《航空器系统工程学》（英文版）Introduction to Aircraft Performance and Static Stability

16885J/ESD35J-oct1,2002 16.885J/ESD35J Aircraft Systems Engineering Introduction to aircraft Performance and Static stability Prof earll murman September 18. 2003

16.885J/ESD.35J - Oct 1, 2002 Introduction to Aircraft Performance and Static Stability 16.885J/ESD.35J Aircraft Systems Engineering Prof. Earll Murman September 18, 2003

16885J/ESD35J-oct1,2002 Today's topics Specific fuel consumption and breguet range equation Transonic aerodynamic considerations Aircraft Performance Aircraft turning Energy analysis Operating envelope Deep dive of other performance topics for jet transport aircraft in Lectures 6 and 7 Aircraft longitudinal static stability

16.885J/ESD.35J - Oct 1, 2002 Today’s Topics • Specific fuel consumption and Breguet range equation • Transonic aerodynamic considerations • Aircraft Performance – Aircraft turning – Energy analysis – Operating envelope – Deep dive of other performance topics for jet transport aircraft in Lectures 6 and 7 • Aircraft longitudinal static stability

16885J/ESD35J-oct1,2002 Thrust Specific Fuel Consumption(tsfc) Definition: TSFC= lb of fuel burned (b of thrust delivered)( hour) Measure of jet engine effectiveness at converting fuel to useable thrust Includes installation effects such as bleed air for cabin, electric generator, etc Inlet effects can be included(organizational dependent) pendent ypical numbers are in range of 0. 3 to 0.9. Can be up to 1.5 Terminology varies with time units used, and it is not all consistent TSFC uses hours "c is often used for tsfc lb of fuel burned Another term used is C (b of thrust delivered)(sec)

16.885J/ESD.35J - Oct 1, 2002 Thrust Specific Fuel Consumption (TSFC) • Definition: • Measure of jet engine effectiveness at converting fuel to useable thrust • Includes installation effects such as – bleed air for cabin, electric generator, etc.. – Inlet effects can be included (organizational dependent) • Typical numbers are in range of 0.3 to 0.9. Can be up to 1.5 • Terminology varies with time units used, and it is not all consistent. – TSFC uses hours – “c” is often used for TSFC – Another term used is TSFC lb of fuel burned (lb of thrust delivered)(hour) ct lb of fuel burned (lb of thrust delivered)(sec)

16885J/ESD35J-oct1,2002 Breguet Range Equation Change in aircraft weight= fuel burned dw=-c Tdt c=TSPC 3600 T=thrust Solve for dt and multiply by vo to get ds V dw v w ds=vdi d W Set l/D, c, voo constant and integrate R36001L1nW TSFC∞DW empty

16.885J/ESD.35J - Oct 1, 2002 Breguet Range Equation • Change in aircraft weight = fuel burned • Solve for dt and multiply by Vf to get ds • Set L/D, ct, Vf constant and integrate dW ctTdt ct TSPC/3600 T thrust ds Vfdt VfdW ctT VfWctT dWW VfL ctD dWW R 3600 TSFCVf LDln WTO Wempty

16885J/ESD35J-oct1,2002 Insights from breguet range equation R= TSFC v LIn_to dw empty 3600 TSFC represents propulsion effects. Lower TSFC is better oo D represents aerodynamic eftect. L/D is aerodynamic efficiency a is constant above 36.000 ft M.L important Dm D D Iny 1o represents aircraft weight/structures effect on range empty

16.885J/ESD.35J - Oct 1, 2002 Insights from Breguet Range Equation R 3600 TSFCVf LDln WTO Wempty 3600 TSFC represents propulsion effects. Lower TSFC is better Vf LD represents aerodynamic effect. L/D is aerodynamic efficiency Vf LD afMf LD. af is constant above 36,000 ft. Mf LD important ln WTO Wempty represents aircraft weight/structures effect on range

16885J/ESD35J-oct1,2002 Optimized l/d- Transport A/C Sweet spot' is in transonic range osses due to shock D Concorde waves Mach no Ref Shevell

16.885J/ESD.35J - Oct 1, 2002 Optimized L/D - Transport A/C “Sweet spot” is in transonic range. Losses due to shock waves Ref: Shevell Max (L/D) Mach No. 1 2 3 10 20 Concorde

16885J/ESD35J-ct1,2002 Transonic effects on airfoil c. c 1.0 M<1 M<M M<1 I Mcr<M<Mo M<1 divergence

16.885J/ESD.35J - Oct 1, 2002 Transonic Effects on Airfoil Cd, Cl Cd M cr Mdrag divergence M 81.0 M Mdrag divergence 8 Mcr 1 M>1 M<1 Separated flow

16885J/ESD35J-0ct1,2002 Strategies for mitigating transonic effects Wing sweep Developed by Germans Discovered after Wwll by boeing Incorporated in B-52 Area ruling, aka"coke bottling Developed by dick Whitcomb at NASA Langley in 1954 Kucheman in germany and hayes at north american contributors Incorporated in F-102 upercritical airo Developed by dick Whitcomb at NASA Langley in 1965 Percey at rae had some early contributions Incorporated in modern military and commercial aircraft

16.885J/ESD.35J - Oct 1, 2002 Strategies for Mitigating Transonic Effects • Wing sweep – Developed by Germans. Discovered after WWII by Boeing – Incorporated in B-52 • Area Ruling, aka “coke bottling” – Developed by Dick Whitcomb at NASA Langley in 1954 • Kucheman in Germany and Hayes at North American contributors – Incorporated in F-102 • Supercritical airfoils – Developed by Dick Whitcomb at NASA Langley in 1965 • Percey at RAE had some early contributions – Incorporated in modern military and commercial aircraft

16885J/ESD35J-ct1,2002 Basic sweep concept Consider Mach Number normal to leading edge sinμ=1/M M=M.cosA u=Mach angle the direction disturbances travel in supersonic flow For subsonic freestream M.H- Subsonic leading edge M>1,A<H- Supersonic leading edge Extensive analysis available but this is gist of the concept

16.885J/ESD.35J - Oct 1, 2002 Basic Sweep Concept • Consider Mach Number normal to leading edge • For subsonic freestreams, Mn P - Subsonic leading edge – Mn > 1, / < P - Supersonic leading edge • Extensive analysis available, but this is gist of the concept sin P=1/ Mf P = Mach angle, the direction disturbances travel in supersonic flow Mf Mn=Mfcos/ P /

16885J/ESD35J-oct1,2002 Wing Sweep Considerations Moo>1 Subsonic leading edge Can have rounded subsonic type wing section Thicker section pper surface suction More lift and less drag Supersonic leading edge Need supersonic type wing section Thin section Sharp leading edge

16.885J/ESD.35J - Oct 1, 2002 Wing Sweep Considerations Mf > 1 • Subsonic leading edge – Can have rounded subsonic type wing section • Thicker section • Upper surface suction • More lift and less drag • Supersonic leading edge – Need supersonic type wing section • Thin section • Sharp leading edge