上海交通大学：《飞机设计 Aircraft Design》课程教学资源_Aircraft Design - 14 & 15-Performance.pdf_大学文库

2018/4/27 国上活大坐 Overview of Lectures 国上清大学 Course Code:AV314 0.Overview 14/15 Performance(a,b) Term:Undergraduate,Third year Spring Term 16.Aircraft certification Credit:3 2.Overall configuration 17.Aviation economics Hours:51 weight estimation 18.System integration and d weight estimation configuration management Fuselage design 19.Multidisciplinary design 6/7/8 Aerodynamic design(a,b,c) ootimization Aircraft Design (飞行器设计) .hat and ing 20.Military aircraft design-overview 21.Environmental issues 10.Landing gear and Aircraft systems 22.Design skills 11.Power plant Wenbin Song 12.Stability and control School of Aeronautics and Astronautics 13.Loads,materials and structures Shanghai Jiao Tong University swb@sjtu.edu.cn ertin ong Song Performance Topics 圆上清文大些 Overview 国上道大坐 Role of performance analysis Aircraft performance analysis treat aircraft as a point mass,not a Basic concepts and equations rigid body as is done in aircraft stability analysis analysis for different segmentsin a typical flight mission, -Takeoff analysis Airra perfomancer of a -Steady level flight -Steady climbing and descending flight -Level turning flight Gliding flight Acrodynamic fores Engine data Weight estimations -Landina analysis ·Conclusions Aircraft performance calculations itevop☐Payload range☐Takooff Landing Cruise 8oaoT二Wenbin ong Role of Performance Analysis 图上洋大峰 Inputs/Outputs for Performance Calculations 园上海发大坐 Throughout the aircraft life cycle from design,manufacture,flight test to ope Pret)etc sign stagerequirement analysis,engine data(thrust, Engine data from engine supplier Weight estimation including C.G.locations from initial -Manufacture validation of design,full set of technical manuals sizing Flight testsCross validation with wind tunnel data,certificate documents,fault analysis Takeoff and initial climb Climb to operating altitude ·Cruise Descend Approach and landing ·Payload range graph sy-Dr.Wenbin Song 1

2018/4/27 1 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Wenbin Song School of Aeronautics and Astronautics Shanghai Jiao Tong University swb@sjtu.edu.cn Aircraft Design （飞行器设计） Course Code: AV314 Term: Undergraduate, Third year Spring Term Credit: 3 Hours: 51 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Overview of Lectures 0. Overview 1. Introduction 2. Overall configuration 3. Preliminary weight estimation 4. Refined weight estimation 5. Fuselage design 6/7/8 Aerodynamic design(a, b, c) 9. Thrust/Weight ratio and wing loading 10.Landing gear and Aircraft systems 11.Power plant 12.Stability and control 13.Loads, materials and structures 14/15 Performance(a, b) 16.Aircraft certification 17.Aviation economics 18.System integration and configuration management 19.Multidisciplinary design optimization 20.Military aircraft design – overview 21.Environmental issues 22.Design skills © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Performance Topics • Role of performance analysis • Basic concepts and equations • Performance analysis for different segments in a typical flight mission, including – Takeoff analysis – Steady level flight – Steady climbing and descending flight – Level turning flight – Gliding flight – Landing analysis • Conclusions 3 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Overview • Aircraft performance analysis treat aircraft as a point mass, not a rigid body as is done in aircraft