 Subsonic Parasite Drag Coefficient Equivalent skin-friction method The equivalent skin-friction method is an approximative method, which uses a equivalent skin-friction coefficient C fe that is relevant to the aircraft class. This coefficient includes both skin-friction and separation drag and for a supersonic aircraft equals to [9]. This method is very generic and is presented here just to get an initial estimate to use for comparison with the more accurate results obtained later on. is The relevant equation for the parasite (zero-lift) drag coefficient C D0 estimation C D0 = C fe S wet S ref (3.20) The total aircraft wetted area (S wet ) can be obtained from table 2.9 by just summing the relevant wetted areas of each aircraft component. The resulting C D0 is Component buildup method The component buildup method estimates the C D0 for each aircraft component. Every component that has direct contact with air flow, is producing drag. The basic contributing components of an aircraft in cruise are the wing, the fuselage, the tail and the engine nacelles. The C D0 of each component is approximated by computing a flat-plate skin-friction coefficient (C f ) and multiplying it with a component form factor (FF), which is used in order to include the separation drag. 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 the subsonic C D0 is expressed as [9] C D0 = (Cfc F F c Q c S wetc ) S ref + C Dmisc + C DL&P (3.21) The factor C DL&P is related to drag created due to leakages and protuberances. A carefully designed aircraft of this type can almost eliminate the specific drag contribution, so that it can be considered negligible. The factor C DL&P corresponds to 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 different flight phases, like for instance during landing, these drag contributions have to be estimates and added to the total drag. 50

53 In order to compute the friction coefficient C f, it has to be examined in what extend the flow is laminar or turbulent. That was achieved through the Reynolds number (Re) calculation for all the components for Mach number range of 0.2 till 0.8, which is just below the critical Mach number (see subsection 3.7), and for the altitudes of 0, 5 and 10 km, respectively. It has to be mentioned that the flight at the lowest Mach numbers and higher altitudes is not possible, thus not of interest, but the relevant coefficients will be presented just for reasons of completeness. The characteristic length for the Reynolds number calculation has been for the wing, the horizontal and the vertical stabilizer the respective mean aerodynamic chord of each surface, while for the fuselage and the nacelle-engine assembly their longitudinal total length. The Reynolds number has been computed to be grater than for the aforementioned flight conditions, so that the flow can be considered fully turbulent in every case. In order to account for the skin surface roughness, which can possibly increase the viscous forces on the components surface, a fictitious Reynolds number, the so-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 m. Therefore, in the case of an actual Re being higher than the relevant cutoff Re, its actual value has to be replaced by the cutoff one in the equation (3.23) for the C f calculation. ( ) l Re cutoff = (3.22) k The skin-friction coefficient (C f ) can then be estimated for every component using the relation C fc = (log 10 Re c ) 2.58 ( M 2 ) 0.65 (3.23) The form factor (FF) for the wing, the horizontal and the vertical tail can be calculated from the equation (3.24). The parameter (x/c) m corresponds to the chordwise position of the airfoil maximum thickness, which is 0.4 for the selected airfoils, while Λ m is the sweep angle of the maximum thickness line. The form factors (FF) of the fuselage and the nacelle assembly can be computed from the equations (3.25) and (3.26), respectively. The factor f in both equations is equal to the length over the maximum diameter ratio. F F = ( ( ) ( ) ) t t 4 ( M 0.18 (cos Λ m ) 0.28) (3.24) (x/c) m c c F F = ( f 3 + f ) 400 (3.25) 51

54 F F = 1 + (0.35/f) (3.26) The interference factor (Q) for a well-filleted wing design and the fuselage is negligible and can be set to unity. For a conventional tail, it can be assumed as 1.04 for the horizontal and vertical stabilizer surfaces, while for the directly mounted to wing nacelles is about 1.5 [9]. Making all the necessary calculations presented previously, the clean subsonic parasite drag coefficient (i.e. cruise condition configuration) can finally be computed using the aforementioned relation (3.21). The obtained results are presented in table Mach number C D0 0 km 5 km 10 km Table 3.11 Subsonic parasite drag coefficients for the stated Mach number and altitude flight conditions. These results are close to the expected value of parasite drag coefficient, as it has been obtained with the equivalent-skin-friction method. The respective coefficient is also increasing at higher flight altitudes as it can be observed. However, that does not mean a higher drag force, since the relevant dynamic pressure at higher altitude is much smaller. 3.6 Supersonic Parasite Drag Coefficient The supersonic parasite drag includes the skin-friction drag, the miscellaneous drag and the drag due to leakages and protuberances, like in the case of the subsonic flight. In addition to these contributions, it includes the so-called wave drag, which is a drag increment resulting from the shock waves formation in transonic and supersonic speed. The total drag coefficient using the components buildup method, following the same principle like in the subsonic flow case, is given from C D0 = (Cfc S wetc ) S ref + C Dmisc + C DL&P + C Dwave (3.27) 52

55 Since external stores are not incorporated in the SST aircraft design, the C Dmisc is zero. Moreover, the drag due to leakages and protuberances can be assumed negligible, like in the case of the subsonic drag coefficient. From the equation (3.27), it can be seen that for the supersonic skin-friction drag component, the form (FF) and the interference factor (Q) are not included. The skin friction coefficient (C f ) is calculated using the equation (3.23), since the flow is fully turbulent for the supersonic flight conditions. The flight conditions that are evaluated here are flight at 10, 12 and 15 km altitude, with the supersonic Mach number range to be from 1.4 to 1.7. Furthermore, in order to account for the skin roughness, a cutoff Mach number is introduced and used in the exactly same manner for the C f calculation, such as for the subsonic flight. The expression for the supersonic cutoff Mach number is ( ) l Re cutoff = M 1.16 (3.28) k The total skin-friction drag coefficient (C Df ) can then be estimated by summing the respective coefficients of every aircraft component for the aforementioned flight conditions. The results are presented in table Mach number C Df 10 km 12 km 15 km Table 3.12 Supersonic skin-friction drag coefficient component for the stated Mach number and altitude flight conditions. The wave drag is the biggest drag contributor during supersonic flight. The wave drag is dependent on the way the aircraft volume is distributed along its longitudinal axis. The minimum wave drag appears for a so-called Sears-Haack body, 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) = r max (4x(1 x)) 0.75 (3.29) where x is the ratio of the longitudinal distance from the aircraft nose over the tonal length, having thus values between 0 and 1. 53

56 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 distortion of this smooth cross-section area distribution. However, in order to make the distribution smoother and as close to the ideal one as possible, the area ruled fuselage is implemented. The area ruling of the fuselage has been firstly proposed by Whitcomb, who presented this principle for the wing-body combination [31]. In order to achieve a smoother distribution and reduce the wave drag, the fuselage has been squeezed at the location of the wing installation (see figure 3.9). 54

57 Figure 3.10 Aircraft cross-section area distribution. The area rule has been applied in this design, like it was stated in the fuselage lofting section. In figure 3.10, the cross-section area of the designed aircraft can be compared with the Sears-Haack ideal distribution. The presented cross-section area of the aircraft corresponds to intersection with perpendicular to the longitudinal axis and at zero roll angle. The nose location of the aircraft corresponds to the zero longitudinal dimension. The inlet capture area has been subtracted from the cross-section area distribution graph. The most credible way to measure the wave drag, so that to test the design and optimize it, is to conduct experiments on a wind tunnel. However, there are also some analytical methods that can be used in order to make an initial estimation during the conceptual aircraft design. Here two of them will be illustrated, provided from references [9] and [29]. Both of them relate the aircraft wave drag with the Sears-Haack body wave drag, through the relevant coefficient given from relation (3.30), and an efficiency factor E WD. The typical value for the E WD factor of a supersonic fighter and SST is about 1.8 [9]. However, a factor of 1.4 is selected for this area-ruled design, since a very high wave drag would deteriorate the aerodynamic efficiency significantly. The wave drag minimization and optimization of the aircraft shape is a necessary procedure and one of the most important challenges that has to be met for an efficient SST design, and usually demands a lot of experimental testing of the model as well. C DwS H = 9π 2S ref ( Amax l ) 2 (3.30) In the above equation, the A max is the maximum cross-section area, which is about 6.42 m 2 for this design, and l the aircraft s overall length. The aircraft wave 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 arithmetic mean of the values obtained from the two analytical relations. These value are 55

58 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 ( ( C Dwave = C DwS H E W D (M 1.2) πλ )) LE deg (3.31) C Dwave = C DwS H E W D ( cos Λ LE ) (1 0.3 M cos 0.2 Λ LE ) (3.32) Mach number C D0 10 km 12 km 15 km Table 3.13 Supersonic parasite drag coefficient component for the stated Mach number and altitude flight conditions. 3.7 Critical Mach number A method for determining the critical Mach number of an infinite swept wing is illustrated in reference [32]. The equation (3.33) relates the critical Mach number (M crit ) for an infinite swept wing at zero angle of attack with the critical pressure coefficient (C Pcrit ). C Pcrit = 2 γm crit 2 ( 1 + γ 1 2 M 2 crit cos2 Λ c/4 γ+1 2 ) γ γ 1 1 (3.33) The pressure coefficient (C P ) at freestream Mach number M is then obtained using the relation (3.34), where β is the compressibility correction factor. The C P at M=0 is approximated as the minimum airfoil pressure coefficient. For incompressible, inviscid flow using the Bernoulli equation the C P can be obtained from relation (3.35). C PM = C P M=0 β = C PM=0 1 M 2 (cos 2 Λ c/4 C PM=0 ) (3.34) C P = 1 (V/V ) 2 (3.35) The ratio (V /V ) of the local velocity along the chord over the freestream velocity can be obtained for the symmetrical airfoils NACA and NACA 56

