GAUSS, PRANDTL, AND LOW SPEED AERODYNAMICS WITH HUGH SMITH

KARL FRIEDRICH GAUSS, “PRINCE OF MATHEMATICS” Born on April 30, 1777 Childhood prodigy-many stories concerning his abilities at a young age Attracted attention of Duke of Brunswick-sent to Collegium Carolinum and later University of Göttingen Also had strong interest in astronomy – Director of Gottingen Observatory for many years Later Life-made a fortune through bonds and investments Died on February 23, 1855 “It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.”

CONTRIBUTIONS OF GAUSS Proved that a Heptadecagon could be constructed using a compass and straightedge Proved the Fundamental Theorem of Algebra 4 different ways Proved the Fundamental Theorem of Arithmetic Developed the magnetometer Helped build the first successful telegraph Pioneered Non-Euclidean Geometry Gaussian Distribution in Statistics

LUDWIG PRANDTL, “FATHER OF MODERN AERODYNAMICS” Born in February 1875 Earned a Ph.D. from Technische Universität München in 1900 Began his work with fluid mechanics designing factory equipment From 1901, he began working as a professor at the Technical School in Hanover Many important discoveries were made here In 1904, Prandtl became director at University of Göttingen Worked at Göttingen until his death in 1953 “If one age believes too much it is natural that another believes too little.”

CONTRIBUTIONS OF PRANDTL Discovery of Boundary Layer in 1904 led to further understanding of skin friction drag Furthered 3-Dimensional Wing Theory, which became known as Lanchester-Prandtl Wing Theory Published simplified thin-airfoil theory Realized the importance of wing tips and vortices, which were previously ignored First Theories of Supersonic Shock Waves and Flow in 1908 Supersonic wind tunnels Supersonic Rocket Nozzle (1929)

WHAT IS AERODYNAMICS? Aerodynamics is the study of the movement of air and the interaction between air and objects moving through it 4 Main forces: Weight Lift Thrust Drag Thrust

DO YOU EVEN LIFT? Some aircraft generate lift by being lighter than air Modern Airplanes are denser than air and have to generate lift another way Modern Airfoils depend on several factors to generate lift: Angle of Attack Thickness Camber

MAGNUS EFFECT AND THE ZHUKOVSKY TRANSFORMATION Magnus showed that a spinning cylinder was capable of producing lift Boundary Layer transfers motion of cylinder to air particles Zhukovsky was able to come up with a revolutionary transformation to turn the spinning cylinder into an airfoil

DRAG In Aerodynamics, there are 4 main types of drag: Skin Friction Drag is caused by friction between the air molecules and the airfoil itself Pressure Drag due to separation and wake Pressure Drag due to wing-tip vortices Pressure Drag due to shockwaves

THE EFFECT OF STREAMLINING ON DRAG Streamlining reduces pressure drag by reducing the wake Streamlining increases drag from skin friction

REYNOLDS NUMBERS AND THEIR USE IN AERODYNAMICS

3- DIMENSIONAL WING THEORY Wings have a finite length Lift coefficients are integrated across wing length Airfoil may vary across wing: Chord Length Airfoil Thickness Airfoil Profile Twist Wing-tip vortices are created and produce drag Winglets help prevent vortex drag

EFFECTS OF 3D WING DESIGN ON AERODYNAMICS

SOURCES mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/introvisc/node8.html