Aerodynamics 101 How do those things really fly? Dr. Paul Kutler Saturday, March 31, 2007 Monterey Airport Dr. Paul Kutler Saturday, March 31, 2007 Monterey Airport

Airbus 380 An aerodynamics challenge

FA-18 Condensation Pattern Aerodynamics involves multiple flow regimes

Legacy Aircraft Aerodynamics is a maturing science

Outline FTerms and Definitions FForces Acting on Airplane FLift FDrag FConcluding remarks FTerms and Definitions FForces Acting on Airplane FLift FDrag FConcluding remarks

Terms and Nomenclature FAirfoil FAngle of attack FAngle of incidence FAspect Ratio FBoundary Layer FCamber FChord FMean camber line FPressure coefficient FLeading edge FRelative wind FReynolds Number FThickness FTrailing edge FWing planform FWingspan FAirfoil FAngle of attack FAngle of incidence FAspect Ratio FBoundary Layer FCamber FChord FMean camber line FPressure coefficient FLeading edge FRelative wind FReynolds Number FThickness FTrailing edge FWing planform FWingspan

Force Diagram

Airfoil Definitions

Definition of Lift, Drag & Moment L = 1/2  V 2 C L S D = 1/2  V 2 C D S M = 1/2  V 2 C M S c

A Misconception FA fluid element that splits at the leading edge and travels over and under the airfoil will meet at the trailing edge. FThe distance traveled over the top is greater than over the bottom. FIt must therefore travel faster over the top to meet at the trailing edge. FAccording to Bernoulli’s equation, the pressure is lower on the top than on the bottom. FHence, lift is produced. FA fluid element that splits at the leading edge and travels over and under the airfoil will meet at the trailing edge. FThe distance traveled over the top is greater than over the bottom. FIt must therefore travel faster over the top to meet at the trailing edge. FAccording to Bernoulli’s equation, the pressure is lower on the top than on the bottom. FHence, lift is produced.

How Lift is Produced Continuity equation Bernoulli’s equation Pressure differential Lift is produced Continuity equation Bernoulli’s equation Pressure differential Lift is produced

The Truth FA fluid element moving over the top surface leaves the trailing edge long before the fluid element moving over the bottom surface reaches the trailing edge. FThe two elements do not meet at the trailing edge. FThis result has been validated both experimentally and computationally. FA fluid element moving over the top surface leaves the trailing edge long before the fluid element moving over the bottom surface reaches the trailing edge. FThe two elements do not meet at the trailing edge. FThis result has been validated both experimentally and computationally.

Airfoil Lift Curve (c l vs. )

Lift Curve - Cambered & Symmetric Airfoils

Slow Flight and Steep Turns L = 1/2  V 2 C L S Outcome versus Action FSlow Flight FLift equals weight FVelocity is decreased FC L must increase F must be increased on the lift curve FVelocity can be reduced until C L max is reached FBeyond that, a stall results FSlow Flight FLift equals weight FVelocity is decreased FC L must increase F must be increased on the lift curve FVelocity can be reduced until C L max is reached FBeyond that, a stall results

Slow Flight and Steep Turns L = 1/2  V 2 C L S Outcome versus Action (Concluded) FSteep Turns (“Bank, yank and crank”) FLift vector is rotated inward (“bank”) by the bank angle reducing the vertical component of lift FLift equals weight divided by cosine  FEither V (“crank”), C L or both must be increased to replenish lift FTo increase C L, increase  (“yank”) on the lift curve FTo increase V, give it some gas FMore effective since lift is proportional to the velocity squared FSteep Turns (“Bank, yank and crank”) FLift vector is rotated inward (“bank”) by the bank angle reducing the vertical component of lift FLift equals weight divided by cosine  FEither V (“crank”), C L or both must be increased to replenish lift FTo increase C L, increase  (“yank”) on the lift curve FTo increase V, give it some gas FMore effective since lift is proportional to the velocity squared