59 at zero angle of attack from reference [15]. Therefore, the minimum airfoil pressure coefficient for the aforementioned airfoils is and , respectively. Figure 3.11 Wing critical Mach number in two-dimensional flow. At the critical Mach number, the C P from the two equations (3.33) and (3.34) is equal. Thus, the M crit can be found graphically by plotting the C P obtained from both equation for a Mach number range of 0.6 to 1.0. The M crit is the one where the two curves intersect. From figure 3.11, the M crit corresponding to the wing can be obtained. Using the same procedure the M crit for the horizontal and vertical stabilizer can been computed too. The relevant values of the M crit are 0.92 for the wing and the vertical stabilizer, and 0.94 for the horizontal stabilizer. It has to be mentioned that these values for M crit correspond to two-dimensional linearized flow based on the Weber s compressibility correction [32] of equation (3.34). The main reason for illustrating this method is to ensure that the M crit of the wing does not exceed the M crit of the tail, for the selected wing sections and sweep angles. The aircraft M crit can be estimated through the relation [29] ( ( ) ) t 0.6 M crit = cos Λ c/4 (3.36) c max For this SST aircraft design the M crit has been calculated as Another important Mach number related with the transonic flow, is the drag divergence Mach number M dd. The M dd is the Mach number at which the formation of shock waves begins to affect the aircraft drag significantly. As a rule of thumb the M dd is 0.08 Mach higher than the M crit [9], or 0.92 in this case. 57

60 3.8 Drag due to Lift In order to calculate the total aircraft drag the drag produced due to lift has to be added to the parasite drag. The total drag coefficient (C D ) is related to the lift coefficient (C L ) through the following equation known as the drag polar. C D = C D0 + KC 2 L (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. The factor K for subsonic flight can be estimated through the equation K = 1 πare (3.38) The coefficient e is the Oswald efficiency factor, which accounts for the non-elliptical lift distribution over the wing. For a swept-wing aircraft, with leading edge sweep over 30 deg, it can be estimated as [9] e = 4.61( AR 0.68 )(cos Λ LE ) (3.39) Therefore, K for the subsonic flight range for this design is equal to For the supersonic flight range, the factor K can be obtained from the relation (3.40) [9]. The obtained values are presented in table K = AR(M 2 1) cos Λ LE (4AR M 2 1) 2 (3.40) Mach number K Table 3.14 Supersonic drag-due-to-lift factor. 3.9 Miscellaneous Drag 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 drag coefficients calculation [9]. 58

61 C D0flap ( ) ( ) Cf Swf = F flap (δ flap 10) (3.41) C S w C Di = k 2 f ( C Lflap ) 2 cos Λ c/4 (3.42) In the above equations, the factor F flap equals for slotted flaps and the factor k f about The C f /C is the flap over wing chord ratio and the δ flap is the flap deflection in deg. Typical values for a Fowler TE flap is 40 deg at landing and 20 deg at takeoff, while for a slat is 25 deg at landing and 15 at takeoff. 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 drag coefficients during takeoff and landing are presented in table Takeoff Landing C D0 C Di C D0 C Di TE Flaps Slats Table 3.15 Drag coefficients of high lift devices during takeoff and landing Spoilers The spoilers are secondary control surfaces that are used as speed brakes during flight, as lift dumpers during ground roll and takeoff abortion and as roll control surfaces, mainly for higher speed, where the aileron effectiveness is reduced. Figure 3.12 Wing control surfaces (blue) and spoilers (red). 59

62 The initial layout of the spoilers was based on guidance from [33]. The spoiler is 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 % of the semispan, as it can be seen in figure The total spoilers surface (S s ) is about 4.52 m 2 or 7.1% of the reference wing area. The spoilers drag coefficient with respect to the spoiler deflection angle (δ s ) can be roughly approximated through the relation [33] C Dspoiler = 1.9 sin (δ s ) S s S ref (3.43) Using the above relation for a spoilers deflection of 45 deg, the increment of the aircraft C D is estimated as Landing gear A quick estimation for the drag coefficient of a retractable landing gear can be made from the empirical relation 3.44 [21]. This equation is valid for commercial jet aircraft having with deployed flaps, which is the case during takeoff and landing, when the landing gear is deployed too. The value obtained using the following relation for the C D increment due to deployed landing gear is C DLG = m (3.44) S ref 60

63 4. Weights 4.1 Weights Estimation Refined Method There are several approximative methods for estimating the weights of the aircraft components. For a quick estimation, they can be computed as percentage of the total aircraft weight. These methods are good for giving some initial estimates for the basic aircraft components, which can be used as a guide. Aircraft Component Weight (kg) Wing Horizontal tail Vertical tail Fuselage Main landing gear Nose landing gear 97.7 Engines Nacelle group Engine controls 21.2 Starter (pneumatic) 88.3 Fuel system Flight controls APU installed Instruments 69.3 Hydraulics 60.3 Electrical Avionics Furnishings Seats Air conditioning Anti-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 been implemented. The relevant weights are estimated using statistical equations 61

64 based on the aircraft geometric characteristics and initial layout. The analysis is based on the equations correspondent to transport aircraft, which can be found in [9] and will not be reproduced here. The results obtained from the weights estimation analysis are registered in table 4.1. One important parameter, used in the aforementioned equations and not defined before, is the maximum load factor (n m ax), which has been set equal to 3.5 for the SST aircraft design. The total aircraft empty weight after the sum of all the weights of the aircraft components is calculated to be 12,541 kg. The initial estimated aircraft empty weight has been 13,908 kg. Since the weight obtained is lower than the initial estimation with the difference to be not very high, the aircraft dimensions will not be refined. The initial takeoff weight will be considered the same for the rest of analysis and they weight savings of the aircraft structure can be utilized as payload increment. That means that the refined empty weight fraction is dropping to from for this SST design. The relevant value of the empty weight fraction for the Concorde has been calculated to be about 0.417, which means that the value obtained from this refined method is indeed a reasonable estimate. 4.2 Center of Gravity The center of gravity of the aircraft cannot be estimated so accurately during the conceptual design, since the aircraft is susceptible of many changes till the final actual design is obtained. For the symmetric aircraft design, the lateral CG 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, made in the next chapter, makes an initial recommendation for the longitudinal CG placement. The vertical CG location can be calculated from the equation (4.1), where all the N aircraft components have to be included. z CG = N m c z c i=1 (4.1) N m c i=1 An initial approximation of the vertical CG location has been made using just the basic aircraft components, i.e. the wing, the fuselage, the horizontal and vertical tail and the engine-nacelle groups. The estimations of the aforementioned components vertical locations (z c ) are given in table 4.2. The aircraft CG vertical location has been found to be at about 0.75 m with respect to the fuselage centerline and defining the positive z direction as downwards. 62

65 Component z c (m) Wing 1.1 Fuselage 0 Horizontal tail -1.1 Vertical tail Engine - Nacelle assembly 1.69 Table 4.2 CG vertical location of basic aircraft components. 63

66 5. Stability and Control 5.1 Subsonic Static Longitudinal Stability The two criteria that have to be met to achieve static longitudinal condition are that the aircraft pitching moment at zero angle of attack is positive (C m0 > 0) and that the slope of the pitching moment coefficient is negative (C mα < 0). The pitching moment (C m ) is about the aircraft s center of gravity (CG). Meeting this two criteria is meaning that the aircraft can fly in stable equilibrium. The assumptions that have been used for the analysis are presented here. The wing aerodynamic center is modeled to be at 25 % of the wing mean aerodynamic chord and the same holds for the horizontal tail. Moreover, the wing-body assembly aerodynamic center has been assumed to be in the same location as for the wing. The fuselage pitching moment about the wing-body aerodynamic center has been set equal to zero and the propulsive system contribution has been neglected Aircraft Pitching Moments The pitching moment of the wing-body can be calculated from the following equation [28] C mwb = C macwb + C Lαwb α wb (h h nwb ) (5.1) In the above equation α wb is the wing-body angle of attack, h n and h nwb the non-dimensional longitudinal distance of the center of gravity and aerodynamic center from the fuselage nose divided with the wing s mean aerodynamic chord, respectively. Moreover, all the longitudinal locations presented in this chapter are measured as distances from the aircraft nose. The pitching moment C macw of the wing about the aerodynamic center is strongly dependent on the airfoil pitching moment and it can be estimated through the relation [9] ( AR cos 2 ) Λ C macw = C m0airfoil AR + 2 cos Λ (5.2) The airfoil that has been used for the wing is a symmetrical one with C m0 = 0. Thus, the resulting C macw is equals to zero too. 64

