《飞行器系统工程》（英文版） Aerodynamics Primer

16.885J/ESD. 35J-Sept 2003 16.885J/ESD.35J Aircraft systems engineering Aerodynamics Primer Prof earll murman

16.885J/ESD.35J - Sept 2003 16.885J/ESD.35J Aircraft Systems Engineering Aerodynamics Primer Prof. Earll Murman

16. 885J/ESD. 35J-Sept 2003 TopIcs Geometry jargon Standard atmosphere Airflow variables Forces acting on aircraft Aerodynamic coefficients Lift curve Drag polar Reference: Anderson. John D Jr. Introduction to Flight McGraw Hill, 3rd ed. 1989. All figures in this primer are taken from this source unless otherwise noted Note other sources need to be added

16.885J/ESD.35J - Sept 2003 Topics • Geometry jargon • Standard atmosphere • Airflow variables • Forces acting on aircraft • Aerodynamic coefficients • Lift curve • Drag polar • Reference: Anderson, John D. Jr. Introduction to Flight, McGraw Hill, 3rd ed. 1989. All figures in this primer are taken from this source unless otherwise noted. • Note: other sources need to be added

16.885J/ESD. 35J-Sept 2003 Wing and Airfoil Nomenclature t= thickness c= chord t/c is an airfoil parameter

16.885J/ESD.35J - Sept 2003 Wing and Airfoil Nomenclature t = thickness c = chord t/c is an airfoil parameter t c V 8

16.885J/ESD. 35J -Sept 2003 More wing nomenclature C b=wing span ·S= wing area AR=aspect ratio=b2/S For c.=S/b ar= b/c vg avg 入=c/c.= taper ratio b A=leading edge sweep angl le Twist is the difference in the angle of the tip and root airfoil section chord lines

16.885J/ESD.35J - Sept 2003 More Wing Nomenclature b S cr ct / • b = wing span • S = wing area • AR = aspect ratio=b2/S – For cavg = S/b, AR= b/cavg • O = ct/cr = taper ratio • / = leading edge sweep angle • Twist is the difference in the angle of the tip and root airfoil section chord lines

Standard Atmosphere The environme Bo3 16.885J/ESD. 35J-Sept for aircrat aft design The" standard atmosphere is a reference condition every day is different Temperature T, pressure p, density p are functions of altitude h Standard sea level conditions p=101325x105N/m2=2162bf2 T=288160K=518.7R p=1.2250kgm3=000278sug/ft Handy calculator http://aero.stanford.edu/stdatm.html

16.885J/ESD.35J - Sept 2003 Standard Atmosphere: The Environment for Aircraft Design • The “standard atmosphere” is a reference condition. – Every day is different. • Temperature T, pressure p, density U are functions of altitude h. • Standard sea level conditions – p = 1.01325x105 N/m2 = 2116.2 lb/ft2 – T = 288.16 0K = 518.7 0R – U = 1.2250 kg/m3 = 0.00278 slug/ft3 • Handy calculator http://aero.stanford.edu/StdAtm.html

16.885J/ESD. 35J -Sept 2003 Flow Velocities v called the freestream velocity Units ft/sec, mph(I mph=1.47 fps), knot(1 kt=1.69 fps=1. 151 mph) a=speed of sound Function of temperature: a a,=sqrt(T T2) Function of altitude(standard sea level a=1116.4 ft/sec) Mach number is ratio of velocity to speed of sound, M=V/a a Mo I is supersonic flight Mo close to 1(approx 0.8 to 1. 2 )is transonic flight

16.885J/ESD.35J - Sept 2003 Flow Velocities • Vf called the freestream velocity – Units ft/sec, mph (1 mph = 1.47 fps), knot (1 kt = 1.69 fps=1.151 mph) • a = speed of sound – Function of temperature: a1/a2 = sqrt(T1/T2 ) – Function of altitude (standard sea level a = 1116.4 ft/sec) • Mach number is ratio of velocity to speed of sound, M=V/a – Mf = Vf/ af – Mf 1 is supersonic flight – Mf close to 1 (approx 0.8 to 1.2) is transonic flight

16.885J/ESD. 35J-Sept 2003 Pressures For M0.3, pressure and velocity are related by bernoulli equation For M>0., pressure and velocity (or Mach number are related, but equation is more involved Further restricted to no losses due to friction P1+0.5pV12=p2+05pV2=p p called static pressure 0.5pV2 called dynamic pressure =q called stagnation pressure p+q somewhat like potential plus kinetic energy

16.885J/ESD.35J - Sept 2003 Pressures 1 2 • For M 0.3, pressure and velocity (or Mach number) are related, but equation is more involved – Further restricted to no losses due to friction. • p1 + 0.5UV12 = p2 + 0.5UV22 = p0 – p called static pressure – 0.5UV2 called dynamic pressure = q – p0 called stagnation pressure – p + q somewhat like potential plus kinetic energy

16.885J/ESD. 35J-Sept 2003 Pressure coefficient Lift proportional Due to geometry of airfoil, the to area under velocity, and therefore the curve pressure, vary Manifestation of lift It is convenient to express this as a pressure coefficient (p-p) · From bernoulli eg and assuming density is constant (ok for M<0.3) Pick out some features on Pressure coefficient for a figure at left conventional airfoil: NACA 0012 airfoil at a= 30

16.885J/ESD.35J - Sept 2003 Pressure Coefficient • Due to geometry of airfoil, the velocity, and therefore the pressure, vary. – Manifestation of lift • It is convenient to express this as a pressure coefficient Cp = (p - pf)/ qf • From Bernoulli Eq and assuming density is constant (ok for M < 0.3), Cp = 1 - (V/ Vf)2 • Pick out some features on figure at left Lift proportional to area under curve Pressure coefficient for a conventional airfoil: NACA 0012 airfoil at D = 30. Lower surface Upper surface Cp x/c 1 0 -1 -2 +1

16. 885J/ESD. 35J-Sept 2003 F orces Wing imparts downward force on fluid, fluid imparts upward force on wing generating lift Lift Weight for steady level flight Drag is balanced by thrust for non-accelerating flight Aerodynamic leverage -lift is 10-30 times bigger than drag! For l pound of thrust get 10-30 pounds of lift

16.885J/ESD.35J - Sept 2003 Forces Wing imparts downward force on fluid, fluid imparts upward force on wing generating lift. Lift = Weight for steady level flight. Drag is balanced by thrust for non-accelerating flight. Aerodynamic leverage - lift is 10-30 times bigger than drag! For 1 pound of thrust get 10-30 pounds of lift. Aerodynamic leverage - lift is 10-30 times bigger than drag! For 1 pound of thrust get 10-30 pounds of lift

16.885J/ESD. 35J-Sept 2003 LD Definitions Resultant force on body resolved into Lift l and drag d By definition, L is perpendicular to relative wine Relative wind D is parallel to relative wind

16.885J/ESD.35J - Sept 2003 L, D Definitions • Resultant force on body resolved into Lift L and Drag D • By definition, – L is perpendicular to relative wind – D is parallel to relative wind c/4 V 8 α L D Relative wind