Stalling Airfoil

Effect of Bank Angle on Stall Speed FL = 1/2  V 2 C L S F equals the bank angle FAt stall C L equals C Lmax FL = W / cos  FThus FV stall = [2 W / ( C L max S cos )] 1/2 FAirplane thus stalls at a higher speed FLoad factor increases in a bank FThus as load factor increases, V stall increases FThis is what’s taught in the “Pilot’s Handbook” FL = 1/2  V 2 C L S F equals the bank angle FAt stall C L equals C Lmax FL = W / cos  FThus FV stall = [2 W / ( C L max S cos )] 1/2 FAirplane thus stalls at a higher speed FLoad factor increases in a bank FThus as load factor increases, V stall increases FThis is what’s taught in the “Pilot’s Handbook”

Effect of CG Location on Stall Speed

Surface Oil Flow - Grumman Yankee  = 4 0, 11 0, & 24 0

Airfoil Pressure Distribution NACA 0012, M ∞ = 0.345,  =

Supercritical Airfoil & Pressure Distribution

Drag of an Airfoil D = D f + D p + D w D = total drag on airfoil D f = skin friction drag D p = pressure drag due to flow separation D w = wave drag (for transonic and supersonic flows) D = D f + D p + D w D = total drag on airfoil D f = skin friction drag D p = pressure drag due to flow separation D w = wave drag (for transonic and supersonic flows)

Skin Friction Drag FThe flow at the surface of the airfoil adheres to the surface (“no-slip condition”) FA “boundary layer” is created-a thin viscous region near the airfoil surface FFriction of the air at the surface creates a shear stress FThe velocity profile in the boundary layer goes from zero at the wall to 99% of the free- stream value F =  (dV/dy) wall F is the dynamic viscosity of air [3.73 (10) -7 sl/f/s] FThe flow at the surface of the airfoil adheres to the surface (“no-slip condition”) FA “boundary layer” is created-a thin viscous region near the airfoil surface FFriction of the air at the surface creates a shear stress FThe velocity profile in the boundary layer goes from zero at the wall to 99% of the free- stream value F =  (dV/dy) wall F is the dynamic viscosity of air [3.73 (10) -7 sl/f/s]

The Boundary Layer FTwo types of viscous flows FLaminar FStreamlines are smooth and regular FFluid element moves smoothly along streamline FProduces less drag FTurbulent FStreamlines break up FFluid element moves in a random, irregular and tortuous fashion FProduces more drag F w laminar <  w turbulent FReynolds Number FRe x =  V ∞ x /  FRatio of inertia to viscous forces FTwo types of viscous flows FLaminar FStreamlines are smooth and regular FFluid element moves smoothly along streamline FProduces less drag FTurbulent FStreamlines break up FFluid element moves in a random, irregular and tortuous fashion FProduces more drag F w laminar <  w turbulent FReynolds Number FRe x =  V ∞ x /  FRatio of inertia to viscous forces

Boundary Layer Thickness (Flat Plate) FLaminar Flow F = 5 x / R ex 1/2 FTurbulent Flow F = 0.16 x / R ex 1/7 FTurbulent Flow-Tripped B.L. F = 0.37 x / R ex 1/5 FExample: Chord = 5 f, V ∞ = 150 MPH, Sea Level FR ex = 6,962,025 F = inchesLaminar B.L. F = inchesTurbulent B.L. F = inchesTripped Turbulent B.L. FLaminar Flow F = 5 x / R ex 1/2 FTurbulent Flow F = 0.16 x / R ex 1/7 FTurbulent Flow-Tripped B.L. F = 0.37 x / R ex 1/5 FExample: Chord = 5 f, V ∞ = 150 MPH, Sea Level FR ex = 6,962,025 F = inchesLaminar B.L. F = inchesTurbulent B.L. F = inchesTripped Turbulent B.L.

