Air Loads - Clarkson University

7/29/2019 Air Loads - Clarkson University

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AirLoads Airfoil

Geometry

Camberline

linejoiningthemidpointsbetweenupperandlowersurfaces.

Chordline

straightlinejoiningendpointsofcamberline(length=c)

Camber

max.

distance

of

camber

line

from

chord

line

(expressed

as

%c;

usuallylessthan5%c)

Zu

=(Zc

+Zt

) Zl

=(Zc

Zt

)

z thickness

camber

Lowersurface

Chordline

TE

TE

thickness

Zt

ZcZl

ZuLEcircle(radius)

AE212 Jha Loads-1

Uppersurface


2/15

ForcesandMoments

Angleof attack

V

Arbitraryref.pt.

(generallyc/4orcg)

SVRMfF N2

).,,(

Forairfoil,

Liftco

efficient

Dragcoefficient

Pitchingmomentcoefficient

1( )S c unitspan

cossin

l lift Fd drag F

m pitching moment

l

d

F

12

l

l lC qcV c

d

dC

qc

2mmC

qc

AE212 Jha Loads-2

m


3/15

WingPlanform

Aerodynamic characteristics

generally

basedon

gross

wing

area

(assumed

extendeduptofuselagecenterline)

Exposedwing(onlyoutsidefuselage)

areausedforskinfrictiondrag

LE

C(y)Ct

TE

s=b/2

b

chordline

Cr

y

LE

/ 4c

0

2

/ 2

( ) 2 ( ) (1 )

2 2

,

, /

r t r

wing

t r

b

wing

b bS c c c y dy c

bWingaspectratio A

S

Wingtaper ratio c c

AE212 Jha Loads-3


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MeanAerodynamicChord(MAC),

Wingtwistalongspan

+

y/s=1.0Washin

tip Washout

tip Root

MeanAerodynamicChord

/22

/ 22

0

/20

0

21

1

( ) 2 2

( ) 3( )

b

b

b r

c y dy

c c y dy cSc y dy

/2

0

2 1 2( ) ( )

6 1

( (1/ 4) )

b

mac

by c y ydy

S

Aerodynamic center at c for subsonic M

Root

AE212 Jha Loads-4


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TheVnDiagram(FlightEnvelope)

10.0

7.5

5.0

2.5

2.5

5.0

A150 300 450Vs,

1g V4

V* V5

+7.5

3.0

BC

DE

Max.speed

boundary.

M=0.85

approx.

Ve

(knots)

Stall

area

CLmaxboundary

Negativelimitloadfactor

CLmaxboundary

Positivelimitloadfactor

Maxq

Vn(velocity-load factor) diagramforatypicalJet

Trainer (1knot=1.15mph)

Vcruise

3

2

1

AE212 Jha Loads-5

Stall

area


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VnDiagram

Limitloadisthesafelimituptowhichthereisnopermanentdeformation

Ultimateloadfactor

Structuralfailureoccurswhenn>nultimate

V

n(velocity

load

factor)

diagram

includes

both

aerodynamic

and

structurallimitationsandestablishesmaneuverboundaries.

CurveAB:aerodynamiclimitonloadfactor,imposedby(CL

)max

2 max

max

max max

max max

max 4

( )1

2 /

1 ,

2 ,3

, ( )

L

L L

L L

Cn V

W S

Pt C C n n

Pt C C n nPt Outside flight envelope

AsV increases n possiblealsoincreases V

AE212 Jha Loads-6


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VnDiagram

HorizontallineBC:Positivelimitloadfactorofthestructure

LineCD:highspeedlimitsetbymaximumdynamicpressure(designdive

speed,VCD

)

Athigher

speeds,

undesirable

instabilities

(like

flutter,

aileron

reversal,

divergence,buffetingetc.)mayoccur.

VCD

=1.5xVmax,cruise

(max.cruisevelocity)(FARpart25airplanes)

Forsupersonicaircraft,(Vmax

/asL

)=Max.Machno.inlevelflight+0.2

(a=speedofsound)

1/2

max

max

max

2*, * ,

L L

L

n WAtV V whereV C C

C S

AE212 Jha Loads-7


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VnDiagram

Maneuverpt.B: CL andnaresimultaneouslyattheirhighestpossible

values.HighestInstantaneousTurnRate(V*=cornervelocity)

CurveAE:NegativeCLmax

limit(flowseparationfrombottomsurface)

LineED:Negativelimitloadfactor(Whydifferentfromthepositivenmax

?

skinthickness)

22

2

1

2

1VVeSL

; ( )

; ( )

SL eSealevel density V Equivalentair speed EAS

densityat flightaltitude V Trueair speed TAS

AE212 Jha Loads-8


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AirLoadDistributiononLiftingSurfaces

Use

high

(CL

max)

limit

and

max

q

limit

points

for

load

calculationsonwings.