67 The tail pitching moment coefficient can be expressed as [28] S ht C mt = V H C Lt + C Lt (h h nwb ) (5.3) S ref where V H = ( l t S HT )/( cs ref ) with l t to be the distance between the wing body and the horizontal tail mean aerodynamic center (see figure 5.1). Figure 5.1 Wing-body and tail mean aerodynamic centers [28]. where The total aircraft C m can then be written as C m0 = C macwb + C Lαt VH (ɛ 0 + i t ) C m = C m0 + C mα α (5.4) ( 1 C L αt C Lα S HT S ref ( C mα = C Lα (h h nwb ) C Lαt VH 1 ɛ ) α ( 1 ɛ ) ) (5.5) α (5.6) The parameter C m0 corresponds to the pitching moment coefficient at zero lift and is independent of the CG location Subsonic Neutral Point The neutral point (NP) location of the aircraft can be found from the relation h n = h nwb + C L αt C Lα VH ( 1 ɛ ) α (5.7) The aircraft has a positive stiffness (C mα < 0) when the center of gravity is forward of the neutral point. This means that it should hold Static margin (SM) = h n h > 0 (5.8) 65

68 From the equation (5.7) the aircraft s neutral point location for the subsonic aircraft range has been calculated to be 14.6 m, which determines the limit for the center of gravity aft position. The influence of the CG location on the aircraft C m can be observed in the figure 5.2. For positive pitch stiffness (h < h n ) the aircraft can fly in equilibrium, when for zero (h = h n ) or negative pitch stiffness (h > h n ) the aircraft is unbalanced, since the pitching moment cannot be zero for any angle of attack. Figure 5.2 CG position influence on C m at 0.5 Mach Longitudinal Control and Trim Analysis The longitudinal control of the designed aircraft can accomplished through the all moving horizontal tail surface. The change in the tail angle δ t results in the 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-body zero angle of attack reference axis, with the tail thus to create negative lift and a positive (nose up) pitching moment. The tail deflection angle δ t is then, in fact, the tail incidence for the given condition, but with the opposite sign convection. In order to present the δ t as a change of tail incidence with respect to the zero wing-body angle of attack line, the initial tail incidence (i t ) for the trim analysis has been set equal to zero. The results then for the δ t are the opposite signed i t that are required for stable equilibrium. This has been done in order to avoid conversions of the obtained from the trim analysis angles, which would be with respect to the i t, and keep the δ t definition simpler. The derivatives of the lift and the pitching moment with respect to the δ t can be expressed, respectively, as C Lδt = C Lαt S HT S ref (5.9) 66

69 C mδt = C Lαt VH + C Lαt (h h nwb) (5.10) So for the case of linear lift and linear pitching moment the set of equations obtained is C L = C L0 + C Lα α + C Lδt δ t (5.11) where C m = C m0 + C mα α + C mδt δ t (5.12) C L0 = C Lαt S HT S ref (i t + ɛ 0 ) (5.13) The conditions for the aircraft trim are given in (5.14). Solving this system of equations (3.11) and (5.12), the set of angle of attack and tail deflection angle that trims the aircraft for each flight condition can be obtained. It can be observed from the C Ltrim condition that the relevant set of angles is dependent on the flight speed V, flight altitude (through density ρ) and the instant aircraft mass m. The variation of the δ t with the flight speed and the CG location can be seen in figures 5.3, for m = kg, which is a value corresponding to the aircraft mass at the beginning of the cruise phase. C Ltrim = 2W ρv 2 S ref C mtrim = 0 (5.14) Figure 5.3 Variation of δ t to trim with the flight speed and the static margin at SL flight. 67

70 The δ t and α variation with the flight speed for different flight altitudes is presented in figures 5.4 and 5.5, respectively. The given results correspond to a static margin of 0.1. The flight speed range of the presented results and of the trim analysis in general, is restricted from the critical Mach number, which sets the upper limit, and from the aircraft C Lmax for each flight condition, which sets the relevant lower limit. Figure 5.4 Variation of δ t to trim with the flight speed and the flight altitude for the subsonic Mach number range. Figure 5.5 Variation of α trim with the flight speed and the flight altitude for the subsonic Mach number range. 68

71 5.2 Supersonic Static Longitudinal Stability The criteria for static longitudinal stability remain the same for the supersonic flight, although the relevant aerodynamic coefficients are changing. The most important change, during the supersonic flight compared to subsonic speed, is the aft movement of the wing s aerodynamic center. For this analysis, the aerodynamic center of the wing-body has been assumed to be at 45% of the mean aerodynamic chord, which corresponds to an aft movement of 20%. The aerodynamic center of the horizontal tail has been place to the 45% location of its mean aerodynamic chord as well [9] Supersonic Neutral Point The aforementioned change of the aerodynamic center position for supersonic flight affects the aircraft neutral point, which moves aft too. From the equation (5.7), the NP longitudinal location for supersonic flight has been computed to be 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 of increment of the static margin for this design Trim Analysis The aircraft total C L and C m, like for case of the subsonic flight, are given from the equations (5.11) and (5.12). These equations hold for angles of attack lower than 5 deg, since for larger angles of attack, the linearized supersonic theory that was used to obtain the relevant aerodynamic coefficients is not valid. The trim conditions are given in (5.14) as well. Figure 5.6 Variation of δ t to trim with the flight speed and the flight altitude for the supersonic Mach number range and static margin of

72 Similarly to the subsonic trim analysis, the mass of aircraft at trim is considered kg. In figures 5.6 and 5.7, the variation of the δ t with the flight speed and altitude is illustrated, for static margin 0.1 and 0.35, respectively. The relevant variation of the angle of attack for static margin of 0.1 is illustrated in figure 5.8. Figure 5.7 Variation of δ t to trim with the flight speed and the flight altitude for the supersonic Mach number range and static margin of Figure 5.8 Variation of α trim with the flight speed and the flight altitude for the 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 margin are , since a CG shift of 10% that can take place during flight is 70

73 considered tolerable. Thus, setting a static margin of 0.1 the CG has to be placed at 14.1 m for subsonic flight. During the supersonic flight due to the neutral point aft movement, the static margin will increase to Comparing the values for δ t from figures (5.6) and (5.7), it can be seen that the tail deflection angle increases substantially due to the relevant static margin increment at supersonic flight. This is an undesired situation, since the larger δ t is a factor that leads to increased drag during cruise. For that reason, the aircraft CG has to be moved aft too, so that the static margin is kept inside the desired range. This can be achieved through fuel shifting, like in the case of Concorde. Therefore, having a static margin of 0.1 after the fuel shift, means that the location of the CG during supersonic flight has to be at 15.4 m. 5.4 Directional Stability An analysis for the directional or weathercock stability, for subsonic speeds and fixed-rudder, has been accomplished in order to evaluate the vertical stabilizer design. The requirement for static directional stability is that the directional stability derivative, or so-called yaw stiffness, is positive (C nβ > 0). That means that on the aircraft will act restoring moments that will tend to decrease a positive sideslip angle (β). For the normal case that both engines are operating, the yaw stiffness contributions come from the wing, the fuselage and the vertical stabilizer. The C nβ can then be expressed as C nβ = C nβfus + C nβw + C nβv T (5.15) The fuselage, the wing and the vertical tail contributions, for the subsonic range of Mach numbers, can be estimated using the equations (5.16), (5.17) and (5.18) [30]. In equation (5.16) Vol f is the fuselage volume, d f is the fuselage mean depth and w f is the fuselage mean width. C nβfus d f = 1.3 V ol f in radians (5.16) S ref b w f C nβw ( = C 2 L ( 1 4πAR tan Λ c/4 πar(ar + 4 cos Λ c/4 ) cos Λ c/4 AR 2 AR2 + 6(h n h) sin Λ c/4 8 cos λ c/4 AR )) in radians (5.17) where ( 1 + σ β ) qv T q ( C nβv T = V V T C FβV T 1 + σ ) qv T β q (5.18) = (S V T /S ref ) 1 + cos Λ c/ z wf d f AR (5.19) 71

74 The wing-fuselage combination at a sideslip angle creates a sidewash σ, which changes the effective angle of the vertical tail. The sidewash that comes from the fuselage is the dominant factor, in comparison with the wing, and gives a stabilizing air above the fuselage wake [34]. Hence, the effect of the sidewash is stabilizing for a low-wing aircraft. The ratio (q VT /q) is actually equal to the square of the velocity ratio (V VT /V ), and accounts for the propeller slipstream effect [28]. For the case of the propeller absence this ratio equals to one. The contribution of the two aforementioned parameters to the C nβvt can be estimated analytically from the relation (5.19), where S VT is the vertical tail area including the area extended to the fuselage centerline and z wf is the vertical distance of the root chord to the fuselage centerline, being positive for wing root vertical location below it. For this design, the S VT equals to m2 and the z wf to 1.1 m. The V VT is the vertical tail volume coefficient, which can be obtained from equation (2.32), where L VT is the distance of the vertical tail aerodynamic center to the aircraft center of gravity. Finally, the C FβVT is the lift-curve slope of the vertical tail. This can be computed from the equation (3.3), like in the case of the wing, introducing the relevant properties of the vertical tail. However, in this equation it has to be introduced the effective and not the geometric aspect ratio of the vertical tail. The effective aspect ratio of the vertical tail is 1.55 times greater than the geometric one, and this increment comes from the end plate effect of the horizontal tail mounted below the vertical stabilizer [34]. The calculated subsonic directional stability derivatives (C nβ ) are presented in table 5.1. These values are greater than the suggested values of NASA TN D-423, as presented in reference [9], meaning that the aircraft will be directionally stable enough. Mach number C nβ (deg 1 ) C 2 L C 2 L C 2 L C 2 L C 2 L C 2 L C 2 L Table 5.1 Directional stability derivatives for the subsonic Mach number range. 72

