REVEALING THE SECRET OF FLIGHT UNDERSTANDING WHY IT IS POSSIBLE TO FLY JOHAN HOFFMAN JOHAN JANSSON CLAES JOHNSON WEB SITE THE SECRET OF FLIGHT httpsecretofflightwordpresscom MATHEMATICS ID: 1048163
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1. INTRODUCTION TO NEW THEORY OF FLIGHTREVEALINGTHE SECRET OF FLIGHTUNDERSTANDING WHY IT IS POSSIBLE TO FLYJOHAN HOFFMAN JOHAN JANSSON CLAES JOHNSON
2. WEB SITE: THE SECRET OF FLIGHThttp://secretofflight.wordpress.com/MATHEMATICSFLUID MECHANICSCOMPUTATIONMEASUREMENTAPPLICATIONSHISTORY
3. NEW THEORY SUBMITTED TO AIAAMAIN JOURNAL OF AERONAUTICSNOW UNDER SCRUTINY OF EXPERTSFOLLOW THE REVIEW PROCESS ON WEB SITEFIRST VERSION PRESENTED IN NORMAT 2009
4. OLD THEORYKUTTA-ZHUKOVSKY 1904FATHERS OF MODERN AERONAUTICSPRANDTL 1904FATHER OF MODERN FLUID MECHANICSKZP THEORY
5. SCIENTIFIC MATHEMATICAL THEORIESFOR UNEDUCATED: 1. TRIVIAL AND CORRECT 2. TRIVIAL AND INCORRECTFOR EDUCATED: 3. NON-TRIVIAL AND INCORRECT: OLD4. NON-TRIVIAL AND CORRECT: NEW
6. NEW THEORYPHYSICAL MATHEMATICALCORRECTDOES REVEAL THE SECRETUSEFUL
7. OLD THEORY UNPHYSICAL UNMATHEMATICALINCORRECTDOES NOT REVEAL THE SECRETDANGEROUS
8. WHAT TO EXPLAIN: LIFT / DRAG =L/D = 10 - 70AIRBUS L/D=20 GLIDER L/D=70
9. THE SECRET: L/D = 10 - 70 SURPRISINGINGENIOUS ELEGANTINCOMPRESSIBLE FLOWSLIGHTLY VISCOUS FLOW
10. IS THEORY NEEDED?BIRDS HAVE LEARNED TO FLY WITHOUTTHEORY OF FLIGHTBUT IT TOOK 100 MILLION YEARSFROM DINOSAUR TO ARCHAEOPETRYXHUMANS HAVE LEARNED TO FLY WITHOUTTHEORY OF FLIGHTBUT IT TOOK 500 YEARS FROM DA VINCI TO SUCCESS: GOSSAMER CONDOR 1978BECAUSE OF LACK OF THEORY!!
11. DA VINCI FLYING MACHINE 1500
12. GOSSAMER CONDOR 1978FIRST HUMAN POWERED FLIGHT
13. CONFESSIONS ABOUT OLD THEORY
14. 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?
15. NASA LISTS INCORRECT THEORIESLONGER DISTANCESKIPPING STONEVENTURIBUT NO THEORY CLAIMED TO BE CORRECT!!NASA DOES NOT SEEM TO KNOW WHAT KEEPS PLANES IN THE AIR!!
16. LONGER PATH THEORY INCORRECT
17. SKIPPING STONE THEORY: NEWTON
18. VENTURI THEORY: BERNOULLI
19. HOFFREN 2001 AIAAA SATISFACTORY THEORY OF LIFT IS STILL LACKINGTHERE IS A GENUINE NEED FOR ONE
20. WHAT KEEPS PLANES IN THE AIR?INCORRECT THEORY OK AS LONG AS YOU DON’T USE IT NOT USEFULNEW THEORY: CORRECT: USEFUL
21. WHY CORRECT THEORY ONLY 2009?COMPUTE TURBULENT SOLUTIONS OF NAVIER-STOKES EQUATIONS + SLIP BCDIRECT SIMULATION WITHOUT TURBULENCE MODELINGPOSSIBLE WITH ~ 1 MILLION MESH POINTSCOMPUTATION TELLS THE TRUTH STUDY REVEALS THE SECRET
22. DRAG CAR COMPUTABLE
23. LIFT DRAG WING COMPUTABLE VELOCITY PRESSURE
24. PRESSURE DISTRIBUTION C_PUPPER LOWER SURFACE
25. LIFT DRAG OF WING COMPUTABLE MAX L = 1.5 L/D = 50 AOA = 16
