Transonic Aerodynamics • Critical Pressure Coefficient and Critical Mach Number • Drag Divergence • Mitigating the Drag Problem – The supercritical airfoil – Sweep – The Area Rule Limit of the Compressibility Correction NACA 0012 AT 8 DEGREES M∞ -10 -9 C M=0 -16 -8 p1 0.1 C p -14 Cp -7 2 0.2 min 1 M 0.3 -12 -6 040.4 -10 -5 0.5 0.6 -8 -4 0.7 -Cp -6 -3 M∞ 080.8 0.9 -4 -2 -2 -1 0 0 00.51 1 M∞ 0.0 0.2 0.4 0.6 0.8x/c 1.0 Critical Pressure Coefficient PRESSURE COEFFIENT WHERE THE LOCAL MACH NUMBER IS 1 Critical Pressure Coefficient PRESSURE COEFFIENT WHERE THE LOCAL MACH NUMBER IS 1 1 1 1 ( 1)M 2 1 Cp 2 1 CR 1 2 1 2 M 2 ( 1) -16 -14 CpCR -12 -10 -8 -6 -4 -2 0 00.20.40.60.81 M∞ Critical Mach Number Cp1min Cpmin 1 M 2 1 1 1 ( 1)M 2 1 Cp 2 1 CR 1 2 1 2 M 2 ( 1) M∞ -16 -14 -12 -10 -8 MCR -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 M∞ Critical Mach Number MCR Cp1min Cpmin 1 M 2 1 1 1 ( 1)M 2 1 Cp 2 1 CR 1 2 1 2 M 2 ( 1) -16 -14 -12 0012 at 8 deg. -10 -8 MCR MCR 0012 at 4 deg. -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 M∞ M=0.5 Drag Divergence INVISCID CALCULATION M065M=0.65 M=0. 8 Ilan Kroo and J Alonso, Stanford University http://adg.stanford.edu/aa241/drag/dragrise.html Shock Induced Separation www.hq.nasa.gov/pao/History/SP- 440/ch7-2.htm Drag Divergence NACA 2315 Effects on Lift NACA 2315 M∞ Mitigating the Drag Problem • The Supercritical Airfoil • Sweep • The Area Rule The Supercritical Airfoil Designed to maximize MDIV Conventional vs. Supercritical NACA 0012 at 2.3 deg. BiBoeing BACJ at 0 deg. 0.8 C = 0280.28 C = 0280.28 ‐Cp L L 0.4 0.0 ‐0.4 00.5100.51 httpp//://oea.larc.nasa. gov /PAIS /Conce pt2R eality/supercritical.html Sweep ‐ The Independence Principle Necessary Sweep Angle M n M cos M Effects on Drag Divergence M n M cos M R. T. Jones, High Speed Wing Theory, Princeton University Press, 1960 Effects on Lift M M n M cos M Effects on Lift 2 cos Λ C L 2 2 1M cos MMn cos M Figure A,4f or g, P42 R. T. Jones, High Speed Wing Theory, Princeton University Press, 1960 Effects on Lift 2 cos Λ C L 2 2 1M cos MMn cos M Figure A,4h, P43 R. T. Jones, High Speed Wing Theory, Princeton University Press, 1960 The Area Rule THE SEARS HAACK BODY 8 V 3/ 2 A(x) 1 (x / L)2 3 The Area Rule WHITCOMB’S OBSERVATIONS Whitcomb, R., 1952 A Study of the Zero Lift Drag‐Rise Characteristics of Wing Body Combinations Near the Speed of Sound, NACA RM L52H08 Boeing 747 747 200B (Air Force 1), Max Mach 0.89 747 400, Max Mach 0.92 Generalizing the Area Rule • At supersonic Mach numbers the Area is measured along the Mach plane instead of perpendicular to the flight direction • OtiOptima l shapes for more general requitirements (like finite base areas, area requirements at particular cross sections) are given by W.T. Lord and E. Eminton in “Slender Bodies of Minimum Wave Drag,” Journal of the Aeronautical Sciences, August, 1954, pages 569‐ 570. These have been programmed by Prof. Mason, see http://www.aoe.vt.edu/~mason/Mason_f/MRsoft.html #MINDRAG.