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Aerodynamics 101 How do those things really fly?. 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.

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Aerodynamics 101 how do those things really fly

Aerodynamics 101How do those things really fly?

Dr. Paul Kutler

Saturday, March 31, 2007

Monterey Airport

Airbus 380
Airbus 380

An aerodynamics challenge

Fa 18 condensation pattern
FA-18 Condensation Pattern

Aerodynamics involves multiple flow regimes

Legacy aircraft
Legacy Aircraft

Aerodynamics is a maturing science


  • Terms and Definitions

  • Forces Acting on Airplane

  • Lift

  • Drag

  • Concluding remarks

Terms and nomenclature
Terms and Nomenclature

  • Airfoil

  • Angle of attack

  • Angle of incidence

  • Aspect Ratio

  • Boundary Layer

  • Camber

  • Chord

  • Mean camber line

  • Pressure coefficient

  • Leading edge

  • Relative wind

  • Reynolds Number

  • Thickness

  • Trailing edge

  • Wing planform

  • Wingspan

Definition of lift drag moment
Definition of Lift, Drag & Moment

L = 1/2  V2 CL S

D = 1/2  V2 CD S

M = 1/2  V2 CM S c

A misconception
A Misconception

  • A fluid element that splits at the leading edge and travels over and under the airfoil will meet at the trailing edge.

    • The distance traveled over the top is greater than over the bottom.

    • It must therefore travel faster over the top to meet at the trailing edge.

    • According to Bernoulli’s equation, the pressure is lower on the top than on the bottom.

  • Hence, lift is produced.

How lift is produced
How Lift is Produced

  • Continuity equation

  • Bernoulli’s equation

  • Pressure differential

  • Lift is produced

The truth
The Truth

  • A 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.

  • The two elements do not meet at the trailing edge.

  • This result has been validated both experimentally and computationally.

Slow flight and steep turns l 1 2 v 2 c l s outcome versus action
Slow Flight and Steep Turns L = 1/2  V2 CL SOutcome versus Action

  • Slow Flight

    • Lift equals weight

    • Velocity is decreased

    • CL must increase

    •  must be increased on the lift curve

    • Velocity can be reduced until CLmax is reached

    • Beyond that, a stall results

Slow flight and steep turns l 1 2 v 2 c l s outcome versus action concluded
Slow Flight and Steep TurnsL = 1/2  V2 CL SOutcome versus Action(Concluded)

  • Steep Turns (“Bank, yank and crank”)

    • Lift vector is rotated inward (“bank”) by the bank angle reducing the vertical component of lift

    • Lift equals weight divided by cosine 

    • Either V (“crank”), CL or both must be increased to replenish lift

    • To increase CL, increase  (“yank”) on the lift curve

    • To increase V, give it some gas

      • More effective since lift is proportional to the velocity squared

Effect of bank angle on stall speed
Effect of Bank Angle on Stall Speed

  • L = 1/2  V2 CL S

  •  equals the bank angle

  • At stall CL equals CLmax

  • L = W / cos 

  • Thus

    • Vstall = [2 W / ( CL max S cos )] 1/2

  • Airplane thus stalls at a higher speed

  • Load factor increases in a bank

    • Thus as load factor increases, Vstall increases

    • This is what’s taught in the “Pilot’s Handbook”

Airfoil pressure distribution
Airfoil Pressure Distribution

NACA 0012, M ∞ = 0.345,  = 3.930

Drag of an airfoil
Drag of an Airfoil

D = Df+ Dp + Dw

D = total drag on airfoil

Df = skin friction drag

Dp = pressure drag due to

flow separation

Dw = wave drag (for transonic

and supersonic flows)

Skin friction drag
Skin Friction Drag

  • The flow at the surface of the airfoil adheres to the surface (“no-slip condition”)

  • A “boundary layer” is created-a thin viscous region near the airfoil surface

  • Friction of the air at the surface creates a shear stress

  • The velocity profile in the boundary layer goes from zero at the wall to 99% of the free-stream value

  •  =  (dV/dy)wall

  •  is the dynamic viscosity of air [3.73 (10) -7 sl/f/s]

The boundary layer
The Boundary Layer

  • Two types of viscous flows

    • Laminar

      • Streamlines are smooth and regular

      • Fluid element moves smoothly along streamline

      • Produces less drag

    • Turbulent

      • Streamlines break up

      • Fluid element moves in a random, irregular and tortuous fashion

      • Produces more drag

    • w laminar < w turbulent

  • Reynolds Number

    • Rex =  V∞ x / 

    • Ratio of inertia to viscous forces

Boundary layer thickness flat plate
Boundary Layer Thickness(Flat Plate)

  • Laminar Flow

    •  = 5 x / Rex1/2

  • Turbulent Flow

    •  = 0.16 x / Rex1/7

  • Turbulent Flow-Tripped B.L.

    •  = 0.37 x / Rex1/5

  • Example: Chord = 5 f, V∞ = 150 MPH, Sea Level

    • Rex = 6,962,025

    •  = 0.114 inches Laminar B.L.

    •  = 1.011 inches Turbulent B.L.

