MAE 1202: AEROSPACE PRACTICUM

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MAE 1202 AEROSPACE PRACTICUM

• Lecture 7 Airfoils and Finite Wings
• March 23, 2009
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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READING AND HOMEWORK ASSIGNMENTS

• Reading Introduction to Flight, by John D.
  Anderson, Jr.
• Next week, we will finish Chapter 5 in Anderson
• For next weeks lecture Chapter 5, Sections
  5.13-5.19
• Read these sections carefully, most interesting
  portions of Ch. 5
• Lecture-Based Homework Assignment
• Problems 5.7, 5.11, 5.13, 5.15, 5.17, 5.19
• DUE Wednesday, April 1, 2009 by 11 AM
• Turn in hard copy of homework
• Also be sure to review and be familiar with
  textbook examples in Chapter 5

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ANSWERS TO LECTURE HOMEWORK

• 5.7 Cp -3.91
• 5.11 Cp -0.183
• Be careful here, if you check the Mach number it
  is around 0.71, so the flow is compressible and
  the formula for Cp based on Bernoullis equation
  is not valid. To calculate the pressure
  coefficient, first calculate r8 from the equation
  of state and find the temperature from the energy
  equation. Finally make use of the isentropic
  relations and the definition of Cp given in
  Equation 5.27
• 5.13 cl 0.97
• Make use of Prandtl-Glauert rule
• 5.15 Mcr 0.62
• Use graphical technique of Section 5.9
• Verify using Excel or Matlab
• 5.17 m 30
• 5.19 D 366 lb
• Remember that in steady, level flight the
  airplanes lift must balance its weight
• You may also assume that all lift is derived from
  the wings (this is not really true because the
  fuselage and horizontal tail also contribute to
  the airplane lift). Also assume that the wings
  can be approximated by a thin flat plate
• Remember that Equation 5.50 gives a in radians

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MID-TERM EXAM COMMENTS

• Exam is intended to be long, why?
• Exam is out of 100 points
• Only for reference
• You dont need gt 90 to get an A
• Exam will be curved or scaled as appropriate
  (there will be lots of A/B)
• There is no time to learn during exam
• You must read the book probably many times
  over
• Dont cheat in college

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LIFT, DRAG, AND MOMENT COEFFICIENTS (5.3)

• Behavior of L, D, and M depend on a, but also on
  velocity and altitude
• V8, r 8, Wing Area (S), Wing Shape, m 8,
  compressibility
• Characterize behavior of L, D, M with
  coefficients (cl, cd, cm)

Matching Mach and Reynolds (called similarity
parameters)
M8, Re
M8, Re
cl, cd, cm identical
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MID-TERM QUESTION CONCEPT QUIZ

• Consider two different flows over geometrically
  similar airfoils, one airfoil being exactly twice
  the size of the other. The flow over the smaller
  airfoil has freestream properties given by T8200
  K, r81.23 kg/m3, and V8100 m/s. The flow over
  the larger airfoil is described by T8800 K,
  r81.74 kg/m3, and V8200 m/s. Assume that the
  viscosity is proportional to T1/2.
• How would you determine if the two flows
  dynamically similar?
• Answer in Section 5.3 on page 267
• Re and Mach must be identical
• What is definition of Re?
• What is definition of M?

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SAMPLE DATA
cl

• Lift coefficient (or lift) linear variation with
  angle of attack, a
• Cambered airfoils have positive lift when a 0
• Symmetric airfoils have zero lift when a 0
• At high enough angle of attack, the performance
  of the airfoil rapidly degrades ? stall