75 6. Performance 6.1 Climb Performance For the climb performance analysis, the equations of motion for the rigid and mass point geometry body have been utilized. The thrust model has been created according to the thrust lapse expression from the equation (2.19), which gives the variation of the thrust with the Mach number and the flight altitude. The relation of the dry thrust has been used for this analysis, since the aim is the total avoidance of using the afterburner for reasons of increased fuel consumption and noise. 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 aerodynamic coefficients computed in previous chapter. The trim drag has been neglected for 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 from the fuel mass burned during flight. The equations describing this model, for the engine installation angle of zero degrees, can be written as m V = T cos α D mg sin γ (6.1) 0 = T sin α + L mg cos γ (6.2) ḣ = V sin γ (6.3) x E = V cos γ (6.4) ṁ = C T (6.5) With the assumption that the acceleration perpendicular to the flight path is negligible, made in equation (3.2), the nonlinear equation can then be solved to 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 dry and wet thrust of a low-bypass ratio turbofan engine, respectively. C dry = ( M) θ (6.6) 73

76 C wet = ( M) θ (6.7) The C in the above equations is given in fps units, i.e. parameter θ to have been already defined in equation (2.15). 1 /hr, with the Minimum Time to Climb In order to find the optimal path that corresponds to the minimum time for the climb and the acceleration phase, the flight envelope including the specific excess power (SEP) contours for different altitudes has to be created. The SEP is given from the formula SEP = (T cos α D)V W (6.8) The SEP is defined as the excess power divided by the weight, where the excess power is just the excess thrust, (T cos α D), times the velocity, V. This excess power can be used for altitude gain or for acceleration. For load factor equal to one and considering steady and level flight, which means that the flight path angle γ = 0, the relevant flight envelope can be created for a specific aircraft weight. The SEP contours of this SST design for maximum payload and 85 % fuel mass (i.e. aircraft total mass of kg) are presented in figure 6.1. In this figure, the stall angle of attack and maximum dynamic pressure limitations have also been included. The stall angle of attack can be computed by dividing the clean configuration C Lmax with the aircraft C Lα, with the relevant value to be computed as 16 deg. The maximum dynamic pressure has been set to KP a, which is the dynamic pressure corresponding to 1.1 Mach at sea level. Figure 6.1 SEP contours diagram (dry thrust). 74

77 The SEP contours of figure 6.1 are actually corresponding to the aircraft climb rate. In order to obtain the minimum time to climb, the path to be planned has to follow the maximum aircraft climb rates. For that reason the aircraft has to accelerate at the same altitude till Mach 0.9, where the climb with maximum climb rate will take place. The aircraft is climbing till about the desired cruise height and then it dives, so that it accelerates and passes through the transonic region, where the drag is too high that does not allow the aircraft to accelerate any more, due to thrust deficiency. After the aircraft acceleration, the altitude is regained, since the drag becomes lower in supersonic speeds. The dive follows the relevant constant energy height curves, for which the dynamic energy is purely converted to kinetic energy. The final part of the trajectory includes the climb to the final cruise altitude and the acceleration to the cruise Mach number. In figure 6.2, the minimum time to climb trajectory is presented. The flight path angle γ as a function of time has been defined as the control variable that has been used to solve the set of differential equations (6.1) - (6.5), with the initial conditions to be 0.1 km flight altitude and 0.3 Mach flight speed. The fuel 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 taxiing and takeoff. The time needed for this climb at km and Mach 1.7, is about 1430 sec, where the fuel that has been burned has been estimated as 3399 kg or 22.6 % of the total fuel capacity. It has to be mentioned that the initial cruise altitude that can be reached is 450 m lower than the specified from the requirements altitude of the 15 km. Figure 6.2 Flight path for minimum time to climb at cruise conditions. 75

78 6.1.2 Minimum Fuel to Climb The flight path giving the minimum fuel consumption to climb is a bit different in comparison with the minimum time to climb one. The minimum fuel 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 change in specific energy per change in fuel weight [9]. The FSE is defined as F SE = SEP C T (6.9) The FSE contours and the relevant flight path is presented in figure 6.3. The γ(t) is the control variable in this case as well, while the same set of equations has been solved, like for the minimum time to climb trajectory. The initial flight and weight conditions have been considered the same too. The time needed to reach the cruise flight conditions of km and 1.7 Mach has been computed as 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 compared to 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 been calculated as km. Figure 6.3 Flight path for minimum fuel to climb at cruise conditions. 6.2 Range The horizontal range of aircraft during cruise can be calculated from the Breguet range equation (6.10). During the cruise the aircraft is flying at constant C L and speed. However, keeping these two parameters constant means that the aircraft due to the fuel burn, which is reducing its weight during the cruise, will gradually climb to higher altitudes. Moreover, the aircraft is possible to fly at 76

79 constant speed and Mach number, since the speed of sound for cruise altitudes in stratosphere remains unchanged. R = V C ( ) L D ln Winit W final (6.10) Since the target is the range maximization, the minimum fuel to climb flight path is the desired one to be followed before the cruise. Knowing the relevant fuel that has been burned during the climb the W init can be easily obtained. At the end of the cruise, it is assumed that the aircraft has a remaining 12% of the total fuel capacity or W final equal to kg. For the cruise flight conditions of 1.7 Mach at the height of km, the lift-to drag ratio (L/D) has been calculated as Therefore, the horizontal range to be covered during cruise is estimated as km, while the flight altitude at the end of the cruise as km. 6.3 Descent and Loiter After the end of the cruise phase, the aircraft needs to decelerate and descend to 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. That means that the excess power becomes negative and the aircraft decelerates, while a 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 of the (L/D) max with the C is maximum. Thus, the chosen conditions for the loiter have been the 6.8 km altitude and the 0.4 Mach. The thrust has been reduced to 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 the approach 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 = 1 C ( ) L D ln Winit W final (6.11) During the first descent the fuel burned and the horizontal range covered are 207 kg and km, respectively. During the loiter, a total 441 kg of fuel has been burned, corresponding to an endurance of 24 min and 14 sec. The final descent has consumed 179 kg of fuel, covering an additional horizontal range of km. The aircraft weight before the final approach has then been computed to be kg, with 6.51% of the total fuel to be left for usage during the landing and taxiing phases. 77

80 6.4 Takeoff The takeoff distance, as can be seen from figure 6.4, consists of two basic components, 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 (d g ) and the rotation distance (d r ). During the ground roll, the aircraft accelerates from the zero velocity till the takeoff velocity (V TO ), which should be 1.1 times the stall speed (V stall ) [9]. The V stall can be simply calculated setting the lift equal to weight and using the C Lmax for flaps in the takeoff position (about 80% of the landing C Lmax ). The relevant value obtained is 71 m/s. The d g can then be calculated from the integral d g = VT O 0 V dv (6.12) α where the acceleration α is given from the relation (( ) T α = g W µ + ρ ) ) ( C D0 KCL 2 + µc L V 2 2W/S (6.13) For the rolling friction coefficient µ, the typical value of 0.05 for brakes off has been used [13]. The total C D0 at the takeoff has been estimated as , including the flaps, slats and landing gear contributions. The lift coefficient C L being 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 that reason, in order to obtain more accurate results, the integral has been broken into smaller segments for which average thrust has been used. The rotation distance d r can be simply obtained multiplying the V TO with the typical rotation time t r of 3 sec. The total distance during the ground run has then been calculated as 1927 m. In order to obtain the total takeoff distance, the d ab has to be estimated as well. During this airborne phase the aircraft is accelerating from the takeoff speed (1.1V stall ) to the climb speed (1.2V stall ) [9]. Moreover, the aircraft gains 78

81 altitude, in order to achieve the 35 ft obstacle clearance (h ob ), defined from the FAR regulations. The load factor (n) during the pull-up can be calculated from the equation (6.14), where the 90% of the takeoff C Lmax 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 radius is changing. For that reason, they have been computed for the given range of speeds, and then the mean value of the turn radius has been used. n = 1 2 ρs(0.9c Lmax)V 2 W R = V 2 g(n 1) (6.14) (6.15) Having estimated the pull-up R, the airborne distance can be calculated as d ab = R 2 (R h ob ) 2 (6.16) The relevant value obtained for the d ab is m, which means that the total takeoff distance is estimated as m. 6.5 Landing The landing distance includes the approach distance (d a ), the flare distance (d f ), the free roll distance (d fr ) and the ground roll distance (d g ). The landing phases can be observed in figure 6.5. The approach angle θ a is usually small, and for a transport aircraft should be θ a 3 deg [9]. The θ a can then approximated from the equation (6.17). In order to satisfy the aforementioned constraint for the approach angle, the 63% of the thrust has been used during landing, resulting in a θ a equal to 2.79 deg. sin θ a = 1 L/D T W (6.17) During the approach and flare phase, the aircraft should decelerating from the approach speed (V a = 1.3V stall ) to the touchdown speed (V a = 1.15V stall ). The V stall is the one obtained using the CL m ax corresponding to flaps in landing position and is equal to 64.5 m/s. The approach turn radius (R) can then be computed using the relations (6.14) and (6.15), like in the takeoff case, for the previously stated variation of velocities. The approach distance, taking then into account a clearance distance of 50 ft [13], is approximated as d a = R(1 cos θ a) tan θ a (6.18) 79

