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: OLD4. 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• THEORY OF FLIGHT• 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 1978FIRST 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_PUPPER 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 ATTACHMENTUNSTABLE 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:

1. NAVIER-STOKES + BC: GENERAL2. LAPLACE + BC: SPECIAL

• MATHEMATICAL THEORY: SOLVE EQUATION

LAPLACE EQN: POTENTIAL FLOW1. INCOMPRESSIBLE: CORRECT FOR SUBSONIC FLIGHT2. INVISCID - SMALL VISCOSITY: CORRECT3. SLIP BOUNDARY CONDITION: SMALL SKIN FRICTION: CORRECT

4. IRROTATIONAL?? NO VORTICES5. STATIONARY?? 6. 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 COULDUNDERSTAND

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 DESIGNHUMPBACK WHALE LEADING EDGE

NEW THEORY: NEW DESIGNROUNDED TRAILING EDGE WIND TURBIN BLADE

THE SECRET OF FLIGHT WEB SITE

• FULL STORY• MATHEMATICS• PHYSICS• COMPUTATION• APPLICATIONS: SAILING, SWIMMING,….• BACKGROUND• HISTORY INCORRECT THEORY…