Cambered airfoil has lift at a0 At negative a
airfoil will have zero lift
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SAMPLE DATA NACA 23012 AIRFOIL
Flow separation Stall
Lift Coefficient cl
Moment Coefficient cm, c/4
a
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AIRFOIL DATA (5.4 AND APPENDIX D)NACA 23012 WING
SECTION
Re dependence at high a Separation and Stall
cd vs. a Dependent on Re
cl
cl vs. a Independent of Re
cd
RRe
cm,a.c. vs. cl very flat
cm,a.c.
cm,c/4
a
cl
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EXAMPLE SLATS AND FLAPS
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EXAMPLE BOEING 727 FLAPS/SLATS
cl 4.5
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AIRFOIL DATA (5.4 AND APPENDIX D)NACA 1408 WING
SECTION
Flap extended
Flap retracted
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HIGH LIFT DEVICES FLAPS

• Flaps shift lift curve
• Act as effective increase in camber of airfoil

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PRESSURE DISTRIBUTION AND LIFT

• Lift comes from pressure distribution over top
  (suction surface) and bottom (pressure surface)
• Lift coefficient also result of pressure
  distribution

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PRESSURE COEFFICIENT, CP (5.6)

• Use non-dimensional description, instead of
  plotting actual values of pressure
• Pressure distribution in aerodynamic literature
  often given as Cp
• So why do we care?
• Distribution of Cp leads to value of cl
• Easy to get pressure data in wind tunnels
• Shows effect of M8 on cl

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EXAMPLE CP CALCULATION
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COMPRESSIBILITY CORRECTIONEFFECT OF M8 ON CP
For M8 lt 0.3, r const Cp Cp,0 0.5 const
M8
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COMPRESSIBILITY CORRECTIONEFFECT OF M8 ON CP
Effect of compressibility (M8 gt 0.3) is to
increase absolute magnitude of Cp as M8
increases Called Prandtl-Glauert Rule
For M8 lt 0.3, r const Cp Cp,0 0.5 const
M8
Prandtl-Glauert rule applies for 0.3 lt M8 lt 0.7
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OBTAINING LIFT COEFFICIENT FROM CP (5.7)
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COMPRESSIBILITY CORRECTION SUMMARY

• If M0 gt 0.3, use a compressibility correction for
  Cp, and cl
• Compressibility corrections gets poor above M0
  0.7
• This is because shock waves may start to form
  over parts of airfoil
• Many proposed correction methods, but a very good
  on is Prandtl-Glauert Rule
• Cp,0 and cl,0 are the low-speed (uncorrected)
  pressure and lift coefficients
• This is lift coefficient from Appendix D in
  Anderson
• Cp and cl are the actual pressure and lift
  coefficients

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CRITICAL MACH NUMBER, MCR (5.9)

• As air expands around top surface near leading
  edge, velocity and M will increase
• Local M gt M8

Flow over airfoil may have sonic regions even
though freestream M8 lt 1 INCREASED DRAG!
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CRITICAL FLOW AND SHOCK WAVES
MCR
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CRITICAL FLOW AND SHOCK WAVES
bubble of supersonic flow
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AIRFOIL THICKNESS SUMMARY
Note thickness is relative to chord in all
cases Ex. NACA 0012 ? 12

• Which creates most lift?
• Thicker airfoil
• Which has higher critical Mach number?
• Thinner airfoil
• Which is better?
• Application dependent!

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AIRFOIL THICKNESS 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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THICKNESS-TO-CHORD RATIO TRENDS
A-10 Root NACA 6716 TIP NACA 6713
F-15 Root NACA 64A(.055)5.9 TIP NACA 64A203
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MODERN AIRFOIL SHAPES
Boeing 737
Root
Mid-Span
Tip
http//www.nasg.com/afdb/list-airfoil-e.phtml
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SUMMARY OF AIRFOIL DRAG (5.12)
Only at transonic and supersonic speeds Dwave0
for subsonic speeds below Mdrag-divergence
Profile Drag Profile Drag coefficient relatively
constant with M8 at subsonic speeds
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FINITE WINGS
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INFINITE VERSUS FINITE WINGS
High AR
Aspect Ratio b wingspan S wing area
Low AR
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AIRFOILS VERSUS WINGS
Low Pressure
Low Pressure