Spanwise

liftdistributionisproportionaltothecirculationateachspan

station.Foranellipticalplanform,liftdistributioniselliptical.Fornon

ellipticalwings,useSchrenks approximation

(semi

empirical)

to

estimate

liftdistribution(Loaddistributiononawingistheaverageofactual

planform

shapeandanellipticshapeofthesamespanandarea.)

Schrenks

methodisnotapplicabletohighlysweptwings(suchasdelta

wings)due

to

vortex

flow

elliptic

Rectangularplanform

average2

2: ( ) 1 (1 )

4 2: ( ) 1

ryTrapezoidal c y C

b

S yElliptical c y

b b

Wingplanform

AE212 Jha Loads-9


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ShearForcesandBendingMoments

Supportshear

reaction

shear

Support

moment

reaction

Tension

Compression

moment

Ultimate Load on each wing, )2/5.1**( nWLw

Beam (wing) with distributed load

AE212 Jha Loads-10


11/15

0 0.15c 1.0c

actual

Approx.

Foranyspanstation,theshearforceissimplythesumoftheverticalloadsoutboardofthatstation(or,theintegralofdistributedload)

Bendingmomentatanystationequalsthesumofproductofloadateach

outboardstationanditsdistancefromthestation

For

apositive

Bending

Moment

(as

shown

in

the

figure)

,the

internal

forcesproducecompressiononupperpartandtensiononlowerpart

Wingweightisproportionalto .Halving(t/c)increaseswingweight

by41%.

Wing

weight

is

typically

15%

of

total

empty

weight

of

aircraft

Addfuelweighttoemptywingweighttoobtaingrosswingweight

Chordwise

liftdistributionmaybeapproximatedasshownbelow

ShearForcesandBendingMoments

AE212 Jha Loads-11

1

/t c


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(1)Pick

load

cases

from

V

ndiagram

(max

AoA,

max

dynamic

pressure,max.negativeAoA

,etc.)

(2)Calculatetotalliftforce(approx.normalforce);Loadoneachwing,

(3)Approx.wingasstrips

fromcenterlinetotip(e.g.,10stripsof

of 10%

semi

span

each)

(4)DistributeliftforceoneachstripusingSchrenks

approximation

(6)Estimateshearforceandbendingmoment(7)Usewingcenterofpressureat25%chord(subsonicspeeds)

(8)Usingsamestripsasin(3),calculatetorqueaboutfrontspar

location(say,

15%

chord).

Then

sum

torque

values

from

tip

to

root

SF, BM, Torsion Calculation

)2/5.1**( nWLw

AE212 Jha Loads-12


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Rectangularwing:

chord

=0.5

m,

span

=4m,

TOGW

=5,000

N,

nmax

=4

Wingarea=2sqm,AR=b/c

=8

Calculatetotalliftforce(approx.normalforce)oneachwing:

=15,000N(Ultimateloadoneachwing)

DistributeLw

alongwingspanusingstripsofequalwidth

Use3stripsforthisexampleproblem

Chordforellipticalwing

Example - SF, BM, Torsion Calculation

)2/5.1**( nWLw

AE212 Jha Loads-13

y-station Wing chord, c Elliptical c(y) Average chord0 0.5 0.637 0.569

0.66 0.5 0.601 0.5501.33 0.5 0.475 0.4882 0.5 0 0.250

2 2 24 2 4(2) 2

( ) 1 1 0.637 1(4) 4 2

S y y yc y

b b


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Distributelift

force

on

each

strip

using

Schrenks

approximation

Calculatestriparea=(Averageofgeometricandellipticalchord)*width=Averagechord*0.667

Calculatefactor

forliftdistribution:Lw

=(factor)*(sumofstripareas)

15,000N=(factor)*(0.965sqm)

factor=15,544N/sqm

AE212 Jha Loads-14


Strip Strip area Lift on each strip

1 0.373 5798 N2 0.346 5378 N

3 0.246 3824 N


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Estimateshear

force

and

bending

moment

SFatanyystation=sumofliftforceoutboardofystation

BMatanyystation=sumof(liftforce*distance)outboardofystation

Forcalculatingdistance,assumeliftactingthroughthecenterofstripwidth

Calculatetorqueabout15%cusingwingcenterofpressureat25%c(good

approximationatsubsonicspeeds);sumtorquevaluesfromtipto

root

AE212 Jha Loads 15


y-station Shear Force, N Bending Moment, N-m

0 15000 13676 (6361+5381+1934)

0.667 9202 5620 (3826+1794)

1.33 3824 1275

2 0 0

Strip Torque, N-m

1 750 (460.1+289)

2 460.1 (191.2+268.9)

3 191.2

Air Loads - Clarkson University

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