stability analysis • Aircraft performance calculation forms an important part of conceptual design, which links design parameters with performance requirements Aerodynamic forces Engine data Weight estimations Aircraft performance calculations Flight envelop Payload range Takeoff Landing Cruise © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Role of Performance Analysis • Throughout the aircraft life cycle from design, manufacture, flight test to operations… – Project design stage  requirement analysis, engine data (thrust, SFC), etc – Detailed design  wind tunnel data, CFD, CAD drawings, certification data, operational manual, flight test plan – Manufacture  validation of design, full set of technical manuals – Flight tests  Cross validation with wind tunnel data, certificate documents, fault analysis 5 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Inputs/Outputs for Performance Calculations • Aerodynamic forces from engineering estimation methods/CFD/wing tunnel data • Engine data from engine supplier • Weight estimation including C.G. locations from initial sizing • Takeoff and initial climb • Climb to operating altitude • Cruise • Descend • Approach and landing • Payload range graph 6 Inputs Outputs

2018/4/27 2 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Basic Concepts - ISA • International Standard Atmosphere – a model of air, developed from ideal gas law • Sea level (SL) data • Viscosity and speed of sound are given as 7 sea-level data unit gravitational Acceleration 9.80665 kgms-2 T 288 K density 1.225 kgm-3 speed of sound 340.294 ms-2 gas constant 286.9 JKg-1K-1 Tropopause 11000 m Lapse Rate 0.0065 T@Tropopause 216.5 K pressure 101300 Pa viscosity 1.79E-05 kg/m/s kinematic viscosity 1.46E-05 m2 /s Thermal Conductivity 0.02596 w/m/K Specific Heat Cp 1005 J/Kg/K Specific Heat Cv 717.98 J/Kg/K Ratio of Specific Heats 1.4 当 H≤11000m 时， T = 288.15 − 0.065H(K) P = 101325.2 × (1 − 2.25577 × 10−5H)5.25588 (Pa) ρ = 1.225 × (1 − 2.25577 × 10−5H)4.25588 (kg/m3 ) (5.1 当 11000m＜H≤20000m 时， T = 216.65(K) P = 22631.8 × e− 𝐻−11000 6341.62 (Pa) ρ = 0.36392 × e− 𝐻−11000 6341.62 (kg/m3 ) (5.2 当 20000m＜H≤32000m 时， T = 216.65 + 0.001(H − 20000)(K) P = 5474.32 × [1 + 4.61574 × 10−6(H − 20000)]−34.1632 (Pa) ρ = 0.08803 × [1 + 4.61574 × 10−6 (H − 20000)]−34.1632 (kg/m3 ) (5.3 a RT   3/2 0 0 0 ( 110.4) / ( 110.4) T T T T      © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Basic Concepts – various speeds 8 i © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Basic Concepts – cont. • 𝑉ீ: Ground speed, the aircraft speed relative to the ground. It calculated from TAS and wind speed – For takeoff and landing, head wind take +++++ – For climb, cruise, and descend, head wind take ----- 9 Ground speed, true airspeed and wind Airspeed as a function of altitude © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Basic Concepts – cont. • In Summary 10 𝐶𝐴𝑆 = 𝐼𝐴𝑆 ± 𝑖𝑛𝑠𝑡𝑟𝑢𝑚𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟 ± 𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑎𝑡𝑖𝑜𝑛 𝑒𝑟𝑟𝑜𝑟 ± 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑒𝑟𝑟𝑜𝑟 𝑉ா ≡ 𝐶𝐴𝑆 − 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑇𝐴𝑆 = 𝐸𝐴𝑆𝜎 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Basic Concepts – cont. • (Geometry) altitude (𝐻) – the absolute altitude above sea level • Pressure altitude (𝐻௉), the ISA (geometry) altitude with the same pressure level – For a hot day, lower than geometry altitude – For cold day, higher than geometry altitude – 𝑯 = 𝟎~𝟏𝟏𝟎𝟎𝟎𝒎 – 𝐻 = 𝐻௉ − 153.846Δ𝑇𝑙𝑛 1 − 2.25577 × 10ିହ𝐻௉ 𝑚 – 𝐻 = 𝐻௉ − 504.745Δ𝑇𝑙𝑛 1 − 6.87559 × 10ିହ𝐻௉ 𝑓𝑡 – 𝑯 = 𝟏𝟏𝟎𝟎𝟎~𝟐𝟎𝟎𝟎𝟎𝒎 – 𝐻 = 1 + ୼் ଶଵ଺.଺ହ 𝐻௉ − 6.8971ΔT(𝑚) – 𝐻 = 1 + ୼் ଶଵ଺.଺ହ 𝐻௉ − 22.628ΔT(𝑓𝑡) 11 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Basic Equations of Motion • Kinematic equations in earth coordinate system 12 V r x y z Xd , Yd , Zd , 𝜃 𝜓௦

