NOTE…

AEE214-
INTRODUCTION TO AIRCRAFT PERFORMANCE
WEEK 6

Dr. Serhat YILMAZ

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OVERVIEW OF AIRFOILS
HOW DOES AN AIRFOIL GENERATE LIFT?
• HOW DOES AN AIRFOIL GENERATE LIFT?
• Lift due to imbalance of pressure distribution over top and bottom
surfaces of airfoil (or wing)
• If pressure on top is lower than pressure on bottom surface, lift is generated
• Why is pressure lower on top surface?
• We can understand answer from basic physics:
• Continuity (Mass Conservation)
• Newton’s 2nd law (Euler or Bernoulli Equation)

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 HOW DOES AN AIRFOIL GENERATE HOW DOES AN AIRFOIL GENERATE
LIFT? LIFT?
1. Flow velocity over top of airfoil is faster than over bottom surface 2. As V ј pљ
• Streamtube A senses upper portion of airfoil as an obstruction • Incompressible: Bernoulli’s Equation
• Streamtube A is squashed to smaller cross-sectional area • Compressible: Euler’s Equation
• Mass continuity UAV=constant: IF Aљ THEN Vј • Called Bernoulli Effect
3. With lower pressure over upper surface and higher pressure over bottom
surface, airfoil feels a net force in upward direction ї LiŌ
Streamtube A is squashed
most in nose region Most of lift is produced
(ahead of maximum thickness) in first 20-30% of wing
(just downstream of leading edge)

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AIRFOIL THICKNESS:
AIRFOILS VERSUS WINGS
WWI AIRPLANES
English Sopwith Camel

Thin wing, lower maximum CL

Bracing wires required – high drag

German Fokker Dr-1

Higher maximum CL
Internal wing structure
Higher rates of climb
Improved maneuverability
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 AIRFOIL NOMENCLATURE NACA FOUR-DIGIT SERIES
• First digit specifies maximum camber in percentage of chord
• Second digit indicates position of maximum camber in tenths of
chord
• Last two digits provide maximum thickness of airfoil in percentage of
chord

• Mean Chamber Line: Set of points halfway between upper and lower surfaces Example: NACA 2415
• Measured perpendicular to mean chamber line itself
• Leading Edge: Most forward point of mean chamber line • Airfoil has maximum thickness of 15%
• Trailing Edge: Most reward point of mean chamber line of chord (0.15c)
• Chord Line: Straight line connecting the leading and trailing edges • Camber of 2% (0.02c) located 40%
• Chord, c: Distance along the chord line from leading to trailing edge back from airfoil leading edge (0.4c)
• Chamber: Maximum distance between mean chamber line and chord line
• Measured perpendicular to chord line 9 10

WHAT CREATES AERODYNAMIC RESOLVING THE AERODYNAMIC

FORCES? FORCE
• Relative Wind: Direction of Vь
• Aerodynamic forces exerted by airflow • We use subscript ь to indicate far upstream conditions
comes from only two sources: • Angle of Attack, D Angle between relative wind (Vь) and chord line
1. Pressure, p, distribution on surface • Total aerodynamic force, R, can be resolved into two force components
• Acts normal to surface • Lift, L: Component of aerodynamic force perpendicular to relative wind
• Drag, D: Component of aerodynamic force parallel to relative wind
2. Shear stress, Ww, (friction) on surface
• Acts tangentially to surface
• Pressure and shear are in units of force
per unit area (N/m2)
• Net unbalance creates an aerodynamic
force

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 MORE DEFINITIONS VARIATION OF L, D, AND M WITH a
• Total aerodynamic force on airfoil is summation of F1 and F2 • Lift, Drag, and Moments on a airfoil or wing will change as
• Lift is obtained when F2 > F1 D changes
• Misalignment of F1 and F2 creates Moments, M, which tend to rotate
airfoil/wing
• A moment (torque) is a force times a distance • Variations of these quantities are some of most important
• Value of induced moment depends on point about which moments are information that an airplane designer needs to know
taken
• Moments about leading edge, MLE, or quarter-chord point, c/4, Mc/4
• In general MLE т Mc/4
• Aerodynamic Center
• Point about which moments essentially do not vary with D
• Mac=constant (independent of D)
• For low speed airfoils aerodynamic center is near quarter-chord
point, c/4
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SAMPLE DATA: SAMPLE DATA:

SYMMETRIC AIRFOIL CAMBERED AIRFOIL

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 SAMPLE DATA:
SAMPLE DATA
STALL BEHAVIOR

• Lift coefficient (or lift) linear variation with angle of

Lift (for now)

What is really going on here?
attack, a
• Cambered airfoils have positive lift when D=0

Lift (for now)

What is stall?
• Symmetric airfoils have zero lift when D 
Can we predict it?
• At high enough angle of attack, the performance of
the airfoil rapidly degrades ї stall
Can we design for it?

