flight introduction

7/29/2019 flight introduction

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APPLIED AERODYNAMICS

Airfoils and Finite Wings

AVIONICS DEPARTMENT

PAF KIET


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UDPATES

Mid-term grades

Team project

Lab session to work on project this week (Thursday and Friday)

Literature review and motor selection report due on March 25 (will likely push

this back a week)

Mid-Term Exam

Monday, March 21 in class

Covers Chapter 4 and Chapter 5.15.15

Open book / open notes but no time to study during the exam

Sample Mid-Term with Solution on line

Review Session: Tuesday, March 15, Crawford auditorium 112, 810 pm


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PRO|ENGINEER DESIGN CONTEST

Winner

Either increase your grade by an entire letter (C B), or

Buy your most expensive textbook next semester

Create most elaborate, complex, stunningAerospace Relatedproject in

ProEngineer

Criteria: Assembly and/or exploded view


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PRO|ENGINEER CONTEST


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PRO|ENGINEER CONTEST


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If you do the PRO|E challenge

Do not let it consume you!


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SKETCHING CONTEST

Choose any aerospace device you like (airplane, rocket, spacecraft, satellite,

helicopter, etc.) but only 1 entry per person

Drawing must be in isometric view on 8.5 x 11 inch paper Free hand sketching, no rulers, compass, etc.

Submit by April 22, 2011 by 5:00pm

Winner: 10 points on mid-term, 2nd place: 7 points, 3rd place: 5 points

Decided by TAs and other Aerospace Faculty


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DO NOT SUBMIT
http://aaronsquadrant.tripod.com/airplane/pa.jpg


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READING AND HOMEWORK ASSIGNMENTS

Reading: Introduction to Flight, by John D. Anderson, Jr.

For April 4th

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: Friday, March 25, 2011 by 5pm

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 r 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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LIFT, DRAG, AND MOMENT COEFFICIENTS (5.3)

Behavior of L, D, and M depend on a, but also on velocity and altitude

V, r, Wing Area (S), Wing Shape, m, compressibility

Characterize behavior of L, D, M with coefficients (cl, cd, cm)

Re,,2

1

2

1

2

2

Mfc

Sq

L

SV

Lc

ScVL

l

l

l

a

r

r

Matching Mach and Reynolds

(called similarity parameters)

M, Re

M, Re

cl, cd, cm identical


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SAMPLE DATA

Lift coefficient (or lift) linear

variation with angle of attack, a

Cambered airfoils havepositive lift when a = 0

Symmetric airfoils have

zero lift when a = 0

At high enough angle of attack,

the performance of the airfoilrapidly degrades stall

cl

Cambered airfoil has

lift at a=0

At negative a airfoil

will have zero lift


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SAMPLE DATA: NACA 23012 AIRFOIL

LiftCoefficient

cl

Moment

Coefficientcm, c/4

a

Flow separation

Stall

AIRFOIL DATA (5 4 AND APPENDIX D)


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AIRFOIL DATA (5.4 AND APPENDIX D)

NACA 23012 WING SECTION

cl

cm,c

/4

Re dependence at high a

Separation and Stall

a cl

cd

cm,a.c.

cl vs. aIndependent of Re

cd vs. aDependent on Re

cm,a.c.

vs. clvery flat

R=Re


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EXAMPLE: SLATS AND FLAPS


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EXAMPLE: BOEING 727 FLAPS/SLATS

AIRFOIL DATA (5 4 AND APPENDIX D)


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Flap extended

Flap retracted

AIRFOIL DATA (5.4 AND APPENDIX D)

NACA 1408 WING SECTION Flaps shift lift curve

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 M

on cl

2

2

1

V

pp

q

ppCp

r


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EXAMPLE: CP CALCULATION

SS


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For M < 0.3, r ~ const

Cp = Cp,0 = 0.5 = const

COMPRESSIBILITY CORRECTION:

EFFECT OF M ON CP

20,

2

1

V

ppCp

r

M

COMPRESSIBILITY CORRECTION


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22

0,

15.0

1

MMCC pp

For M < 0.3, r ~ const

Cp = Cp,0 = 0.5 = const

Effect of compressibility

(M > 0.3) is to increase

absolute magnitude of Cp as

M increasesCalled: Prandtl-Glauert Rule

Prandtl-Glauert rule applies for 0.3 < M < 0.7

COMPRESSIBILITY CORRECTION:

EFFECT OF M ON CP

M


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OBTAINING LIFT COEFFICIENT FROM CP (5.7)

2

0,

0

,,

1

1

M

cc

dxCCc

c

l

l

c

upperplowerpl


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COMPRESSIBILITY CORRECTION SUMMARY

If M0 > 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 at M

2

0,

1 MCC pp

2

0,

1 Mcc ll


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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 > M

Flow over airfoil may have

sonic regions even though

freestream M < 1

INCREASED DRAG!

CRITICAL FLOW AND SHOCK WAVES


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MCR


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bubble of supersonic flow


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AIRFOIL THICKNESS SUMMARY

Which creates most lift? Thicker airfoil

Which has higher critical Mach number?

