INTRODUCTION TO NEW THEORY OF FLIGHT REVEALING THE SECRET OF FLIGHT UNDERSTANDING WHY IT IS POSSIBLE TO FLY JOHAN HOFFMAN JOHAN JANSSON CLAES JOHNSON

WEB SITE: THE SECRET OF FLIGHT http://secretofflight.wordpress.com/ MATHEMATICS FLUID MECHANICS COMPUTATION MEASUREMENT APPLICATIONS HISTORY

NEW THEORY SUBMITTED TO AIAA MAIN JOURNAL OF AERONAUTICS NOW UNDER SCRUTINY OF EXPERTS FOLLOW THE REVIEW PROCESS ON WEB SITE FIRST VERSION PRESENTED IN NORMAT 2009

OLD THEORY KUTTA-ZHUKOVSKY 1904 FATHERS OF MODERN AERONAUTICS PRANDTL 1904 FATHER OF MODERN FLUID MECHANICS KZP THEORY

SCIENTIFIC MATHEMATICAL THEORIES FOR UNEDUCATED: 1. TRIVIAL AND CORRECT 2. TRIVIAL AND INCORRECT FOR EDUCATED: 3. NON-TRIVIAL AND INCORRECT: OLD 4. NON-TRIVIAL AND CORRECT: NEW

NEW THEORY PHYSICAL MATHEMATICAL CORRECT DOES REVEAL THE SECRET USEFUL

OLD THEORY UNPHYSICAL UNMATHEMATICAL INCORRECT DOES NOT REVEAL THE SECRET DANGEROUS

WHAT TO EXPLAIN: LIFT / DRAG =L/D = 10 - 70 AIRBUS L/D=20 GLIDER L/D=70

THE SECRET: L/D = 10 - 70 SURPRISING INGENIOUS ELEGANT INCOMPRESSIBLE FLOW SLIGHTLY VISCOUS FLOW

IS THEORY NEEDED? BIRDS HAVE LEARNED TO FLY WITHOUT THEORY OF FLIGHT BUT IT TOOK 100 MILLION YEARS FROM DINOSAUR TO ARCHAEOPETRYX HUMANS HAVE LEARNED TO FLY WITHOUT BUT IT TOOK 500 YEARS FROM DA VINCI TO SUCCESS: GOSSAMER CONDOR 1978 BECAUSE OF LACK OF THEORY!!

DA VINCI FLYING MACHINE 1500

GOSSAMER CONDOR 1978 FIRST HUMAN POWERED FLIGHT

CONFESSIONS ABOUT OLD THEORY

NEW YORK TIMES 2003 (CHANG) To those who fear flying, it is probably disconcerting that physicists and aeronautical engineers still passionately debate the fundamental issue underlying this endeavor: WHAT KEEPS PLANES IN THE AIR?

NASA LISTS INCORRECT THEORIES LONGER DISTANCE SKIPPING STONE VENTURI BUT NO THEORY CLAIMED TO BE CORRECT!! NASA DOES NOT SEEM TO KNOW WHAT KEEPS PLANES IN THE AIR!!

LONGER PATH THEORY INCORRECT

SKIPPING STONE THEORY: NEWTON

VENTURI THEORY: BERNOULLI

HOFFREN 2001 AIAA A SATISFACTORY THEORY OF LIFT IS STILL LACKING THERE IS A GENUINE NEED FOR ONE

WHAT KEEPS PLANES IN THE AIR? INCORRECT THEORY OK AS LONG AS YOU DON’T USE IT NOT USEFUL NEW THEORY: CORRECT: USEFUL

WHY CORRECT THEORY ONLY 2009? COMPUTE TURBULENT SOLUTIONS OF NAVIER-STOKES EQUATIONS + SLIP BC DIRECT SIMULATION WITHOUT TURBULENCE MODELING POSSIBLE WITH ~ 1 MILLION MESH POINTS COMPUTATION TELLS THE TRUTH STUDY REVEALS THE SECRET

DRAG CAR COMPUTABLE

LIFT DRAG WING COMPUTABLE VELOCITY PRESSURE

PRESSURE DISTRIBUTION C_P UPPER LOWER SURFACE

LIFT DRAG OF WING COMPUTABLE MAX L = 1.5 L/D = 50 AOA = 16

TO UNDERSTAND: STABILITY STABILITY - INSTABILITY OF FLUID MOTION STABLE COMPUTABLE ASPECTS OF TURBULENT FLOW LIFT DRAG MOMENTS..: COMPUTABLE ALL YOU MAY WANT TO KNOW: COMPUTABLE