2018/4/27 4 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off Run, Take-off Distance and Accelerate-Stop Distance • Take-off distance = max(ASDOEI, TODOEI, 1.15TORAEO) • Available take-off distance – TORA: Take-off run available = runway length available – TODA: Take-off distance available = runway length available + clearway if available – ASDA: Accelerate-stop distance available = runway length available + stopway if available 19 Clearway, CWY, 净空道 Stopway, SWY, 停止道 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off path in detail BR 35 ft TO distance TO flight path Take-off path VEF Critical engine is made inoperative AEO OEI V2 minimum acceleration height = 400 ft End = the higher of : either - 1500 ft, or - the point where en-route configuration is achieved, with remaining engine(s) at MCT, and minimum climb gradient at green dot speed. © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Aircraft characteristics and Airport planning • Aircraft manufactures provide runway chart – Sea-level, standard day – Balanced field length – Should be adjusted based on TOW, altitude, pressure, surface conditions, etc. • FAR Takeoff Field/Runway Length definition – max(ASDOEI, TODOEI, 1.15TORAEO) 21 TOR(Takeoff Run) ≤ TORA (Takeoff Run Available) TOD(Takeoff Distance) ≤ TODA (Takeoff Distance Available) ASD(Accelerate-Stop Distance) ≤ ASDA (Accelerate-Stop Distance Available) © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off Distance - all engines operating (Ia) 22 T  D  M dV dt R R  Mg  L M dV dt F T D D T D (Mg L)     roll      D D  0.5qSC 2 D L C  a  bC dV dt T W    W S a bCL CLV g 2 2     2    © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off Distance - all engines operating (lb) • Ground roll distance can be computed by integral • Approximation can be assumed by 23               LOF LOF V LOF roll V V g dV W D D g T W F MVdV s dx 0 2 0 0 2 1     5 0.75 4 T Tstatic      L t o roll C W D D       ,max,  0.02 0.01   2 ,max, 5 2 0.75 0.02 0.01 4 t o g static L t o V S T g c W                      𝜆 is BPR of the turbofan engine © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off Distance - all engines operating (II) • Transition flight path 24

2018/4/27 5 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off distance - all engines operating (III) • Transition to Climb • Aircraft accelerate from VLOF to V2 • Simple estimation can be made by assuming that – CL=0.9CLmax – VTRANS=(VLOF+V2)/2 – Flying along an arc 25 L Mg MV r TRANS cos / 2    n  L / Mg max 2 L 0.5 VTRANS S 0.9 CL        /[ ( 1)] 2 r VTRANS g n  cos 1 s  r T h  r  2 T    0.5 2 2 s r h r s   s  Screen height © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off Distance - all engines operating (IV) 26 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Take-off distance - all engines operating (V) • Climb after transition to screen height • Climb distance: the ground distance from the end of transition to the screen height • where, ht is the height at the end of transition, γc is the best climb angle • Total