5_Configuration Aerodynamics - 2.pdf
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Transcript of 5_Configuration Aerodynamics - 2.pdf
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Configuration Aerodynamics - 2Robert Stengel, Aircraft Flight Dynamics, MAE 331,
2010
Drag
Induced drag
Compressibility effects
P-51 example
Newtonian Flow
Pitching Moment
Copyright 2010 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE331.html
http://www.princeton.edu/~stengel/FlightDynamics.html
Aerodynamic Drag
Drag = CD1
2!V 2S " CD
0
+ #CL2( )1
2!V 2S
" CD0
+ # CLo + CL$$( )2%
&'()*1
2!V 2S
Induced Drag
Induced Drag
Lift produces downwash (angle proportional to lift)
Downwash rotates velocity vector
Lift is perpendicular to velocity vector
Axial component of rotated lift induces drag
-
Induced Drag
CDi = CLi sin! i " CL0 + CL!!( )sin! i" CL0 + CL!!( )! i # $CL
2
#CL2
%eAR=CL21+ &( )
%AR
where
e = Oswald efficiency factor = 1 for elliptical distribution
& = departure from ideal elliptical lift distribution
Spitfire Spanwise Lift Distribution
of 3-D (Trapezoidal) WingsStraight Wings (@ 1/4 chord)
(McCormick)
TR = taper ratio, !
For some taper ratio between 0.35 and 1,lift distribution is nearly elliptical
Spanwise Lift Distributionof 3-D Wings
Wing does nothave to have anellipticalplanform to havea nearly ellipticallift distribution
Sweep moves liftdistributiontoward tips
Straight and Swept Wings(NASA SP-367)
CL2!D (y)c(y)
CL3!D c
Induced Drag Factor Graph for " (McCormick, p. 172)
Lower AR
CDi=CL
21+ !( )
"AR
-
Oswald Efficiency Factor Approximation for e (Pamadi, p. 390)
e !1.1C
L"
RCL"+ (1# R)$AR
where
R = 0.0004%3# 0.008%
2+ 0.05% + 0.86
% =AR &
cos'LE
CDi=
CL
2
!eAR
P-51 Mustang
http://en.wikipedia.org/wiki/P-51_Mustang
Wing Span = 37 ft (9.83m)
Wing Area = 235 ft (21.83m2)
Loaded Weight = 9,200 lb (3, 465 kg)
Maximum Power = 1,720 hp (1,282 kW )
CDo = 0.0163
AR = 5.83
! = 0.5
P-51 Mustang Example
CL! ="AR
1+ 1+AR
2
#$%
&'(2)
*++
,
-..
= 4.49 per rad (wing only)
e = 0.947
/ = 0.05570 = 0.0576
CDi= !C
L
2=
CL
2
"eAR=CL
21+ #( )
"AR
Mach Number Effects
-
Drag Due toPressure Differential
Blunt base pressure drag
CDbase = CpressurebaseSbase
S! 0.29Sbase
C frictionSwetM < 1( ) Hoerner[ ]
1( )
!
CDM ! 2
M2"1
M > 1( )
Air Compressibility EffectShock Waves in
Supersonic Flow
Drag rises due to pressureincrease across a shock wave
Subsonic flow
Local airspeed is less than sonic(i.e., speed of sound)everywhere
Transonic flow
Airspeed is less than sonic atsome points, greater than sonicelsewhere
Supersonic flow
Local airspeed is greater thansonic virtually everywhere
Critical Mach number
Mach number at which localflow first becomes sonic
Onset of drag-divergence
Mcrit ~ 0.7 to 0.85
Effect of Chord
Thickness on Wing
Pressure Drag
Thinner chord sections lead to higher Mcrit
Lockheed P-38
Lockheed F-104
Pressure Drag on WingDepends on Sweep Angle
Sweep AngleEffect on Wing Drag
Mcritswept
=
Mcritunswept
cos!
-
Air CompressibilityEffect
Subsonic
SupersonicTransonic
Incompressible
Sonic Boomshttp://www.youtube.com/watch?v=gWGLAAYdbbc
Transonic Drag Rise and the Area Rule
Richard Whitcomb (NASA Langley) and Wallace Hayes (Princeton)
YF-102A (left) could not break the speed of sound in level flight;
F-102A (right) could
Transonic Drag Rise and the Area Rule Supercritical
Wing
Richard Whitcomb!s supercritical airfoil
Wing upper surface flattened to increase Mcrit Wing thickness can be restored
Important for structural efficiency, fuel storage, etc.
Pressure Distribution on
Supercritical Airfoil
()
(+)
NASA Supercritical
Wing F-8
Airbus A320
-
Large Angle Variations in Subsonic
Drag Coefficient (0 < # < 90)
All drag coefficients converge to Newtonian-likevalues at high angle of attack
Low-AR wing has less drag than high-AR wing
Newtonian Flow andHigh-Angle-of-Attack
Lift and Drag
Newtonian Flow
No circulation
Cookie-cutter
flow
Equal pressureacross bottom of
the flat plate
Normal Force =
Mass flow rate
Unit area
!