Thinner airfoil

Which is better?

Application dependent!

Note: thickness is relative

to chord in all cases

Ex. NACA 0012 12 %

A O C SS A A S


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AIRFOIL THICKNESS: WWI AIRPLANES

English Sopwith Camel

German Fokker Dr-1

Higher maximum CLInternal wing structure

Higher rates of climb

Improved maneuverability

Thin wing, lower maximum CLBracing wires requiredhigh drag

THICKNESS TO CHORD RATIO TRENDS


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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

MODERN AIRFOIL SHAPES
http://upload.wikimedia.org/wikipedia/commons/1/1a/A10Thunderbolt2_990422-F-7910D-517.jpg


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MODERN AIRFOIL SHAPES

http://www.nasg.com/afdb/list-airfoil-e.phtml

Root Mid-Span Tip

Boeing 737

SUMMARY OF AIRFOIL DRAG (5 12)
http://www.airliners.net/open.file?id=800463&size=L&sok=JURER%20%20%28ZNGPU%20%28nvepensg%2Cnveyvar%2Ccynpr%2Ccubgb_qngr%2Cpbhagel%2Cerznex%2Ccubgbtencure%2Crznvy%2Clrne%2Cert%2Cnvepensg_trarevp%2Cpa%2Cpbqr%29%20NTNVAFG%20%28%27%2B%22737%22%27%20VA%20OBBYRNA%20ZBQR%29%29%20%20beqre%20ol%20cubgb_vq%20QRFP&photo_nr=23http://www.airliners.net/open.file?id=800463&size=L&sok=JURER%20%20%28ZNGPU%20%28nvepensg%2Cnveyvar%2Ccynpr%2Ccubgb_qngr%2Cpbhagel%2Cerznex%2Ccubgbtencure%2Crznvy%2Clrne%2Cert%2Cnvepensg_trarevp%2Cpa%2Cpbqr%29%20NTNVAFG%20%28%27%2B%22737%22%27%20VA%20OBBYRNA%20ZBQR%29%29%20%20beqre%20ol%20cubgb_vq%20QRFP&photo_nr=23


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SUMMARY OF AIRFOIL DRAG (5.12)

wdpdfdd

wavepressurefriction

cccc

DDDD

,,,

Only at transonic andsupersonic speeds

Dwave=0 for subsonic speedsbelow Mdrag-divergence

Profile Drag

Profile Drag coefficient

relatively constant with

M at subsonic speeds


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FINITE WINGS

INFINITE VERSUS FINITE WINGS


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INFINITE VERSUS FINITE WINGS

S

bAR

2

Aspect Ratio

b: wingspan

S: wing area

High AR

Low AR

AIRFOILS VERSUS WINGS


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Upper surface (upper side of wing): low pressure

Recall discussion on exactly why this is physically

Recall discussion on how to show this mathematically

http://www.airliners.net/open.file?id=790618&size=L&sok=JURER%20%20%28ZNGPU%20%28nvepensg%2Cnveyvar%2Ccynpr%2Ccubgb_qngr%2Cpbhagel%2Cerznex%2Ccubgbtencure%2Crznvy%2Clrne%2Cert%2Cnvepensg_trarevp%2Cpa%2Cpbqr%29%20NTNVAFG%20%28%27%2B%22777%22%27%20VA%20OBBYRNA%20ZBQR%29%29%20%20beqre%20ol%20cubgb_vq%20QRFP&photo_nr=341


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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

FINITE WINGS


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FINITE WINGSFront View

Wing TipVortices

EXAMPLE: 737 WINGLETS


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EXAMPLE: 737 WINGLETS

EXAMPLES: AIRCRAFT WAKE TURBULENCE
http://www.penmachine.com/photoessays/2004_08_aerial2/14-wing.jpg


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EXAMPLES: AIRCRAFT WAKE TURBULENCE

FINITE WING DOWNWASH (5 13)


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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

Local relative wind

Two Consequences:

1. Increase in drag, called induced drag (drag due to lift)

2. Angle of attack is effectively reduced, aeff

as compared with V

Chord line

ANGLE OF ATTACK DEFINITIONS


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ANGLE OF ATTACK DEFINITIONS

geometric: what you see, what you would see in a wind tunnel

Simply look at angle between incoming relative wind and chord line

effective: what the airfoil sees locally

Angle between local flow direction and chord line

Small than ageometric because of downwash

induced: difference between these two angles

Downwash has induced this change in angle of attack

inducedeffectivegeometric aaa

INFINITE WING DESCRIPTION


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INFINITE WING DESCRIPTION

LIFT is always perpendicular to the RELATIVE WIND

LIFT

Relative Wind, V

FINITE WING DESCRIPTION


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FINITE WING DESCRIPTION

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

incomingrelative wind results in a new type of drag

inducedeffectivegeometric aaa

Induced Drag, Di

3 PHYSICAL INTERPRETATIONS


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3 PHYSICAL INTERPRETATIONS

1. Local relative wind is canted downward, lift vector is tilted back so a

component of L acts in direction normal to incoming relative wind

2. Wing tip vortices alter surface pressure distributions in direction of

increased drag

3. Vortices contain rotational energy put into flow by propulsion system to

overcome induced drag

INDUCED DRAG: IMPLICATIONS FOR WINGS


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INDUCED DRAG: IMPLICATIONS FOR WINGS

dD

lL

cCcC

Finite WingInfinite Wing

(Appendix D)