26. TO UNDERSTAND: STABILITYSTABILITY - INSTABILITY OF FLUID MOTIONSTABLE COMPUTABLE ASPECTS OF TURBULENT FLOWLIFT DRAG MOMENTS..: COMPUTABLEALL YOU MAY WANT TO KNOW: COMPUTABLE
27. OPPOSING FLOW INSTABILITY
28. STABLE ATTACHMENTUNSTABLE SEPARATION: OPPOSING FLOW
29. FROM CYLINDER TO AIRFOIL: ROUNDED LEADING + TRAILING EDGEUNDERST CYL = UNDERSTAND AIRFOIL
30. SHORT STORY: THEORIES OF FLIGHTNEWTON 17H MATH: IMPOSSIBLE: WRONGD’ALEMBERT 18TH MATH: IMPOSSIBLE: WRONGWRIGHT BROTHERS 1903 REAL EXP : POSSIBLEKUTTA-ZHUKOVSKY 1904 MATH: POSSIBLE: WRONG: OLD THEORY OF FLIGHTHOFFMAN-JOHNSON 2009 MATH: POSSIBLE: RIGHT: NEW THEORY OF FLIGHT
31. NEW VS OLD THEORY NEW THEORY REVEALS THE SECRET OF FLIGHTOLD THEORY HIDES THE SECRET OF FLIGHT OLD: RULING PARADIGMOLD: NOT FUNCTIONALNEW INCOMPATIBLE WITH OLDSCIENTIFIC REVOLUTION A LA KUHN
32. LIFT AND DRAG OF LONG WINGSUCTION ON UPPER LEADING EDGE/SURFACE:LIFT + NEGATIVE DRAGPUSH ON LOWER LEADING EDGE/SURFACE:LIFT + POSITIVE DRAGFLOW SEPARATES AT TRAILING EDGE WITHOUT PRESSURE RISE/DROP: ELEGANT SEPARATION
33. AIRFOIL – AIRPLANE WING
34. OBSERVATION WIND TUNNEL
35. OBSERVATION: 2D SECTION OF 3D
36. OBSERVATIONLIFT UPPER LEADING EDGE SUCTIONLOWER LEADING EDGE PUSHDRAGLEADING EDGE PUSH/SUCTIONSEPARATION WITHOUT PRESSURE RISE/DROPDOWNWASH
37. RECALL C_P UPPER LOWER
38. NAVIER-STOKES
39. PRESSURE AOA = 5
40. VELOCITY AOA = 10
41. VELOCITY AOA = 10
42. VELOCITY AOA = 15
43. UNDERSTANDING: THEORYMATHEMATICAL MODEL OF PHYSICSASSUMPTIONSMATHEMATICAL MODEL = EQUATION:NAVIER-STOKES + BC: GENERALLAPLACE + BC: SPECIALMATHEMATICAL THEORY: SOLVE EQUATION
44. LAPLACE EQN: POTENTIAL FLOWINCOMPRESSIBLE: CORRECT FOR SUBSONIC FLIGHTINVISCID - SMALL VISCOSITY: CORRECTSLIP BOUNDARY CONDITION: SMALL SKIN FRICTION: CORRECTIRROTATIONAL?? NO VORTICESSTATIONARY?? 2D??V = GRADIENT OF HARMONIC FUNCTION2D FOR CYLINDER LONG WING1 + 2 + 3 VALID!! EVERYWHERE!! NAVIER-STOKES4 + 5 +6 VALID?? SOMEWHERE BUT NOT EVERYWHERE!! LAPLACE??
45. 1- 4 : LAPLACE’S EQN: POTENTIAL: HARMONIC FUNCTION + SLIP
46. LAPLACE VS NAVIER-STOKESLAPLACE SIMPLIFIED VERSION OF NAVIER-STOKESPOTENTIAL SOLUTION:2DSTATIONARYIRROTATIONALLAPLACE SOLUTIONS NOT TURBULENTNAVIER-STOKES SOLUTIONS TURBULENT
47. CIRC CYLINDER: POTENTIAL FLOW:P = 0 P = 1 P = - 3 V = 1 V = 0 V = 2
48. POTENTIAL FLOW: BERNOULLI’S LAW ½ V2 + P = CONSTANTHIGH PRESSURE P – LOW VELOCITY VLOW PRESSURE P – HIGH VELOCITY V
49. CIRC CYLINDER: POTENTIAL FLOW:ZERO LIFT + ZERO DRAG(L/D = 3)
50. LIFT OF HALF CYLINDER
51. THEORY: POTENTIAL FLOW: D’ALEMBERT’S PARADOX 1752: ZERO LIFT AND DRAG
52. POTENTIAL FLOW VS OBSERVATION
53. POTENTIAL FLOWSEPARATION BEFORE TRAILING EDGE HIGH PRESSURE AT SEPARATION REQUIRED TO BRING FLOW TO STAGNATIONNO DOWNWASHMATHEMATICAL SOLUTIONBUT NOT OBSERVED IN REALITYUNPHYSICAL!! WHY??
