Introduction to new theory of flight revealing the secret of flight
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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

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INTRODUCTION TO NEW THEORY OF FLIGHT REVEALING THE SECRET OF FLIGHT

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INTRODUCTION TONEW THEORY OF FLIGHTREVEALINGTHE 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 - 70AIRBUS 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


WHYCORRECT 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_PUPPERLOWER 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 EDGEUNDERST 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 UPPERLOWER


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 ATTACHMENTUNSTABLE 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 EDGEUNDERST 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…


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