82 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]. d f = R sin θ a (6.19) d fr = t r V T D (6.20) Finally, the ground roll distance can be computed using from the integral d g = 0 V T D V α dv (6.21) where α is given again from the equation (6.13). The integral has been computed using the same method, as for the takeoff. The total C D0 at the landing has been estimated as 0.175, including the flap, slats, landing gear and spoilers contribution. A spoilers deflection of 45 deg has been assumed. The value of rolling friction coefficient used is the one corresponding to brakes usage. The typical value of 0.5 has been used for the µ [13]. The total landing distance can be estimated by just summing all the relevant contributions. The obtained value is then increased, so that the FAA requirements that allow for pilot technique are met [9]. Hence, the final landing distance can be estimated from the equation (6.22) as m. 80

83 d land = 5 3 (d a + d f + d fr + d g ) (6.22) 6.6 Total Mission The evaluation of the above results shows that the aircraft is meeting the requirements regarding the takeoff and landing distances. The total horizontal range is 6053 km and the maximum endurance about 24 min. The maximum range without any loiter can reach the 6354 km. The obtained range is lower than the desired one, but yet enough to execute transatlantic flights. The main focus for getting a bigger range should be the improvement of the lift-to-drag ratio during cruise. A slight increment of the (L/D) cruise to 6.2 from would result to a total horizontal range of 6437 km or an increment of 384 km. This value assigned for the (L/D) cruise is quite reasonable and feasible to be obtained, when compared with the relevant value of the Concorde. According to reference [36], the Concorde had a (L/D) max of 7.5 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 and wing twist optimization. For a flight between London and New York, the total time of the climb, cruise and descent is 3 hrs and 35 min. Assuming that no loiter is needed, which is the case 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 normal time of a subsonic airliner for that route is 7 hrs and 40 min to 8 hrs, the time saving is very significant. Although the SST cannot follow the minimum fuel to climb flight path for practical reasons, like the overland sonic boom ban, which might impose an initial small subsonic cruise part on the mission, the time saved remains still substantial and would be about 3 hrs and 30 min for the whole trip. 81

84 7. Test Flight 7.1 Simulation The flying and handling qualities of the design have been flight tested using the Merlin MP521 Engineering Flight Simulator. The MP521 Simulator comprises a capsule with a six axis motion system, visual and instrument displays, touch control panels, and hardware flight controls [37]. The software of the flight simulator that has been run is the Excalibur II, while the design has been created at the Excalibur Data Editor. The model in the editor has utilized the geometrical data and mass properties of the design, in addition to the aerodynamics and propulsion data, acquired during the conceptual design. The mass moments of inertia are calculated by the editor, using empirical relations, from the inserted values that correspond to the aircraft mass parameters, center of mass and wing span, assuming one plane of symmetry, i.e. I xy = I yz = 0. The wing is split into panels for which the relevant data are inserted to the editor. The wing is divided according to its control surfaces, particularly there is a change when a control surface is met, so that there can be lifting surfaces with or without control surface. In this case, the wing semi-span has been split in a total six panels, where the other half includes six more panels, which are automatically mirrored due to symmetry. For the horizontal tail, just one panel has been used, since it has been modeled as a whole moving surface, while two more panels have been considered for the vertical tail. For each panel the control surfaces data, and the wing geometrical characteristics, in addition to the used airfoil aerodynamic data, have been specified. The aerodynamic center of each panel has to be independently calculated and set in the model editor too. The model includes excessive data for the undercarriage as well, such as the nose-wheel steering and the brakes, determining the aircraft ground performance. These data have been specified using typical values recommended from the software 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-freedom equations of motion of a rigid body, and thus does not take into account any aeroelastic effects. The translational positions are integrated in earth (NED) axes and the angular positions (aircraft attitudes) are represented in the standard four-parameter Quaternion format, in order to allow the attitudes be integrated 82

85 through the 90 degrees pitch attitude singularity. The simulator includes a flight data recorder (FDR) with a recording frequency that 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 body variables and atmosphere parameters. The recorded data have then been read and 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 and long-term response [38]. The short-term characteristics of the aircraft are very essential, since poor behavior can make the aircraft very hard or even impossible for the pilot to handle. Thus, the primary goal when evaluating the flight and handling qualities of the design is to achieve satisfactory short-term response, which are related to its short period dynamic modes. The long-term response is substantial in maintaining steady flight of the aircraft and is determined from the static stability and its long period dynamic modes [38]. However, these modes having a long period, can be handled a lot easier by the pilot, so that even marginally unstable modes can be considered satisfactory. Taking the above into consideration, the flight test of the design aimed to the dynamic modes evaluation, in terms of both longitudinal and lateral-directional dynamic stability. The aircraft has been trimmed by determining the necessary throttle setting and horizontal tail deflection for each flight condition being considered. Then each mode has been excited and the results have been recorded using the simulator s FDR. For the executed measurements, the highest recording frequency of 25 Hz has been implemented. Finally the obtained results have been rated using the relevant guidelines and margins as specified in the Military Specification MIL-F-8785C. The aircraft flying and handling qualities have been evaluated for three different altitudes, in particular at 10, 20 and 30 kft, and for subsonic Mach numbers. The design was tried to be assessed for the supersonic cruise conditions as well, however the results obtained from the simulation have been considered as inaccurate and hence will not be presented 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 dynamic stability modes during flight is given in reference [38], which is briefly described in this subsection. These procedures help to measure and quantify the relevant modes properties during test flight in a way that they can be comparable with the analytical values. 83

86 The longitudinal dynamic stability modes consist of the short-period pitching mode and the long-period or phugoid mode, which are both related to oscillatory motion. The two modes have a significant difference as regards their frequency, which makes possible their independent excitation. The short-period oscillation can be excited by applying a short duration disturbance in pitch to the trimmed aircraft. In order to achieve this a unit impulse is applied to the elevator for about one sec. This impulse will more likely excite the phugoid mode too. However, due to its low frequency, which requires significantly more time in comparison with the short-period mode to develop the phugoid oscillatory motion, the short-period measurements will not get affected. In order to excite the phugoid mode, a small step input is applied to the elevator, which causes the aircraft to accelerate, when descending, while the thrust level setting is kept constant. The elevator is returned to its initial position, when the aircraft speed has increased by about 5% compared to relevant speed at the trimmed condition. It has to be mentioned that it is essential this speed disturbance to be small for the results to be accurate, since the modes are being evaluated using the small-perturbation model, which should not be violated. In contrast with the longitudinal dynamic modes, the lateral-directional ones are 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 carefully and accurately for the relevant measurements to be taken. The lateral-directional stability 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 the short-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 roll attitude angle of the aircraft would contrarily increase and thus diverge from the initial balance condition. The spiral mode is a weak mode with a big time constant, and thus does not affect substantially the flying and handling qualities of the aircraft, so that unstable modes can be acceptable too. The roll subsidence mode can be excited when a square pulse is applied to the aileron. In order to specify this dynamic mode during flight test, the roll attitude angle is set initially at about -30 deg. Then the relevant aileron deflection is applied, so that the aircraft rolls steadily to the +30 deg roll attitude, when the aileron has returned to the neutral position. The roll subsidence mode is the one that governs the transient exit of the steady part of the rolling motion. Its time constant 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 rudder pedals. The period of the rudder deflection should approximately match the 84

87 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 rudder to the neutral position, the aircraft will continue to execute a free oscillation, which corresponds to the oscillatory motion related to the dutch roll mode. The dutch roll mode having short period should be stable and demonstrate adequate damping, so that the aircraft flying qualities can be considered satisfactory Dynamic Stability Requirements A common method for the flying and handling qualities evaluation of the aircraft is the so-called Cooper-Harper rating scale. This is a qualitative rating scale that expresses the pilot opinion. The pilot rates the aircraft behavior, respective with the different flying phases that are needed to be tested, using an 1 to 10 scale, where the lower the grade the better the flying and handling qualities the aircraft exhibits. However, in order for the results to be impartial, the modes obtained from the flight test will be quantified, following the guidelines given in the previous subsection. Then the calculated modes will be compared to the requirements presented in reference [39], which correspond to specific values that determine the margins for the aircraft s flying and handling qualities assessment. Before presenting the relevant requirements, the aircraft has to be classified and categorized, according to instructions given in [39]. The classification is related 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 and low-to-medium maneuverability aircraft, which means that it belongs in Class II. The mission profile of the SST is in accordance with the flight phases defined for a category B aircraft, for which accurate flight-path control is required and gradual, without precision tracking, maneuvers accomplishment. The dynamic stability requirements, for both the longitudinal and lateraldirectional modes of an Class II and Category B aircraft, are presented in the tables and in figure 7.1. The time to double or half is the time required for the initial perturbation of the trimmed condition to be doubled or halved and is defined, for the case of an oscillatory motion, in equation 7.1, where the symbol n corresponds to the real part of the relevant eigenvalue. The damping ratio ζ is defined in relation 7.2, and the ω n is the undamped angular frequency given from the relation 7.3 [28]. Therefore, obtaining the period (T) of the oscillation and the t half or t double after processing the recorded flight data, both ζ and ω n can be estimated using the aforementioned equations. t double or t half = ln2 n = ln2 ζ ω n (7.1) ζ = n/ω n (7.2) ω n = (ω 2 + n 2) 0.5 (7.3) 85