OPPOSING FLOW INSTABILITY

STABLE ATTACHMENT UNSTABLE SEPARATION: OPPOSING FLOW

FROM CYLINDER TO AIRFOIL: ROUNDED LEADING + TRAILING EDGE UNDERST CYL = UNDERSTAND AIRFOIL

SHORT STORY: THEORIES OF FLIGHT NEWTON 17H MATH: IMPOSSIBLE: WRONG D’ALEMBERT 18TH MATH: IMPOSSIBLE: WRONG WRIGHT BROTHERS 1903 REAL EXP : POSSIBLE KUTTA-ZHUKOVSKY 1904 MATH: POSSIBLE: WRONG: OLD THEORY OF FLIGHT HOFFMAN-JOHNSON 2009 MATH: POSSIBLE: RIGHT: NEW THEORY OF FLIGHT

NEW VS OLD THEORY NEW THEORY REVEALS THE SECRET OF FLIGHT OLD THEORY HIDES THE SECRET OF FLIGHT OLD: RULING PARADIGM OLD: NOT FUNCTIONAL NEW INCOMPATIBLE WITH OLD SCIENTIFIC REVOLUTION A LA KUHN

LIFT AND DRAG OF LONG WING SUCTION ON UPPER LEADING EDGE/SURFACE: LIFT + NEGATIVE DRAG PUSH ON LOWER LEADING EDGE/SURFACE: LIFT + POSITIVE DRAG FLOW SEPARATES AT TRAILING EDGE WITHOUT PRESSURE RISE/DROP: ELEGANT SEPARATION

AIRFOIL – AIRPLANE WING

OBSERVATION WIND TUNNEL

OBSERVATION: 2D SECTION OF 3D

OBSERVATION LIFT UPPER LEADING EDGE SUCTION LOWER LEADING EDGE PUSH DRAG LEADING EDGE PUSH/SUCTION SEPARATION WITHOUT PRESSURE RISE/DROP DOWNWASH

RECALL C_P UPPER LOWER

NAVIER-STOKES

PRESSURE AOA = 5

VELOCITY AOA = 10

VELOCITY AOA = 10

VELOCITY AOA = 15

UNDERSTANDING: THEORY MATHEMATICAL MODEL OF PHYSICS ASSUMPTIONS MATHEMATICAL MODEL = EQUATION: NAVIER-STOKES + BC: GENERAL LAPLACE + BC: SPECIAL MATHEMATICAL THEORY: SOLVE EQUATION

LAPLACE EQN: POTENTIAL FLOW INCOMPRESSIBLE: CORRECT FOR SUBSONIC FLIGHT INVISCID - SMALL VISCOSITY: CORRECT SLIP BOUNDARY CONDITION: SMALL SKIN FRICTION: CORRECT IRROTATIONAL?? NO VORTICES STATIONARY?? 2D?? V = GRADIENT OF HARMONIC FUNCTION 2D FOR CYLINDER LONG WING 1 + 2 + 3 VALID!! EVERYWHERE!! NAVIER-STOKES 4 + 5 +6 VALID?? SOMEWHERE BUT NOT EVERYWHERE!! LAPLACE??

1- 4 : LAPLACE’S EQN: POTENTIAL: HARMONIC FUNCTION + SLIP

LAPLACE VS NAVIER-STOKES LAPLACE SIMPLIFIED VERSION OF NAVIER-STOKES POTENTIAL SOLUTION: 2D STATIONARY IRROTATIONAL LAPLACE SOLUTIONS NOT TURBULENT NAVIER-STOKES SOLUTIONS TURBULENT

CIRC CYLINDER: POTENTIAL FLOW: P = 0 P = 1 P = - 3 V = 1 V = 0 V = 2

POTENTIAL FLOW: BERNOULLI’S LAW ½ V2 + P = CONSTANT HIGH PRESSURE P – LOW VELOCITY V LOW PRESSURE P – HIGH VELOCITY V

CIRC CYLINDER: POTENTIAL FLOW: ZERO LIFT + ZERO DRAG (L/D = 3)

LIFT OF HALF CYLINDER

THEORY: POTENTIAL FLOW: D’ALEMBERT’S PARADOX 1752: ZERO LIFT AND DRAG

POTENTIAL FLOW VS OBSERVATION

POTENTIAL FLOW SEPARATION BEFORE TRAILING EDGE HIGH PRESSURE AT SEPARATION REQUIRED TO BRING FLOW TO STAGNATION NO DOWNWASH MATHEMATICAL SOLUTION BUT NOT OBSERVED IN REALITY UNPHYSICAL!! WHY??

WHAT’S WRONG WITH POTENTIAL FLOW?? D’ALEMBERT COULD NOT UNDERSTAND 1752

D’ALEMBERT’S PARADOX 1752 It seems to me that the theory (potential flow), developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future Geometers to elucidate”.