Vaa eff

HOW TO ESTIMATE INDUCED DRAG


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ii

ii

LD

LD

a

a

sin

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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Calculation of angle ai is not trivial (MAE 3241)

Value ofai depends on distribution of downwash along span of wing

Downwash is governed by distribution of liftover span of wing

WHY A LIFT DISTRIBUTION?


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CHORD MAY VARY IN LENGTH

Thinner wing near tipdelay onset of high-speed

compressibility effects

Retain aileron control



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SHAPE OF AIRFOIL MAY VARY ALONG WING

NACA 64A210

NACA 64A209

F-111



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WING (AIRFOIL) MAY BE TWISTED

P&W / G.E. GP7000 FAMILY


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P&W / G.E. GP7000 FAMILY



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Special Case: Elliptical Lift Distribution (produced by elliptical wing)

Lift/unit span varies elliptically along span

This special case produces a uniform downwash

AR

CC

AR

C

Sq

DAR

CSq

AR

CLLD

AR

C

LiD

Li

LLii

Li

a

a

2

,

2

2

Key Results:

Elliptical Lift Distribution

ELLIPTICAL LIFT DISTRIBUTION


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ELLIPTICAL LIFT DISTRIBUTION

For a wing with same airfoil shape across span and no twist, an elliptical liftdistribution is characteristic of an elliptical wing plan form

Example: Supermarine Spitfire

AR

CC

AR

C

LiD

Li

a

2

,

Key Results:

Elliptical Lift Distribution



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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 < 1

0.85 < e < 0.99

eAR

CC LiD

2

,

Span Efficiency Factor

Goes with square of CLInversely related to AR

Drag due to lift

DRAG POLAR


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DRAG POLAR

eAR

C

cC

L

dD

2

Total Drag = Profile Drag + Induced Drag

{cd

EXAMPLE: U2 VS. F-15


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Cruise at 70,000 ft Air density highly reduced

Flies at slow speeds, low q

high angle of attack, high CL

U2 AR ~ 14.3 (WHY?)

eAR

CcC LdD

2

LSCVWL2

2

1 r

Flies at high speed (and loweraltitudes), so high q low

angle of attack, low CL

Low AR (WHY?)

U2 F-15

EXAMPLE: U2 SPYPLANE


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: U S N

Cruise at 70,000 ft

Out of USSR missile range

Air density, r, highlyreduced

In steady-level flight, L = W

As r reduced, CL mustincrease (angle of attack mustincrease)

AR CD

U2 AR ~ 14.3

eAR

CcC LdD

2

LSCVWL2

2

1 r

EXAMPLE: F-15 EAGLE


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Flies at high speed at low angle

of attack low CL

Induced drag < Profile Drag Low AR, Low S

eAR

CcC LdD

2

LSCVWL2

2

1 r

WHY HIGH AR ON PREDATOR?


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CHANGES IN LIFT SLOPE: SYMMETRIC WINGS


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ageom

cl Infinite wing:

AR=

Infinite wing:

AR=10

Infinite wing:

AR=5cl=1.0

Slope, a0 = 2/rad ~ 0.11/deg

CHANGES IN LIFT SLOPE: CAMBERED WINGS


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ageom

cl Infinite wing:

AR=

Infinite wing:

AR=10

Infinite wing:

AR=5cl=1.0

Zero-lift angle of attack independent of AR

Slope, a0 = 2/rad ~ 0.11/deg

FINITE WING CHANGE IN LIFT SLOPE


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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

ieffgeom aaa

Infinite Wing

Finite Wing

ageom= aeff+ ai = aeff

ageom= aeff+ ai

FINITE WING CHANGE IN LIFT SLOPE


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Lift curve for a finite wing has a smallerslope than corresponding curve for aninfinite wing with same airfoil cross-section

Figure (a) shows infinite wing, ai = 0, soplot is CL vs. ageom or aeffand slope is a0

Figure (b) shows finite wing, ai 0

Plot CL vs. what we see, ageom, (orwhat would be easy to measure in a

wind tunnel), not what wing sees, aeff

1. Effect of finite wing is to reduce lift curve slope

Finite wing lift slope = a = dCL/da

2. At CL = 0, ai = 0, so aL=0 same for infinite or

finite wings

ieffgeom aaa Infinite Wing

Finite Wing

SUMMARY: INFINITE VS. FINITE WINGS


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Properties of a finite wing differ in two major respects from infinite wings:

1. Addition of induced drag

2. Lift curve for a finite wing has smaller slope than corresponding lift curve for

infinite wing with same airfoil cross section (depends on AR)

EXTRA CREDIT


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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?

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.
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