54. WHAT’S WRONG WITH POTENTIAL FLOW??D’ALEMBERT COULD NOT UNDERSTAND 1752
55. D’ALEMBERT’S PARADOX 1752It 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”.
56. WHAT’S WRONG WITH POTENTIAL FLOW??EULER COULD NOT UNDERSTAND???? 18THPOTENTIAL FLOW SOLVES EULER’S EQNS
57. WHAT’S WRONG WITH POTENTIAL FLOW??LAPLACE COULD NOT UNDERSTAND???? 19THPOTENTIAL FLOW SOLVES LAPLACE’S EQN
58. WHAT’S WRONG WITH POTENTIAL FLOW??CAUCHY COULD NOT UNDERSTAND???? 19THMASTER OF HARMONIC FCNS
59. WHAT’S WRONG WITH POTENTIAL FLOW??POISSON COULD NOT UNDERSTAND??? 19THNOBODY COULDUNDERSTAND
60. WILBUR + ORWILLE WRIGHT: FLYER DEC 17 1903
61. KUTTA-ZHUKOVSKY 1904 SEPARATION AT TRAILING EDGE BY ADDING CIRCULATION LIFT BUT NO DRAG
62. FATHERS OF MODERN AERODYNAMICS
63. CIRCULATION: LIFT BUT NO DRAG
64. FATHER OF MODERN FLUID MECHANICS
65. LUDWIG PRANDTL 1904 SLIP BOUNDARY CONDITION IS WRONG NO-SLIP IS RIGHT:THIN BOUNDARY LAYERDRAG BUT NO LIFT
66. TURBULENT WAKE: DRAG BUT NO LIFT
67. INCORRECT + INCORRECT = CORRECT?(-1) x (-1) = 1NO!!PRANDTL INCORRECTKUTTA-ZHUKOVSKY INCORRECTWHAT IS THEN CORRECT?
68. RESOLUTION OF D’ALEMBERT’S PARADOXJOHAN HOFFMAN AND CLAES JOHNSONJ MATHEMATICAL FLUID MECHANICS 2008FINALLY AFTER 256 YEARSSPIN-OFF: SECRET OF FLIGHT 2012
69. POTENTIAL FLOW: STABLE ATTACHMENTUNSTABLE SEPARATION: OPPOSING FLOW
70. POTENTIAL FLOW SEPARATION INSTABILITY
71. TROUBLE: TRAILING EDGEPOTENTIAL FLOW SEPARATION: UNPHYSICAL UNSTABLE: OPPOSING FLOWPOTENTIAL FLOW ATTACHMENT: PHYSICAL STABLENON-POTENTIAL FLOW SEPARATION??3D ROTATIONAL SEPARATION: PHYSICAL STABLE: AVOIDS OPPOSING FLOW
72. CIRC CYLINDER: POTENTIAL FLOW:P = 0 P = 1 P = - 3 V = 1 V = 0 V = 2 ZERO LIFT DRAG
73. CIRCULAR CYLINDER: 3D ROTATIONAL SEPARATION: LOW MEAN PRESSURE
74. 3D ROTATIONAL SEPARATION
75. KUTTA-ZHUKOVSKY CIRCULATION THEORY VS NEW THEORY
76. STREAMWISE VORTICITY
77. 3D SEPARATION AT TRAILING EDGE3D ROTATIONAL SEPARATION: WITHOUT PRESSURE RISEWITHOUT PRESSURE DROP: WAKEELEGANT SEPARATIONPRESSURE RISE: 2D IRROTATIONAL POTEN. FLOW SEPARATIONPRESSURE DROP: WAKE SEPARATION
78. THE SECRETPOTENTIAL FLOW: BEFORE SEPARATIONNON-POTENTIAL AT SEPARATION:3D ROTATIONAL SLIP SEPARATION WITH POINT STAGNATION256 YEARS: 1752 - 2008 TO UNDERSTAND
79. FROM CYLINDER TO AIRFOIL: ROUNDED LEADING + TRAILING EDGEUNDERST CYL = UNDERSTAND AIRFOIL
80. THE SECRET: L/D = 10
81. THE SECRETINCOMPRESSIBLESLIGHTLY VISCOUS FLOWPOTENTIAL FLOW BEFORE SEPARATION3D TRAILING EDGE SEPARATION WITHOUT PRESSURE RISE/DROP
82. SECRET OF FLIGHTHOW TO SEPARATE IN AN ELEGANT WAY:WITHOUT PRESSURE RISE/DROPENGAGEMENT: EASYDIVORCE: DIFFICULTTHE TRICK: ELEGANT DIVORCE
83. NEW THEORY: NEW WING DESIGNHUMPBACK WHALE LEADING EDGE
84. NEW THEORY: NEW DESIGNROUNDED TRAILING EDGE WIND TURBIN BLADE
85. THE SECRET OF FLIGHT WEB SITEFULL STORYMATHEMATICSPHYSICSCOMPUTATIONAPPLICATIONS: SAILING, SWIMMING,….BACKGROUNDHISTORY INCORRECT THEORY…