Cambered airfoil has

lift at D=0
At negative D airfoil
will have zero lift 21 22

REAL EFFECTS:
WHY DOES LIFT CURVE BEND OVER?
VISCOSITY (P)
• To understand drag and actual airfoil/wing behavior we need an
understanding of viscous flows (all real flows have friction)

• Inviscid (frictionless) flow around a body will result in zero drag!

• This is called d’Alembert’s paradox
• Must include friction (viscosity, P) in theory

• Flow adheres to surface because of friction between gas and solid

boundary
• At surface flow velocity is zero, called ‘No-Slip Condition’
• Thin region of retarded flow in vicinity of surface, called a ‘Boundary Layer’
• At outer edge of B.L., Vь
• At solid boundary, V=0

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 TYPES OF FLOWS:
COMMENTS ON VISCOUS FLOWS
FRICTION VS. NO-FRICTION

Flow very close to surface of airfoil is

Influenced by friction and is viscous
(boundary layer flow)
Stall (separation) is a viscous phenomena

Flow away from airfoil is not influenced

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by friction and is wholly inviscid 26

THE REYNOLDS NUMBER, Re LAMINAR VS. TURBULENT FLOW

• One of most important dimensionless numbers in fluid mechanics/
aerodynamics • Two types of viscous flows
• Reynolds number is ratio of two forces:
• Inertial Forces
• Viscous Forces • Laminar: streamlines are smooth and
• c is length scale (chord) regular and a fluid element moves
smoothly along a streamline
• Reynolds number tells you when viscous forces are important and when
viscosity may be neglected
Outside B.L. flow Within B.L. flow • Turbulent: streamlines break up and fluid
Inviscid (high Re) highly viscous elements move in a random, irregular, and
(low Re) chaotic fashion

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LAMINAR VS. TURBULENT FLOW FLOW SEPARATION
• Key to understanding: Friction causes flow separation within boundary layer
• Separation then creates another form of drag called pressure drag due to separation
All B.L.’s transition from
laminar to turbulent

Turbulent velocity cf,turb > cf,lam

profiles are ‘fuller’

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REVIEW: SUMMARY OF VISCOUS EFFECTS ON

AIRFOIL STALL DRAG
• Key to understanding: Friction causes flow separation within
boundary layer • Friction has two effects:
1. B.L. either laminar or turbulent 1. Skin friction due to shear stress at wall
2. All laminar B.L. ї turbulent B.L.
3. Turbulent B.L. ‘fuller’ than laminar B.L., more resistant to 2. Pressure drag due to flow separation
separation
• Separation creates another form of drag called pressure drag
due to separation
• Dramatic loss of lift and increase in drag

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COMPARISON OF DRAG FORCES EIFFEL TOWER MODEL

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TRUCK SPOILER EXAMPLE RELATIVE LOCATION OF CARS

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 LIFT, DRAG, AND MOMENT
CAR – TRUCK EXAMPLE
COEFFICIENTS
• Behavior of L, D, and M depend on D, but also on velocity and
altitude
• Vь, U ь, Wing Area (S), Wing Shape, P ь, compressibility
• Characterize behavior of L, D, M with coefficients (c l, cd, cm)

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LIFT, DRAG, AND MOMENT SAMPLE DATA:

COEFFICIENTS NACA 23012 AIRFOIL
• Behavior of L, D, and M depend on D, but also on velocity and altitude
• Vь, U ь, Wing Area (S), Wing Shape, P ь, compressibility
• Characterize behavior of L, D, M with coefficients (cl, cd, cm)

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AIRFOIL DATA EXAMPLE:
NACA 23012 WING SECTION SLATS AND FLAPS

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AIRFOIL DATA
NACA 1408 WING SECTION

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