• Upper surface (upper side of wing) low pressure
• Recall discussion on exactly why this is
  physically
• Recall discussion on how to show this
  mathematically

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AIRFOILS VERSUS WINGS
Low Pressure
Low Pressure
High Pressure
High Pressure

• Upper surface (upper side of wing) low pressure
• Lower surface (underside of wing) high pressure

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AIRFOILS VERSUS WINGS
Low Pressure
Low Pressure
High Pressure
High Pressure

• Upper surface (upper side of wing) low pressure
• Lower surface (underside of wing) high pressure
• Flow always desires to go from high pressure to
  low pressure
• Flow wraps around wing tips

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FINITE WINGS
Front View
Wing Tip Vortices
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EXAMPLE 737 WINGLETS
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EXAMPLES AIRCRAFT WAKE TURBULENCE
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FINITE WING DOWNWASH (5.13)

• Wing tip vortices induce a small downward
  component of air velocity near wing by dragging
  surrounding air with them
• Downward component of velocity is called
  downwash, w

Chord line
Local relative wind

• Two Consequences
• Increase in drag, called induced drag (drag due
  to lift)
• Angle of attack is effectively reduced, aeff as
  compared with V8

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ANGLE OF ATTACK DEFINITIONS
ageometric what you see, what you would see in a
wind tunnel Simply look at angle between
incoming relative wind and chord line aeffective
what the airfoil sees locally Angle between
local flow direction and chord line Small than
ageometric because of downwash ainduced
difference between these two angles Downwash has
induced this change in angle of attack
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INFINITE WING DESCRIPTION
LIFT
Relative Wind, V8

• LIFT is always perpendicular to the RELATIVE WIND
• Local relative wind is canted downward, lift
  vector is tilted back so a component of L acts in
  direction normal to incoming relative wind

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FINITE WING DESCRIPTION
Induced Drag, Di

• Relative wind gets tilted downward under the
  airfoil
• LIFT is still always perpendicular to the
  RELATIVE WIND
• Lift vector is tilted back so a component of L
  acts in direction normal to incoming relative
  wind ? results in a new type of drag

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3 PHYSICAL INTERPRETATIONS

• Local relative wind is canted downward, lift
  vector is tilted back so a component of L acts in
  direction normal to incoming relative wind
• Wing tip vortices alter surface pressure
  distributions in direction of increased drag
• Vortices contain rotational energy put into flow
  by propulsion system to overcome induced drag

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INDUCED DRAG IMPLICATIONS FOR WINGS
V8
Infinite Wing (Appendix D)
Finite Wing
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HOW TO ESTIMATE INDUCED DRAG

• Local flow velocity in vicinity of wing is
  inclined downward
• Lift vector remains perpendicular to local
  relative wind and is tiled back through an angle
  ai
• Drag is still parallel to freestream
• Tilted lift vector contributes a drag component

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HOW TO ESTIMATE INDUCED DRAG

• Calculation of angle ai is not trivial (MAE 3241)
• Value of ai depends on distribution of downwash
  along span of wing
• Downwash is governed by distribution of lift over
  span of wing

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WHY A LIFT DISTRIBUTION?CHORD MAY VARY IN LENGTH
Thinner wing near tip delay onset of
high-speed compressibility effects Retain aileron
control
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WHY A LIFT DISTRIBUTION?SHAPE OF AIRFOIL MAY
VARY ALONG WING
F-111
NACA 64A209
NACA 64A210
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WHY A LIFT DISTRIBUTION?WING (AIRFOIL) MAY BE
TWISTED
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PW / G.E. GP7000 FAMILY
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HOW TO ESTIMATE INDUCED DRAG

• Special Case Elliptical Lift Distribution
  (produced by elliptical wing)
• Lift/unit span varies elliptically along span
• This special case produces a uniform downwash

Key Results Elliptical Lift Distribution
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ELLIPTICAL LIFT DISTRIBUTION