88 Level Min ζ Max ζ Table 7.1 Short-period mode damping ratio limits. Figure 7.1 Short-period mode frequency requirements [39]. 86

89 In figure 7.1, the parameter n/α correspond to the normal load factor per unit angle of attack α. Level Requirement 1 ζ > ζ > 0 3 T > 55 sec Table 7.2 Phugoid mode stability requirements. Level t double 1 < 20 sec 2 < 8 sec 3 < 4 sec Table 7.3 Minimum time to double amplitude limits for spiral mode. Level Time constant 1 < 1.4 sec 2 < 3.0 sec 3 < 10 sec Table 7.4 Roll subsidence mode time constant limits. Level Min ζ Min ζ ω n (rad/sec) Min ω n (rad/sec) Table 7.5 Dutch roll mode damping ratio and frequency limits Longitudinal Dynamic Stability Short-period pitching mode The short period pitching mode has been measured for the aforementioned flight altitudes and for the Mach numbers of 0.5 and 0.8, except for the altitude of 30 kft, where due to the aircraft stall restriction, the lower Mach number has been set to 0.6. The same flight conditions have been used for the other modes measurements too. 87

90 In figures 7.2 and 7.3, the elevator impulse for the short period mode excitation and the resulting oscillation as depicted in the body axis pitch rate are presented for the stated flight conditions. Figure 7.2 Elevator impulse input flight recording of the short period mode for 0.6 Mach at 30 kft. Figure 7.3 Body axis pitch rate flight recording of the short period mode for 0.6 Mach at 30 kft. The obtained values corresponding to the short-period pitching mode, after processing the data of the flight recorder for all the tested flight conditions, as well as their evaluation regarding the aircraft s flying and handling qualities, can be seen in table

91 Mach Altitude (kft) T (sec) t half (sec) ω n (rad/sec) ζ Level Table 7.6 Variation of short-period pitching mode characteristics with speed and altitude. Phugoid mode Similarly to the short-period mode, the relevant values of the phugoid mode characteristics are presented in table 7.7, while in figure 7.5, the oscillatory motion of the mode as regards the aircraft s true airspeed is illustrated. Mach Altitude (kft) T (sec) t half (sec) ω n (rad/sec) ζ Level Table 7.7 Variation of phugoid mode characteristics with speed and altitude. Figure 7.4 Elevator step input flight recording of the phugoid mode for 0.6 Mach at 30 kft. 89

92 Figure 7.5 True airspeed flight recording of the phugoid mode for 0.6 Mach at 30 kft Lateral-Directional Dynamic Stability Spiral mode In figure 7.6, the flight recording for the roll attitude angle can be observed for the stated flight conditions. It can be seen from the graph that the spiral mode 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 are presented. Figure 7.6 Euler roll angle flight recording of the spiral mode for 0.6 Mach at 30 kft. 90

93 Mach Altitude (kft) t half (sec) Level Table 7.8 Variation of spiral mode characteristics with speed and altitude. Roll subsidence mode In figures are presented the graphs obtained for the roll subsidence mode from the flight test at the stated flight conditions, regarding the aileron input, the roll attitude angle and the roll rate. In table 7.9, the roll convergence time constant and evaluation regarding the previously specified flying and handling qualities requirements are presented. It can be observed in figure 7.9, that the the roll response stabilizes when the moment due to damping in roll is the opposite to the disturbing moment in roll caused by the aileron deflection [38]. Moreover, from figure 7.8 can be seen that after the roll angle becomes steady, it starts decreasing. This is an effect of the spiral mode, which tends to recover the aircraft s wings level, after returning the aileron to its zero deflection position. Figure 7.7 Aileron input flight recording of the roll subsidence mode for 0.6 Mach at 30 kft. 91

94 Figure 7.8 Euler roll angle flight recording of the roll subsidence mode for 0.6 Mach at 30 kft. Figure 7.9 Body axis roll rate flight recording of the roll subsidence mode for 0.6 Mach at 30 kft. Mach Altitude (kf t) Time constant (sec) Level Table 7.9 Variation of roll subsidence mode characteristics with speed and altitude. 92

95 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 yaw rate graphs, for the stated flight conditions. From these two graphs, it is visible the expected phase shift between the roll and the yaw rate too. It can be seen from the graphs that the dutch roll oscillation is the motion starting for this case after the first 4 sec. In the first 4 sec, the observed oscillation is the one enforced from the rudder input. In table 7.10, the dutch roll characteristics for the tested flight conditions are presented. Figure 7.10 Rudder input flight recording of the dutch roll mode for 0.6 Mach at 30 kft. Figure 7.11 Body axis roll rate flight recording of the dutch roll mode for 0.6 Mach at 30 kft. 93

96 Figure 7.12 Body axis yaw rate flight recording of the dutch roll mode for 0.6 Mach at 30 kft. Mach Altitude (kft) T (sec) t half (sec) ω n (rad/sec) ζ Level Table 7.10 Variation of dutch roll mode characteristics with speed and altitude. 94

97 8. Environmental Impact 8.1 Sonic Boom One of the most important environmental impacts of the SST operation is the aerodynamic noise generated by the shock waves. The so-called sonic boom has imposed a ban on the overland supersonic flight, which can now be performed only overseas. NASA is conducting research in this field in order to create a low boom design, which could be quiet enough to overcome the applied restrictions. The early sonic boom research was conducted according to modified linear methods, based on Whitham s theory for the sonic boom prediction. According to the linear theory, the pressure signatures reaching the ground are N-waves, which are typical for aircraft with high wing loading. However, later work has shown 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, having thus variable ambient conditions, and the atmospheric turbulence modeling, which made necessary the development of more accurate methods and their experimental validation through flight testing. Therefore, the later studies focused on creating aircraft concepts with lift and volume distributions that would shape non-n-waveforms at the ground, rather than trying to reduce the noise generated by the N-waves, which created substantial limitations. The focus of the High-Speed Research (HSR) program of NASA was the creation of a big SST, which could carry more than 250 passengers. The idea behind that concept was that the opening of more supersonic corridors overland due to a low boom design, would result in a more excessive usage of supersonic transports. Therefore, the development cost of the aircraft would be smaller due to increased demand for its purchase. The SST design proposed in this project refers to a small aircraft carrying 15 passengers. However, some sonic boom minimization design guidelines could be implemented to smaller aircraft and evaluated too. In reference [41], several concepts are examined based on a reference design as regards the sonic boom loudness. The delta baseline design wing has been changed into a wing arrow design, having about the same aerodynamic efficiency The relevant baseline and the low boom design and specifications are presented in figures 8.1 and

98 Figure 8.1 Drawing and specifications of the baseline configuration [41]. It can be seen from the two drawings that the low boom design incorporates a bigger wing. It has been found that a bigger wing is beneficial since the lower wing loading results in reduced pressure levels to sonic boom for the lift contribution [41]. The result is a reduction of about 7 PLdB between the two designs. However, this sonic boom loudness reduction comes with a significant price, which is an increase of about 12 % on the maximum takeoff weight per passenger. The modified wing planform with the larger area and the higher wing sweep demands higher structural weight, which makes the low boom configuration heavier. Thus, it has been become clear that the low boom design is related with a performance penalty, as an effect of the increased aircraft structural weight. Moreover, the high wing sweep, in addition to the low aspect ratio, makes the low speed performance of the aircraft very challenging. The above observations conclude that there is a trade-off between the aircraft performance and the sonic boom loudness, which has to be balanced [42]. Furthermore, the low boom design usually leads to the aircraft wave drag increment. The sonic boom minimization concepts adopt blunt nose, which is far from the optimal configuration for minimal wave drag. A blunt nose creates a strong bow shock, so that the secondary shocks are weak and do not overtake 96

99 and enhance the front shock. The far field pressure signature produced in this way, thus, comes to be much weaker than in the case of a sharp nose, where the front bow shock coalesces with the stronger secondary shock waves [43]. In this case, the nose shape is a trade-off between the sonic boom loudness and the wave 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 has shown that it was very difficult to achieve theoritical ground overpressure substantially less than 1 psf [44]. For that reason a lighter and smaller aircraft would be perhaps a better candidate for decreasing the sonic boom loudness. A lighter aircraft demands a lower amount of lift to sustain level flight, which is a factor that decreases the sonic boom intensity [45]. It has to be mentioned here that the sonic boom is measured in psf or Pa of overpressure. For shaped pressure signatures, reference [46] provides with a method to obtain the relevant perceived level of noise loudness (PLdB). As it has been stated before, the wing planform is an important factor for achieving reduced sonic boom. In the case of the small SST design, still reduced 97