distance for take-off is the sum of ground roll, transition, and climb distance 27   C t C s  screen height - h / tan © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics STEADY CLIMB & DESCEND FLIGHT 28 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Typical Climb Profile and Speed 29 Climb carried out mainly at constant equivalent airspeed or constant Mach number constant Mach number climb 0 150 250 320 500 VE (kts) Z (kft) 36 25 10 0 constant equivalent airspeed climb constant equivalent airspeed climb M=0.86 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Initial Climb to 1500ft after Takeoff (I) • Initial climb is typically divided into four segments • Airworthiness demands certain climb gradient with one engine failure for twin engine or four engine aircraft – refer to certification code • Take-off climb performance is usually defined by second segment performance requirement which is the most critical 30

2018/4/27 6 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Horizontal T W Wcosθθ θ θ L D Initial Climb to 1500ft after Takeoff (II) • Climb rate (vertical velocity) can be obtained by analyzing forces • Therefore, the climb rate is related to thrust, drag, and weight of the aircraft – Thrust is 85% of the static value – Drag of the basic configuration – The asymmetric drag due to a failed engine, • windmill drag, CD＝0.3Af/S • Additional trim drag, 5% of the basic profile drag 31 T  D  W sin  L  W cos   W 𝜃 = sinିଵ 𝑇 − 𝐷 𝑊 = sinିଵ( 𝑇𝑊 − 𝑐𝑜𝑠𝜃 𝐿/𝐷 ) ≅ sinିଵ( ்ௐ − ଵ ௅/஽ ) 𝑉௩ = 𝑉𝑠𝑖𝑛𝜃 = 𝑉 𝑇 − 𝐷 𝑊 ≅ V 𝑇𝑊 − 1 𝐿/𝐷 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Climb Performance: further analysis • Given a climb angle: • Best rate of climb and Best angle of clime – Best rate of climb provides the max climb rate – Best angle of climb provides the max climb angle • Time to climb and fuel to climb – Time to clime a certain distance and corresponding fuel used can be calculated as follows – Integration or approximation can be used to calculate from 𝑡ଵ to 𝑡ଶ 32 ©Raymer 𝑉 = 2𝜌𝐶௅ 𝑊 𝑆 𝑐𝑜𝑠𝜃 𝑇𝑊 = 𝑐𝑜𝑠𝜃 𝐿/𝐷 + 𝑠𝑖𝑛𝜃 ≅ 1 𝐿𝐷 + 𝑠𝑖𝑛𝜃 𝑑𝑡 = 𝑑ℎ𝑉௩ 𝑑𝑊௙ = −𝑆𝐹𝐶𝑑𝑡𝑇 Difference between the two modes of climb: • Best rate of climb gives higher altitude for a given time • Best angle of climb gains more altitude for a given horizontal distance © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics STEADY LEVEL FLIGHT 33 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics 34 Equilibrium equations T = D + Wsinγ=D L = Wcosγ=W Equations for Level Cruise Rate of change of aircraft weight SFC T dt dW    L D W V Horizontal axis γ=0 α φp T © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Steady Level Cruise Analysis • Analysis for unaccelerating level flight • Therefore • These equations can be used in further analysis – Minimum cruise thrust requirement for jet aircraft – Minimum cruise power requirement for propeller aircraft 35 𝑇 = 𝐷 = 𝑞𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ 𝐿 = 𝑊 = 𝑞𝑆𝐶௅ 𝑉 = ଶఘ஼ಽ (ௐ ௌ ) and ்ௐ = ଵ ௅/஽ = ௤஼ವబ (ௐ/ௌ) + ௐ ௌ ௄ ௤ © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Thrust required for level flight – jet aircraft • Minimum thrust for given aircraft weight can be found from • Therefore, 36 𝜕 𝑇 𝑊⁄𝜕𝑉 = 𝜌𝑉𝐶஽଴ 𝑊 𝑆⁄ − 𝑊 𝑆 2𝐾 1 2 𝜌𝑉ଷ = 0 𝑉୫୧୬ ௧௛௥௨௦௧ = ଶௐ ఘௌ 𝐾/𝐶஽଴ and 𝐶௅௠௜௡ ௧௛௥௨௦௧ = ஼ವబ ௄ At any given weight, the aircraft can be flown at the optimal lift coefficient for minimum drag by varying velocity or air density (altitude). Question one: What is formula for total drag?

