air loads - clarkson university
TRANSCRIPT
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
Example - SF, BM, Torsion Calculation
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
Example - SF, BM, Torsion Calculation
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