100 wing loading is needed and thus a large wing. It is important too that the wing incorporates a long wing root, which will result in the gradual development of the area and lift. Moreover, the span cannot be decreased too much, in order to 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 the conventional one, so that its interaction with the aircraft nose shock is reduced. However, this creates serious problems with the aircraft stability. The center of gravity of the fuel placed in the wing can be at a long distance with respect to the empty aircraft center of gravity, which can result in large shifts of the total aircraft center of gravity location [47]. For that reason as much fuel as possible has to be placed in the front portion of the wing, which due to its increased size and thus volume will perhaps offer this opportunity. Finally, this fact would not allow the wing to incorporate very thin airfoils, in order to achieve the desired volume for the fuel storage, which would subsequently increase the drag. The fuselage design of a small SST design has also the disadvantage of the decreased fineness ratio, since the length of the body is smaller but the maximum diameter cannot be decreased too much in order to be able to house the passengers and of course the aircraft systems. That has anyway an important wave drag penalty on the design. Furthermore, the optimal position of the engines, according to [44], would be the aft fuselage behind the wing trailing edge. This wing-nacelle interference would be in this way avoided and the flow field disturbances of the nacelles would correspond just to volume and not to lift contribution effects. Another advantage would be increased space for the trailing edge devices placement on the wing. However, the engines support in this 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), capable of carrying 8-10 passengers, is illustrated. This SBJ design incorporates a canard, instead of a horizontal tail, and all the relevant specifications of the concept can be found in reference [44]. Due to its decreased size and weight 98

101 compared to the bigger SST concepts, which is also a result of flying at Mach numbers below 2, this design was able to generate significant lower ground overpressure of about 0.5 psf at cruise start. However, the drag and weight penalties that are accompanied with the low boom design are becoming even more apparent. The consequence is an aircraft with lower performance, which although makes the design environmentally viable, its economical viability is questioned. Furthermore, the increased weight of the low boom design creates some difficulties regarding the incorporation of engines with reasonable size and weight, that would be capable of producing the necessary thrust for satisfying the aircraft supercruise requirement. The development of engines with improved performance and the usage of composite materials would be substantial factors in achieving an economic viable concept as well. 8.2 Air Pollution Air Pollutants Identification During the flight, various pollutants substances are being emitted into the atmosphere and are primarily due to the combustion gases from the propulsion system. During the combustion process in general the most important pollutant emissions that can be identified are the carbon dioxide (CO 2 ), the nitrogen oxides (NO x ), the water vapor (H 2 O), the carbon monoxide (CO), the hydrocarbons (HC), the sulfur oxides (SO x ) and the soot particles (C). In reference [48], a detailed analysis is presented regarding the chemical mechanisms of the pollutants creation. Here only a brief description of them and their environmental impact will 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 to produce CO 2. It is the most significant gas that contributes to the greenhouse effect. Carbon dioxide emissions from aircraft can be calculated from a knowledge of the amount of fuel consumed during the flight. Fuel consumption does not scale linearly with distance traveled due to the extra fuel burn required to lift the plane up to cruising altitude, and the necessity to carry large quantities of fuel for long distance flights. The highest fuel burn rate, thus the highest rate emission of gases, occurs during the take-off and climb section, because of the increased thrust needed to climb to cruise altitude and the heavier configuration of the aircraft comparing to the other stages of the flight. The cruise is the most fuel-efficient stage of the flight because the air is less dense and the aircraft is flying at its most efficient operating speed, so the emissions are less than the first stage of the flight. However, for the intercontinental flight that will be executed in this case, the cruise time and distance is a lot longer than the corresponding ones of the take-off and climb part. Thus the biggest part of the CO 2 emissions are carried out at the cruise altitude. These emissions from an individual flight depend mainly on the distance traveled, the weather conditions (head or tail wind), the flight altitude, the cargo and passengers load. 99

102 Nitrogen oxides are produced when air passes through high temperature/high pressure combustion, where nitrogen and oxygen present in the air combine to form NO x. The nitrogen oxides are one of the most dangerous and toxic air pollutant of aviation activity. They contribute to various environmental effects and have significant impact throughout the whole flight, on both higher and lower altitudes. The NO x are produced in higher engine power settings in contrast to the CO and the HC, and its emissions are maximum near the stoichiometric condition. In figure 8.4, the various air pollutants emissions dependence on the equivalence ratio (Φ), can be observed. The Φ is defined as the fuel-to-air ratio of 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 in the fuel combines with oxygen in the air to produce H 2 O and is released by the propulsion system into the atmosphere after the combustion process. For the low layers of the atmosphere these emissions can be neglected, since they are too low compared to the natural emissions. However, at high altitude, under certain atmospheric conditions, because of the very low temperature of the air, the vapor condenses into droplets to form contrails and cirrus clouds. So, the impact of this pollutant should be taken into account only on the cruise part of the flight. It is considered to have an effect to global warming and possibly to precipitation inducement. Carbon monoxide is formed due to the incomplete combustion of the carbon in the fuel. It is a short-lived greenhouse gas (2 months) and its concentration is extremely 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 the atmosphere can contribute to the increase of the tropospheric ozone, through its 100

103 photochemical oxidation. The CO is a result of the incomplete combustion of the fuel and is mainly formed because of the absence of sufficient O 2 during the combustion. Thus, the emissions of CO are maximized at lean mixture operation at low power settings, such as during idle. The presence of carbon monoxide can be detected and measured with CO detectors, in order to prevent poisoning. Hydrocarbons are emitted due to incomplete fuel combustion. They are also referred to as volatile organic compounds (VOCs). Many VOCs are also hazardous air pollutants. The formation of unburned hydrocarbons (UHC) are a result of engines with low pressure increase in the compressor and relatively low temperatures in the combustor. Hence, the largest amount of UHC are produced during 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 essentially all hydrocarbon fuels, combine with oxygen from the air during combustion. SO x emissions are directly related to the sulfur content of the fuel, so it can be 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 small enough to be inhaled, are referred to as particulate matters. They can be solid or liquid. Particulate emissions were a problem on the earlier jet engines when operating on high thrust settings. For normal operating conditions of the modern engines, the production of smoke in every stage of the flight has been radically reduced, so that the amount of particulate emissions can be considered negligible Environmental Concerns of Supersonic Flight The major environmental impacts of aviation include primarily the climate change and the ozone layer depletion. The two more prominent differences between supersonic and subsonic cruise are the increased fuel consumption, which leads to an increase in combustion products, and the higher cruise altitude of the supersonic compared to the subsonic aircraft. The relevant influence of the supersonic transport on the aforementioned environmental impacts is examined in the following subsections. Climate Change The climate change, which is particularly being referred as enhanced greenhouse effect or global warming, is one of the most important environmental concerns. The uniqueness of the aircraft operation, compared to the other human activities affecting the climate change, is the direct emission of air pollutants into the higher levels of the atmosphere. The gases, which are being emitted from the jet engines and contribute to the greenhouse effect, are the carbon dioxide, the nitrogen oxides and the water vapor. The greenhouse effect increases the temperature of the Earth by trapping heat in the atmosphere. This heat is a result of the sun radiation absorption from the greenhouse gases, which are 101

104 hindering the heat absorbed from the ground to bounce back to space. The global average surface temperature of the earth has increased by 0.6 C during the 20th century, while a increment of at least 1.8 C is expected for the next one [49]. Apart from the global temperature rise, this trapping of heat in the atmosphere can also affect the weather conditions on the planet, such as the appearance of heavier rainfall, floods, tornadoes, thunderstorms. Investigations have also shown that the oceans are possible to expand, the ice on the poles to melt 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 portion of the total greenhouse gases emissions, the increment of the air traffic over the last years and the forecasts for the upcoming ones, show that can develop in a rather serious factor as regards the climate change. According to the European Environmental Agency [51], the emissions of CO 2 have increased about 80 % between 1990 and 2014, while the prediction is for a further grow of 45 % between 2014 and There are currently no requirements for the engine certification respective with the greenhouse gases. However, the recent trend of the aviation emissions increment, make their influence on the enhanced greenhouse effect more substantial. From the emitted gases the most problematic for the greenhouse effect is considered to be the CO 2, which among else has a long life cycle. The H 2 O can be considered a significant emission too, especially for flying vehicles in the stratosphere, like the supersonic transport. Flying in such high altitudes, with very low temperatures, the water vapor produced is converted into persistent contrails, which evaporate very slowly. These contrails may be very long (dozens of kilometers), forming the so-called cirrus cloud fields, which can potentially have a strong influence in the climate change. The water is produced as a fixed ratio to fuel which is consumed for complete combustion of kerosene, like in the case of the carbon dioxide. In particular, the combustion of 1 kg kerosene produces 3.16 kg CO 2 and 1.24 kg H 2 O [48]. In tables 8.1 and 8.2, the emissions of CO 2 and H 2 O of the supersonic transport design are compared to the relevant emissions of a commercial subsonic airliner. 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, which is a consequence of its smaller payload (just 15 passengers instead of the 416 of the Boeing 747) and thus size. However, the emissions of CO 2 and H 2 O per km per seat of the SST are about 5.85 times greater than the subsonic airliner s. That comes from the fact that the SST cruises at a significantly smaller drag-to-lift ratio and with a larger thrust specific fuel consumption. In particular, the specific fuel consumption of the RB H installed in Boeing 747 during cruise is g/kn/s [52], which is a value considerably lower. From the obtained results, it can be inferred that the influence of small supersonic aircraft flight would not be so environmentally problematic concerning the greenhouse effect. However, an excessive growth of the supersonic transportation, especially in the case of large supersonic transports replacing part of the current 102