2018/4/27 7 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Thrust required for level flight – propeller aircraft • Minimum power required for propeller aircraft can be derived by first calculate the power • Similar to the derivation on previous slide • Therefore 37 𝑃 = 𝐷𝑉 = 𝑞𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ 𝑉 = 1 2 𝜌𝑉ଷ 𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ = 1 2 𝜌𝑉ଷ 𝑆𝐶஽଴ + 𝐾𝑊ଶ 1 2 𝜌𝑉𝑆 𝜕𝑃 𝜕𝑉 = 3 2 𝜌𝑉ଶ 𝑆𝐶஽଴ − 𝐾𝑊ଶ 1 2 𝜌𝑉ଶ𝑆 = 0 𝑉୫୧୬ ௣௢௪௘௥ = ଶௐ ఘௌ 𝐾/3𝐶஽଴ and 𝐶௅௠௜௡ ௣௢௪௘௥ = ଷ஼ವబ ௄ Question one: What is formula for total drag? Question two: Will the total drag be higher than flying at min thrust? © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Breguet Range Equation 38 Rate of weight change dt=dx/V=dx/aM <<1, because γ<<1 SFC T SFC   D W sin dt dW        dt L D dt SFC W D SFC W dW                        sin 1 sin dx aM L D SFC W dW             sin 1       W dW SFC L D aM L D R dx W W R      2 1 1 sin 0  © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Breguet Equations - Simplification • During Cruise – SFC remains roughly constant (0.5 lbs/hr/lb) – Constant M – L/D also roughly constant – Cruising in tropopause, a = constant • Therefore 39   W dW SFC aM L D R dx W W R     2 1 0            2 1 log W W SFC aM L D R © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Payload Range Graph • Range is related to fuel/weight ratio                        1 1 2 log log 1 W W SFC aM L D W W SFC aM L D R F Maximum payload Maximum takeoff weight Maximum fuel capacity Range (nm) Payload © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics More Analysis on Cruise • Minimum thrust level cruise • Minimum power level cruise 41 𝐷 = 𝑞𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ = 𝑞𝑆 𝐶஽଴ + 𝐶஽଴ 𝐷 = 𝑞𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ = 𝑞𝑆 𝐶஽଴ + 𝐶஽଴ 𝐷 = 𝑞𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ = 𝑞𝑆 𝐶஽଴ + 3𝐶஽଴ 𝐷 = 𝑞𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ = 𝑞𝑆 𝐶஽଴ + 3𝐶஽଴ 𝑉୫୧୬ ௧௛௥௨௦௧ = ଶௐ ఘௌ 𝐾/𝐶஽଴ and 𝐶௅௠௜௡ ௧௛௥௨௦௧ = ஼ವబ ௄ 𝑉୫୧୬ ௣௢௪௘௥ = ଶௐ ఘௌ 𝐾/3𝐶஽଴ and 𝐶௅௠௜௡ ௣௢௪௘௥ = ଷ஼ವబ ௄ The velocity for minimum power is ~0.76 times the velocity for minimum thrust cruise, while lift coefficient is ~73% higher for minimum power flight. But total drag for min power is not twice that for min drag! © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics LEVEL TURNING FLIGHT 42

2018/4/27 8 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Analysis of Level Turning • Turn-rate or rate of turn (ROT) – Defined as radial acceleration divided by the velocity – Angular velocity • Force analysis – Vertical lift component equals weight – Load factor is 𝑛 – Therefore turning rate 43 𝜓̇ = 𝑊 𝑛ଶ − 1 𝑊 𝑔⁄ 𝑉 = 𝑔 𝑛ଶ − 1 𝑉 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Analysis of Level Turning (Cont.) • Turning radius – Smaller