Infinite vs. Finite Wings AR = b 2 / S

Finite Wings

The Origin of Downwash

The Origin of Induced Drag D i = L sin  i

Elliptical Lift Distribution C D,I = C L 2 / (  e AR)

Change in Lift Curve Slope for Finite Wings

Ground Effect FOccurs during landing and takeoff FGives a feeling of “floating” or “riding on a cushion of air” between wing and ground FIn fact, there is no cushion of air FIts effect is to increase the lift of the wing and reduce the induced drag FThe ground diminishes the strength of the wing tip vortices and reduces the amount of downwash FThe effective angle of attack is increased and lift increases FOccurs during landing and takeoff FGives a feeling of “floating” or “riding on a cushion of air” between wing and ground FIn fact, there is no cushion of air FIts effect is to increase the lift of the wing and reduce the induced drag FThe ground diminishes the strength of the wing tip vortices and reduces the amount of downwash FThe effective angle of attack is increased and lift increases

Ground Effect (Concluded) FMathematically Speaking FL = 1/2  ∞ V ∞ 2 S C L FAn increased angle of attack, increases C L FHence L is increased FD = 1/2  ∞ V ∞ 2 S [C D,0 +  C L 2 /( e AR)] FC D,0 is the zero lift drag (parasite) F C L 2 /( e AR) is the induced drag Fe is the span efficiency factor F = (16 h / b) 2 / [1 + (16 h / b) 2 ] Fb is the wingspan Fh is the height of the wing above the ground FMathematically Speaking FL = 1/2  ∞ V ∞ 2 S C L FAn increased angle of attack, increases C L FHence L is increased FD = 1/2  ∞ V ∞ 2 S [C D,0 +  C L 2 /( e AR)] FC D,0 is the zero lift drag (parasite) F C L 2 /( e AR) is the induced drag Fe is the span efficiency factor F = (16 h / b) 2 / [1 + (16 h / b) 2 ] Fb is the wingspan Fh is the height of the wing above the ground

Wing Dihedral () FWings are bent upward through an angle , called the dihedral angle FDihedral provides lateral stability, i.e., an airplane in a bank will return to its equilibrium position FThis is a result of the lift on the higher wing being less than the lift on the lower wing providing a restoring rolling moment FWings are bent upward through an angle , called the dihedral angle FDihedral provides lateral stability, i.e., an airplane in a bank will return to its equilibrium position FThis is a result of the lift on the higher wing being less than the lift on the lower wing providing a restoring rolling moment

Drag of a Finite Wing D = D f + D p + D w + D i D = total drag on wing D f = skin friction drag D p = pressure drag due to flow separation D w = wave drag (for transonic and supersonic flows) D i = Induced drag (drag due to lift) D = D f + D p + D w + D i D = total drag on wing D f = skin friction drag D p = pressure drag due to flow separation D w = wave drag (for transonic and supersonic flows) D i = Induced drag (drag due to lift)

Drag of a Wing (Continued) FInduced drag - drag due to lift FParasite drag - drag due to non-lifting surfaces FProfile drag FSkin friction FPressure drag (“Form drag”) FInterference drag (e.g., wing- fuselage, wing-pylon) FInduced drag - drag due to lift FParasite drag - drag due to non-lifting surfaces FProfile drag FSkin friction FPressure drag (“Form drag”) FInterference drag (e.g., wing- fuselage, wing-pylon)

Flaps A Mechanism for High Lift

Effect of Flaps on Lift Curve

High Lift Devices 1.No flap 2.Plain flap 3.Split flap 4.L. E. slat 5.Single slotted flap 6.Double-slotted flap 7.Double-slotted flap with slat 8.Double-slotted flap with slat and boundary layer suction 9.Not shown - Fowler flap 1.No flap 2.Plain flap 3.Split flap 4.L. E. slat 5.Single slotted flap 6.Double-slotted flap 7.Double-slotted flap with slat 8.Double-slotted flap with slat and boundary layer suction 9.Not shown - Fowler flap