105 subsonic flee, could essentially affect the total aviation emissions. Moreover, the phenomenon of the persistent contrails and cirrus clouds formation at the stratosphere and its consequences on the environment would need to be further investigated. Aircraft CO 2 (kg/km) CO 2 (kg/km/seat) Boeing [53] SST Table 8.1 Carbon dioxide emissions of subsonic airliner and SST design (6050 km distance flown). Aircraft H 2 O (kg/km) H 2 O (kg/km/seat) Boeing SST 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 the biggest 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 to about 57,300 ft, it is obvious that the aircraft will directly emit the produced NO x in the stratosphere and thus in the ozone layer. The subsonic airliners executing long haul flights at a cruise altitude of around 35,000 ft are emitting NO x in the low level of the stratosphere as well. The NO x in the stratosphere are participating in a catalytic chemical reaction, which leads to the ozone destruction. The ozone layer breakdown could allow the ultraviolet B radiation from the sun to pass through this ozone shield and reach the Earth, which could cause among else skin cancer and cataract in humans, but could harm the animals too. However, both the subsonic and supersonic aircraft emit NO x in the stratosphere, the impact of the SST flying at higher flight altitudes is more significant due to the increased ozone concentration. It is shown in figure 8.5 that the highest ozone concentrations are observed between 60,000 and 80,000 ft, which comprise the typical flight altitudes of supersonic aircraft at speeds equal to Mach 2 and higher. Thus, the excessive flight of large supersonic transports with speeds greater than Mach 2, cruising at altitudes near the maximum ozone concentration while burning big amount of fuel, could potentially be the most problematic SST concept regarding the ozone depletion environmental impact. 103

106 Figure 8.5 Atmosphere ozone concentration and temperature till the altitude of 100,000 ft [54]. The NO x are produced during the combustion of the kerosene. In reference [55], it is shown a simple correlation between the NO x emission index (EI NOx ) and the combustor inlet total temperature (T tc ). The equation (8.1) is an empirical relation for the prediction of the NO x emissions based on the so-called Lipfert correlation, stated previously [48], where δ is defined in equation (2.16). EI NOx = 10 ( (Ttc )) δ (8.1) The above equation demonstrates that for high combustor inlet temperatures and thus high engine pressure ratios, the NO x emissions of the engine are significantly increased. The pressure ratio, determining the total temperature at the compressor exit, influences the actual primary zone temperature in the combustion chamber [48], and thus the NO x production as well. In figure 8.6, the NO x emissions index variation is presented with respect to the overall pressure ratio for a subsonic airliner and the SST design. The example of the subsonic aircraft that was used is the Boeing , and the relevant cruise conditions are 0.85 Mach at a flight altitude of 11 km. For the SST the cruise speed is 1.7 Mach at an average flight altitude of 16 km. The upper limit of the overall pressure ratio, including the fan, of the RB H engine of the Boeing is set to 33 [52], while for the EJ200 is set to 22, so that the total temperature at the compressor exit does not exceed 900 K, which is a practical limit of the compressor materials and its cooling requirements [50]. For the RB H a 104

107 diffuser isentropic efficiency of 0.97 has been assumed, while the intake isentropic efficiency 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 Figure 8.6 NO x emissions index for SST design (red) and for a typical subsonic long haul airliner (blue). From the calculated values illustrated on figure 8.6, the maximum EI NOx of the subsonic aircraft is about 16.2 g/kg fuel at its maximum compression ratio of 33, which is a value that agrees with the relevant ones stated in reference [56] for long range subsonic transports. On the contrary, the pressure ratio effect on the EI NOx of the SST is much more prominent with an emissions index of g/kg fuel at the maximum set pressure ratio of 22. The increased fuel consumption of the SST is also a parameter that contributes to even higher NO x emissions, creating great concerns about the environmental viability of an excessive turn in supersonic transportation in the near future. In order to keep NO x emissions within acceptable limits, an emissions index as low as 5 during cruise, which corresponds to about a 80% reduction of the above calculated values, would be necessary, which has been the goal set to be investigated during the NASA s High Speed Research Program as well [54]. In order to achieve such low NO x emissions, new engine concepts have to be developed emphasizing on this reduction, while maintaining the other engine requirements of low thrust specific fuel consumption, high thrust-to-weight ratio and reliability. Moreover, the economic viability of the undertaking to build a new engine capable to be incorporated at supersonic aircraft has to be examined as well. In order to reduce the NO x emissions, the equivalence ratio Φ has to be controlled, so that the engine operates in the low emissions region of Φ, according to figure 8.4. Moreover, it is important to reduce the time of the gases remaining in high temperatures. There are different types of combustor concepts, referred 105

108 to as dry low NO x combustors, which focus on more efficient, as regards the relevant emissions, combustion process. Three types of them are the lean premixed pre vaporized combustor, the staged combustor type and the rich burn quick quench lean combustor. The concepts behind the aforementioned combustion chambers operation, in addition to their pros and cons, are more thoroughly described in reference [48]. Finally, the water emissions in the stratosphere is believed to have some influence on the ozone destruction too, since it can affect the affect the composition, growth and aerosol reactions and provide a source of HO x radicals that enhance ozone loss [54]. However, this is an effect that has to be further investigated, so that the consequences of the water vapor emissions in the ozone layer become more certain. 106

109 9. Discussion - Conclusions Since the Concorde retirement, there is no supersonic transport aircraft in operation, but the possibility of a new SST development is becoming a reality once again. Efforts are being made in both the development of a low-boom design and a SST able to fly supersonically just overseas. The design proposed in this project is a supersonic transport aircraft able to carry 15 passengers and 4 crew members, having a maximum payload of 1900 kg. The aircraft is being able to fly at supersonic speeds just overseas, since it has not be designed for reduced aerodynamic noise generation. The cruise flight conditions are 1.7 Mach at an initial altitude of km. The aircraft s take off mass is estimated as kg, while the wing area is about m 2. The total dry thrust at SL is 120 kn, provided by two low-bypass ratio turbofan EJ200 engines. In order to surpass the sound barrier, the aircraft has to incorporate a carefully area-ruled design, with a parasite drag coefficient at the given cruise conditions that should not exceed The aircraft, in order to exhibit satisfactory static longitudinal stability in both subsonic and supersonic speeds, keeping the static margin to 0.1 for every flight condition, uses fuel shifting for the aft movement of the aircraft center of gravity during supersonic flight. The design incorporates a whole moving horizontal tail is used instead of an elevator. During the supersonic cruise, the aircraft 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 drag during cruise. During the mission a total horizontal range of 6053 km can be covered, in addition to a maximum loiter of 24 min. This range is rather smaller than the desired requirement of 7200 km. However, it could be increased through camber and wing twist optimization, so that the estimated drag-to-lift ratio of reaches a more efficient value. The estimated time of a transatlantic flight between 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 flight test measurements. However, these qualities was not possible to be assessed for the supersonic speeds as well, since the flight test failed to give reasonable results using the simulation model created. The two most important environmental concerns about the supersonic flight 107

110 are the noise generated by the shock waves, the so-called sonic boom, and the air pollutants emissions. A discussion made about low-boom design shows that the sonic boom is quite hard to be reduced in larger and heavier aircraft. Moreover, the low-boom design and the aircraft performance optimization contradict each other, so that this trade-off between them questions the economic viability of the reduced sonic boom loudness designs. As regards the air pollution, the excessive turn in supersonic flight could lead to two significant environmental impacts, named the climate change and the ozone layer depletion. It has been shown that the emissions of greenhouse gases, like the carbon dioxide, are bigger compared to subsonic airliners, as a result of the higher fuel consumption. The higher nitrogen oxide emissions, resulting from the supersonic flight, at the stratosphere, especially in altitudes where the ozone concentration is maximum, constitute an even more significant problem to be tackled. During the conceptual design and the flight test, the aeroelastic effects have been disregarded. Moreover, the aerodynamic coefficients referring to transonic flights have been just interpolated following charts and theoretical guidelines given from Raymer in reference [9], due to lack of valid empirical relations. CFD simulation would be a more accurate way for obtaining the transonic aerodynamic coefficients. Finally, CFD simulations could be used for the evaluation and validation of the used subsonic and supersonic wing aerodynamic coefficients as well. 108

111 109

112 Appendices A. Airfoils Coordinates NACA coordinates [15]. 110

113 NACA coordinates [15]. 111

114 B. Airfoils Aerodynamic Characteristics NACA lift and pitching moment coefficient [15]. 112

115 NACA drag polar [15]. 113

116 NACA lift and pitching moment coefficient [15]. 114

117 NACA drag polar [15]. 115