V and higher n gives smaller R • Two types of turning, depends on time period – Instantaneous , for short period of time – Sustained turning, for an extended period of time 44 𝑅 = 𝑉𝜔 = 𝑉 ଶ 𝑔 𝑛ଶ − 1 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Instantaneous Turning • Instantaneous turn – aircraft is allowed to slow down during the turn • The load factor 𝑛 will only be limited by the maximum lift coefficient (stall) or structural strength • Corner speed is important for dog fight • Drag is greater than thrust • Turning rate higher than sustained turning 45 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Sustained Turning • In sustained turning, the aircraft is not allowed to slow down or lose altitude, which implies that • Therefore • Based on this, the following equation holds • This gives the load factor n 46 𝑇 = 𝐷 and 𝐿 = 𝑛𝑊 𝑇 = 𝐷 = 𝑞𝑆 𝐶஽଴ + 𝐾𝐶௅ଶ with 𝐶௅ = 𝑛𝑊 𝑞𝑆 𝑛 = 𝑞 𝐾(𝑊/𝑆) 𝑇𝑊 − 𝑞𝐶஽଴ 𝑊/𝑆 Iterative process is required to solve this as K and n are both functions of the CL © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Sustained Turning Rate • In a sustained turning given flight conditions (speed, altitude, payload), n satisfy the following equation • From minimum drag level flight analysis, there is • The maximum sustained-turn load factor can be solved using 𝑛 = 𝑇 𝑊 𝐿 𝐷 𝐿 = 𝑛𝑊 = 𝑞𝑆 𝐶஽଴ 𝐾 𝑉୫୧୬ ௧௛௥௨௦௧ = ଶௐ ఘௌ 𝐾/𝐶஽଴ and 𝐶௅௠௜௡ ௧௛௥௨௦௧ = ஼ವబ ௄ 𝑛 = 𝑞𝑆𝑊 𝐶஽଴ 𝐾 𝜓̇ = 𝑊 𝑛ଶ − 1 𝑊 𝑔⁄ 𝑉 = 𝑔 𝑛ଶ − 1 𝑉 Maximum n can be achieved with min Drag © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics GLIDING FLIGHT 48

2018/4/27 9 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Straight Gliding Flight • Conditions for straight gliding flight – The thrust is set to zero (no fuel left?) – The direction of the gliding angle is negative Horizontal axis γ<0 α T=0 𝐷 = 𝑊𝑠𝑖𝑛𝛾 𝐿 = 𝑊𝑐𝑜𝑠𝛾 𝐿𝐷 = 𝑊𝑐𝑜𝑠𝛾 𝑊𝑠𝑖𝑛𝛾 = ctan 𝛾 ≅ 1 𝛾 𝐿𝐷 = 𝑊𝑐𝑜𝑠𝛾 𝑊𝑠𝑖𝑛𝛾 = ctan 𝛾 ≅ 1 𝛾 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Glide Ratio • Glide ratio is defined as the ratio between horizontal distance travelled and altitude lost • Glide ratio is equal to the lift-to-drag ratio • Max glide ratio gives the maximum range for gliding flight, therefore requires flying at max L/D – min CD 50 𝑉୫୧୬ ௧௛௥௨௦௧ = ଶௐ ఘௌ 𝐾/𝐶஽଴ and 𝐶௅௠௜௡ ௧௛௥௨௦௧ = ஼ವబ ௄ 𝐿 𝐷 ௠௔௫ = 1 2 𝐶஽଴𝐾 = 1 2 𝜋𝐴𝑒 𝐶஽଴ © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Sink Rate • Another parameters of interest for gliding flight – Determine the time that a glider may remain in the air – Vertical velocity, Vv • Minimum sink rate can be obtained by maximizing 𝐶௅ଷ /𝐶஽ ଶ , which leads to 51 𝑉௩ = Vsin γ = sin 𝛾 ( 𝑊 𝑆 ) 2 cos 𝛾 𝜌𝐶௅ = 𝑊 𝑆 2 cosଷ 𝛾𝐶஽ ଶ 𝜌𝐶௅ଷ 𝑉௩ ≅ 𝑊 𝑆 2 𝜌𝐶௅ଷ /𝐶஽ ଶ 𝐶௅௠௜௡,௦௜௡௞ = ଷ஼ವబ ௄ 𝐶௅௠௜௡,௦௜௡௞ = ଷ஼ವబ ௄ , and ௅஽ ୫୧୬ ௦௜௡௞ = ଷ ଵ଺௄஼ವబ = ଷగ஺௘ ଵ଺஼ವబ ௅஽ ୫୧୬ ௦௜௡௞ = ଷ ଵ଺௄஼ವబ = ଷగ஺௘ ଵ଺஼ವబ 𝐿𝐷 = 𝑊𝑐𝑜𝑠𝛾 𝑊𝑠𝑖𝑛𝛾 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Turning Gliding