WHAT’S WRONG WITH POTENTIAL FLOW?? EULER COULD NOT UNDERSTAND ???? 18TH POTENTIAL FLOW SOLVES EULER’S EQNS

WHAT’S WRONG WITH POTENTIAL FLOW?? LAPLACE COULD NOT UNDERSTAND ???? 19TH POTENTIAL FLOW SOLVES LAPLACE’S EQN

WHAT’S WRONG WITH POTENTIAL FLOW?? CAUCHY COULD NOT UNDERSTAND ???? 19TH MASTER OF HARMONIC FCNS

WHAT’S WRONG WITH POTENTIAL FLOW?? POISSON COULD NOT UNDERSTAND ??? 19TH NOBODY COULD UNDERSTAND

WILBUR + ORWILLE WRIGHT: FLYER DEC 17 1903

KUTTA-ZHUKOVSKY 1904 SEPARATION AT TRAILING EDGE BY ADDING CIRCULATION LIFT BUT NO DRAG

FATHERS OF MODERN AERODYNAMICS

CIRCULATION: LIFT BUT NO DRAG

FATHER OF MODERN FLUID MECHANICS

LUDWIG PRANDTL 1904 SLIP BOUNDARY CONDITION IS WRONG NO-SLIP IS RIGHT: THIN BOUNDARY LAYER DRAG BUT NO LIFT

TURBULENT WAKE: DRAG BUT NO LIFT

INCORRECT + INCORRECT = CORRECT? (-1) x (-1) = 1 NO!! PRANDTL INCORRECT KUTTA-ZHUKOVSKY INCORRECT WHAT IS THEN CORRECT?

RESOLUTION OF D’ALEMBERT’S PARADOX JOHAN HOFFMAN AND CLAES JOHNSON J MATHEMATICAL FLUID MECHANICS 2008 FINALLY AFTER 256 YEARS SPIN-OFF: SECRET OF FLIGHT 2012

POTENTIAL FLOW: STABLE ATTACHMENT UNSTABLE SEPARATION: OPPOSING FLOW

POTENTIAL FLOW SEPARATION INSTABILITY

TROUBLE: TRAILING EDGE POTENTIAL FLOW SEPARATION: UNPHYSICAL UNSTABLE: OPPOSING FLOW POTENTIAL FLOW ATTACHMENT: PHYSICAL STABLE NON-POTENTIAL FLOW SEPARATION?? 3D ROTATIONAL SEPARATION: PHYSICAL STABLE: AVOIDS OPPOSING FLOW

CIRC CYLINDER: POTENTIAL FLOW: P = 0 P = 1 P = - 3 V = 1 V = 0 V = 2 ZERO LIFT DRAG

CIRCULAR CYLINDER: 3D ROTATIONAL SEPARATION: LOW MEAN PRESSURE

3D ROTATIONAL SEPARATION

KUTTA-ZHUKOVSKY CIRCULATION THEORY VS NEW THEORY

STREAMWISE VORTICITY

3D SEPARATION AT TRAILING EDGE 3D ROTATIONAL SEPARATION: WITHOUT PRESSURE RISE WITHOUT PRESSURE DROP: WAKE ELEGANT SEPARATION PRESSURE RISE: 2D IRROTATIONAL POTEN. FLOW SEPARATION PRESSURE DROP: WAKE SEPARATION

THE SECRET POTENTIAL FLOW: BEFORE SEPARATION NON-POTENTIAL AT SEPARATION: 3D ROTATIONAL SLIP SEPARATION WITH POINT STAGNATION 256 YEARS: 1752 - 2008 TO UNDERSTAND

FROM CYLINDER TO AIRFOIL: ROUNDED LEADING + TRAILING EDGE UNDERST CYL = UNDERSTAND AIRFOIL

THE SECRET: L/D = 10

THE SECRET INCOMPRESSIBLE SLIGHTLY VISCOUS FLOW POTENTIAL FLOW BEFORE SEPARATION 3D TRAILING EDGE SEPARATION WITHOUT PRESSURE RISE/DROP

SECRET OF FLIGHT HOW TO SEPARATE IN AN ELEGANT WAY: WITHOUT PRESSURE RISE/DROP ENGAGEMENT: EASY DIVORCE: DIFFICULT THE TRICK: ELEGANT DIVORCE

NEW THEORY: NEW WING DESIGN HUMPBACK WHALE LEADING EDGE

NEW THEORY: NEW DESIGN ROUNDED TRAILING EDGE WIND TURBIN BLADE

THE SECRET OF FLIGHT WEB SITE FULL STORY MATHEMATICS PHYSICS COMPUTATION APPLICATIONS: SAILING, SWIMMING,…. BACKGROUND HISTORY INCORRECT THEORY…