• For a wing with same airfoil shape across span
  and no twist, an elliptical lift distribution is
  characteristic of an elliptical wing plan form
• Example Supermarine Spitfire

Key Results Elliptical Lift Distribution
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HOW TO ESTIMATE INDUCED DRAG

• For all wings in general
• Define a span efficiency factor, e (also called
  span efficiency factor)
• Elliptical planforms, e 1
• The word planform means shape as view by looking
  down on the wing
• For all other planforms, e lt 1
• 0.85 lt e lt 0.99

Goes with square of CL Inversely related to
AR Drag due to lift
Span Efficiency Factor
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DRAG POLAR
Total Drag Profile Drag Induced Drag

cd
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EXAMPLE U2 VS. F-15
U2
F-15

• Cruise at 70,000 ft
• Air density highly reduced
• Flies at slow speeds, low q8 ? high angle of
  attack, high CL
• U2 AR 14.3 (WHY?)

• Flies at high speed (and lower altitudes), so
  high q8 ? low angle of attack, low CL
• Low AR (WHY?)

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EXAMPLE U2 SPYPLANE

• Cruise at 70,000 ft
• Out of USSR missile range
• Air density, r8, highly reduced
• In steady-level flight, L W
• As r8 reduced, CL must increase (angle of attack
  must increase)
• AR ? CD ?
• U2 AR 14.3

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EXAMPLE F-15 EAGLE

• Flies at high speed at low angle of attack ? low
  CL
• Induced drag lt Profile Drag
• Low AR, Low S

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WHY HIGH AR ON PREDATOR?
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CHANGES IN LIFT SLOPE SYMMETRIC WINGS
cl
Infinite wing AR8
Slope, a0 2p/rad 0.11/deg
Infinite wing AR10
Infinite wing AR5
cl1.0
ageom
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CHANGES IN LIFT SLOPE CAMBERED WINGS
cl
Slope, a0 2p/rad 0.11/deg
Infinite wing AR8
Infinite wing AR10
Infinite wing AR5
cl1.0
ageom
Zero-lift angle of attack independent of AR
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FINITE WING CHANGE IN LIFT SLOPE

• In a wind tunnel, the easiest thing to measure is
  the geometric angle of attack
• For infinite wings, there is no induced angle of
  attack
• The angle you see the angle the infinite wing
  sees
• With finite wings, there is an induced angle of
  attack
• The angle you see ? the angle the finite wing
  sees

Infinite Wing
ageom aeff ai aeff
Finite Wing
ageom aeff ai
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FINITE WING CHANGE IN LIFT SLOPE
Infinite Wing

• Lift curve for a finite wing has a smaller slope
  than corresponding curve for an infinite wing
  with same airfoil cross-section
• Figure (a) shows infinite wing, ai 0, so plot
  is CL vs. ageom or aeff and slope is a0
• Figure (b) shows finite wing, ai ? 0
• Plot CL vs. what we see, ageom, (or what would be
  easy to measure in a wind tunnel), not what wing
  sees, aeff
• Effect of finite wing is to reduce lift curve
  slope
• Finite wing lift slope a dCL/da
• At CL 0, ai 0, so aL0 same for infinite or
  finite wings

Finite Wing
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SUMMARY INFINITE VS. FINITE WINGS

• Properties of a finite wing differ in two major
  respects from infinite wings
• Addition of induced drag
• Lift curve for a finite wing has smaller slope
  than corresponding lift curve for infinite wing
  with same airfoil cross section (depends on AR)

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EXTRA CREDIT
A380 burns about four liters (one gallon) of fuel
per passenger every 80 miles and can fly some
8,000 nautical miles and seat as many as 550
passengers.

• What is the aspect ratio of this airplane?
• What is the aspect ratio of a 747?
• What aerodynamics decisions went into selected
  the A380 aspect ratio?
• What non-aerodynamics decisions went into
  limiting the A380 aspect ratio?