Flight • when sailplane turns at a bank angle ∅, the following relation holds (a component of the lift is used to turn) • This leads to a modified sink rate 52 𝐿𝑐𝑜𝑠∅ = 𝑊𝑐𝑜𝑠𝛾 ∅ R 𝑉௩ ≅ 1 cosଷ/ଶ ∅ 𝑊 𝑆 2 𝜌𝐶௅ଷ /𝐶஽ ଶ © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Sink Rate and Glide Ratio • Difference between sink rate and glide ratio 53 𝑉 ≅ 2𝑊 𝜌𝑆 𝐾 3𝐶஽଴ 𝑉௩௠௜௡ ≅ 2𝑊 𝜌𝑆 𝐾 3𝐶஽଴ 𝑉 = 2𝑊 𝜌𝑆 𝐾 𝐶஽଴ 𝑉୫୧୬ ௧௛௥௨௦௧ = 2𝑊 𝜌𝑆 𝐾 𝐶஽଴ The velocity for min sink rate is 76% of that for best glide ratio © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics LANDING PERFORMANCE 54

2018/4/27 10 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Approach and Landing Sequence • The landing phase is split into several segments – Approach – Flare – Ground roll • Landing distance is the sum of distances required by each phase 55 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Approach • The approach path is typically made at 3°to the horizontal • FAR certification specifies the approach starts at a screen height of 50ft and ends at the flare height hF • Approach speed is defined as (1.2~1.3)Vs 56   SA obstacle height hF A   / tan hF  r A  A / 2 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Flare – Air Run • A simplified approach assumes that the angular acceleration may be ignored 57 T + Wsinγ –D =mdV/dt L – Wcosγ=md(Rdγ/dt)/dt ~ 0 T – D + Wγ =mVdV/dx =(W/2g)dV2 /dx L – W= 0 dV2 /dx = 2g[(T – D)/L +γ] Vl2 – Va 2 = 2g[–(D/L)eff +γa ]Sa Assuming T=0, and γa takes the average value Sa = (1/2g){[Vl2 – Va 2 ]/ [– (D/L)eff + γa ]} Vl=(1.2-1.25)Vs Va=1.3Vs Sa = [(W/S)l/(4gρsl б CL,lmax)]/ [– (D/L)eff + γa ] © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Ground Run Distance • On the simplest level, assuming constant deceleration (-a), the distance covered from 𝑉௟ to 0 is 𝑉௟ଶ /2 • On the next level, • Ground distance can be computed from the above equation 58 dV/dt = (1/2g)dV2 /dx = (T/W)l – (D/W)l – (Fbrake/W)l (D/W)l =CD,lρslбV2 /2(W/S)l (Fbrake/W)l = mbrake (1-L/W) = mbrake [1 – CL,lρslбV2 /2(W/S)l] © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Other Aircraft Performance Characteristics • Common set of performance measures – Turn rate, corner speed, load factor etc. • Other performance measures of merit – Control speed and altitude separately – Post stall behavior, 60-degree AOA operations, for example are typical for 4th generation fighters – Performance with Thrust vectoring – Store release – Dynamic turn 59 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Most Important Aircraft Performance Characteristics • Capabilities of aircraft can be mostly represented by – Maximum speed – Stalling speed – Besting climbing speed – Best glide speed – Rate of climb – Ceilings – Maximum rang and speed for maximum range – Maximum endurance and speed for maximum endurance – Takeoff/landing distance 60