    •  = 7.049 inches Tripped Turbulent B.L.

Elliptical lift distribution
Elliptical Lift Distribution

CD,I = CL2/ (e AR)

Ground effect
Ground Effect

  • Occurs during landing and takeoff

  • Gives a feeling of “floating” or “riding on a cushion of air” between wing and ground

  • In fact, there is no cushion of air

  • Its effect is to increase the lift of the wing and reduce the induced drag

  • The ground diminishes the strength of the wing tip vortices and reduces the amount of downwash

  • The effective angle of attack is increased and lift increases

Ground effect concluded
Ground Effect(Concluded)

  • Mathematically Speaking

    • L = 1/2  ∞V∞2S CL

      • An increased angle of attack, increases CL

      • Hence L is increased

    • D = 1/2 ∞ V∞2 S [CD,0 +  CL2/( e AR)]

      • CD,0is the zero lift drag (parasite)

      •  CL2/( e AR) is the induced drag

      • e is the span efficiency factor

      •  = (16 h / b)2 / [1 + (16 h / b)2 ]

      • b is the wingspan

      • h is the height of the wing above the ground

Wing dihedral
Wing Dihedral ()

  • Wings are bent upward through an angle , called the dihedral angle

  • Dihedral provides lateral stability, i.e., an airplane in a bank will return to its equilibrium position

  • This 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
Drag of a Finite Wing

D = Df+ Dp + Dw + Di

D = total drag on wing

Df = skin friction drag

Dp = pressure drag due to

flow separation

Dw = wave drag (for transonic

and supersonic flows)

Di = Induced drag (drag due to


Drag of a wing continued
Drag of a Wing(Continued)

  • Induced drag - drag due to lift

  • Parasite drag - drag due to non-lifting surfaces

    • Profile drag

      • Skin friction

      • Pressure drag (“Form drag”)

    • Interference drag (e.g., wing-fuselage, wing-pylon)

Flaps a mechanism for high lift
FlapsA Mechanism for High Lift

High lift devices
High Lift Devices

  • No flap

  • Plain flap

  • Split flap

  • L. E. slat

  • Single slotted flap

  • Double-slotted flap

  • Double-slotted flap with slat

  • Double-slotted flap with slat and boundary layer suction

  • Not shown - Fowler flap

Shape comparison modern vs conventional airfoils
Shape ComparisonModern vs. Conventional Airfoils

Maximum lift coefficient comparison modern vs conventional airfoils
Maximum Lift Coefficient ComparisonModern vs. Conventional Airfoils

What s next on the agenda
What’s Next on the Agenda

  • Boeing 787 Dreamliner

Boeing 787

What s next on the agenda1
What’s Next on the Agenda

  • Boeing Blended Wing-Body Configuration

Boeing 797

Concluding remarks
Concluding Remarks

  • What was not discussed

    • Transonic flow

    • Drag-divergence Mach number

    • Supersonic flow

    • Wave drag

    • Swept wings

    • Compressibility effects

    • Boundary layer theory

    • The history of aerodynamics

Airbus 380 interior
Airbus 380 Interior

Good aerodynamics results in improved creature comforts


  • Reduced induced drag

  • Equivalent to extending wingspan 1/2 of winglet height

  • Less wing bending moment and less wing weight than extending wing

  • Hinders spanwise flow and pressure drop at the wing tip

  • Looks modern/esthetically pleasing

Boeing 737 Winglet

Hondajet engine position
HondaJetEngine Position

  • The “Sweet Spot”

    • Location where the engine coexists with the wing and enjoys favorable interference effects

  • The reason - “Transonic Area Rule”

    • Richard Whitcomb - NASA Scientist

    • The total cross-sectional area must vary smoothly from the nose to tail to minimize the wave drag

    • Wave drag is created by shock waves that appear over the aircraft as a result of local regions of embedded supersonic flow

Hondajet aerodynamics

  • Engine inlet is positioned at 75% chord

  • As the cross-sectional area decreases at the trailing edge of the wing, the engine adds area thus yielding a smooth area variation

  • This engine position also slows the flow and decreases the wing-shock strength

  • The critical Mach number is thus increased from .70 to .73

  • The pylon is positioned near the outer portion of the nacelle and cambered inward to follow the flow direction

  • During stall, separation starts outboard of the pylon; separation does not occur between the pylon and fuselage

Hondajet aerodynamics continued

  • Natural laminar flow fuselage nose

    • Following the area rule, the nose expands from its tip and then contracts as the windshield emerges.

    • As the wing is approached, the fuselage cross-sectional area increases smoothly; this helps maintain the laminar flow

Hondajet aerodynamics concluded

  • Natural laminar flow wing

  • Utilizes integral, machined panels that minimizes the number of parts for smoother flow when mated together

  • Employs winglets to reduce induced drag

  • 30% more efficient than other business jets

Eagle in flight
Eagle in Flight

cl = 2 L/

 V2 S







Smart Structures





Tail ?



Elastic Flaps

Tilting Control Center

cd,i = cl2 /

π AR

Minimized Noise

& Detectability



Retractable Landing Gear