Shape Comparison Modern vs. Conventional Airfoils

Maximum Lift Coefficient Comparison Modern vs. Conventional Airfoils

What’s Next on the Agenda FBoeing 787 Dreamliner Boeing 787

What’s Next on the Agenda FBoeing Blended Wing-Body Configuration Boeing 797

Concluding Remarks FWhat was not discussed FTransonic flow FDrag-divergence Mach number FSupersonic flow FWave drag FSwept wings FCompressibility effects FBoundary layer theory FThe history of aerodynamics FWhat was not discussed FTransonic flow FDrag-divergence Mach number FSupersonic flow FWave drag FSwept wings FCompressibility effects FBoundary layer theory FThe history of aerodynamics

Airbus 380 Interior Good aerodynamics results in improved creature comforts

Questions and Answers

Backup Slides

Winglets FReduced induced drag FEquivalent to extending wingspan 1/2 of winglet height FLess wing bending moment and less wing weight than extending wing FHinders spanwise flow and pressure drop at the wing tip FLooks modern/esthetically pleasing FReduced induced drag FEquivalent to extending wingspan 1/2 of winglet height FLess wing bending moment and less wing weight than extending wing FHinders spanwise flow and pressure drop at the wing tip FLooks modern/esthetically pleasing Boeing 737 Winglet

Vortex Generators

Swept-Wing Principle

Wave Drag

HondaJet

HondaJet Engine Position FThe “Sweet Spot” FLocation where the engine coexists with the wing and enjoys favorable interference effects FThe reason - “Transonic Area Rule” FRichard Whitcomb - NASA Scientist FThe total cross-sectional area must vary smoothly from the nose to tail to minimize the wave drag FWave drag is created by shock waves that appear over the aircraft as a result of local regions of embedded supersonic flow FThe “Sweet Spot” FLocation where the engine coexists with the wing and enjoys favorable interference effects FThe reason - “Transonic Area Rule” FRichard Whitcomb - NASA Scientist FThe total cross-sectional area must vary smoothly from the nose to tail to minimize the wave drag FWave drag is created by shock waves that appear over the aircraft as a result of local regions of embedded supersonic flow

HondaJet Aerodynamics FEngine inlet is positioned at 75% chord FAs the cross-sectional area decreases at the trailing edge of the wing, the engine adds area thus yielding a smooth area variation FThis engine position also slows the flow and decreases the wing-shock strength FThe critical Mach number is thus increased from.70 to.73 FThe pylon is positioned near the outer portion of the nacelle and cambered inward to follow the flow direction FDuring stall, separation starts outboard of the pylon; separation does not occur between the pylon and fuselage FEngine inlet is positioned at 75% chord FAs the cross-sectional area decreases at the trailing edge of the wing, the engine adds area thus yielding a smooth area variation FThis engine position also slows the flow and decreases the wing-shock strength FThe critical Mach number is thus increased from.70 to.73 FThe pylon is positioned near the outer portion of the nacelle and cambered inward to follow the flow direction FDuring stall, separation starts outboard of the pylon; separation does not occur between the pylon and fuselage

HondaJet Aerodynamics (Continued) FNatural laminar flow fuselage nose FFollowing the area rule, the nose expands from its tip and then contracts as the windshield emerges. FAs the wing is approached, the fuselage cross-sectional area increases smoothly; this helps maintain the laminar flow FNatural laminar flow fuselage nose FFollowing the area rule, the nose expands from its tip and then contracts as the windshield emerges. FAs the wing is approached, the fuselage cross-sectional area increases smoothly; this helps maintain the laminar flow

HondaJet Aerodynamics (Concluded) FNatural laminar flow wing FUtilizes integral, machined panels that minimizes the number of parts for smoother flow when mated together FEmploys winglets to reduce induced drag F30% more efficient than other business jets FNatural laminar flow wing FUtilizes integral, machined panels that minimizes the number of parts for smoother flow when mated together FEmploys winglets to reduce induced drag F30% more efficient than other business jets

Eagle in Flight Winglets Elastic Flaps Minimized Noise & Detectability Variable Camber Retractable Landing Gear STOL/VTOL Capabilities Smart Structures Tilting Control Center Smooth Fairings Variable Twist Adaptive Dihedral Turbulator Tail ? b/2 c c d,i = c l 2 / π AR c l = 2 L/  V 2 S