"#$
%&Change in velocity( ) Projected Area( ) Angle between plate and velocity( )
Newtonian Flow
N = !V( ) V( ) S sin"( ) sin"( )
= !V 2( ) S sin2"( )
= 2sin2"( )
1
2!V 2#
$%&'(S
) CN1
2!V 2#
$%&'(S = CNqS
Lift = N cos!
CL = 2sin2!( )cos!
Drag = N sin!
CD = 2sin3!
Normal Force =
Mass flow rate
Unit area
!
"#$
%&Change in velocity( ) Projected Area( ) Angle between plate and velocity( )
-
Application of Newtonian Flow
Hypersonic flow (M ~> 5) Shock wave close to surface
(thin shock layer), merging withthe boundary layer
Flow is ~ parallel to the surface
Separated upper surface flow
Space Shuttle in
Supersonic Flow
High-Angle-of-Attack Research
Vehicle (F-18) All Mach numbers at
high angle of attack Separated flow on upper
(leeward) surfaces
Lift vs. Drag for Large Variation
in Angle-of-Attack (0 < # < 90)Subsonic Lift-Drag Polar
Low-AR wing has less drag than high-AR wing, but less lift as well
High-AR wing has the best overall L/D
Lift-to-Drag Ratio vs.Angle of Attack
L/D is an important performance metric for aircraft
High-AR wing has best overall L/D
Low-AR wing has best L/D at intermediate angle of attack
L
D=
CLq S
CDq S=
CL
CD
Pitching Moment
-
Pitching Moment
Body ! Axis Pitching Moment = MB
= ! "pz + "sz( )xdxdysurface
## + "px + "sx( )"pxzdydzsurface
##
Pressure and shear stress differentials times moment armsintegrate over the surface to produce a net pitching moment
Center of mass establishes the moment arm center
Pitching Moment
MB ! " Zix1 +i=1
I
# Xiz1 + Interference Effects+ Pure Couplesi=1
I
#
Distributed effects can be aggregated tolocal centers of pressure
Pure Couple
Net force = 0
Net moment " 0
Rockets Cambered Lifting Surface
Fuselage
Net Center of Pressure
Local centers of pressure can be aggregatedat a net center of pressure (or neutral point)
xcpnet =xcpCn( )wing + xcpCn( ) fuselage + xcpCn( )tail + ...
!"
#$
CNtotal
-
Static Margin
Static Margin = SM =100 xcm ! xcpnet( )
c, %
" 100 hcm ! hcpnet( )%
Static margin reflects the distance between thecenter of mass and the net center of pressure
Static Margin
Static Margin = SM =100 xcm ! xcpnet( )
c, %
" 100 hcm ! hcpnet( )%
Effect of Static Margin onPitching Moment
MB = Cmq Sc ! Cmo " CN# hcm " hcpnet( )#$% &'q Sc ! Cmo " CL# hcm " hcpnet( )#$% &'q Sc
! Cmo +(Cm(#
#)*+
,-.q Sc = Cmo + Cm##( )q Sc
= 0 in trimmed (equilibrium) flight
For small angle of attack and no control deflection
Typically, static margin is positive and !Cm/!# is negative forstatic pitch stability
Pitch-Moment Coefficient
Sensitivity to Angle of Attack
MB = Cmq Sc ! Cmo + Cm""( )q Sc
For small angle of attack and no controldeflection
-
Pitch-Moment Coefficient
Sensitivity to Angle of Attack For small angle of attack and no control deflection
Cm! " #CN!net hcm # hcpnet( ) " #CL!net hcm # hcpnet( ) = #CL!netxcm # xcpnet
c
$%&
'()
= #CL!wingxcm # xcpwing
c
$
%&'
()# CL!ht
xcm # xcphtc
$%&
'()= #CL!wing
lwing
c
$%&
'()# CL!ht
lht
c
$%&
'()
= Cm!wing+ Cm!ht
= #CL!totalStatic Margin (%)
100
$%&
'()
referenced to wing area, S
Horizontal Tail Lift Sensitivity
to Angle of Attack
!CL!"
#$%
&'( horizontailtail
)
*
++
,
-
.
.aircraftreference
= CL"ht( )aircraft =Vtail
VN
#
$%&
'(
2
1/!0!"
#$%
&'(1elas
Sht
S
#$%
&'(CL"ht( )ht
Upwash effect on acanard (i.e., forward)surface
Vtail
: Airspeed at the horizontal tail [Flow over body (), Scrubbing (), Propeller slipstream(+)]
! : Downwash angle due to wing lift at the horizontal tail
"! "# : Sensitivity of downwash angle to angle of attack
$elas
: Correction for aeroelastic effect
Horizontal Tail MomentSensitivity to Angle of Attack
Cm!ht
= "Vtail
VN
#
$%&
'(
2
1")*)!
#$%
&'(+elas
Sht
S
#$%
&'(CL!ht
( )ht
lht
c
#$%
&'(
Normal force (~lift) x moment arm
Effects of Static Margin and Elevator
Deflection on Pitching Coefficient
Zero crossingdetermines trim angleof attack
Negative sloperequired for staticstability
Slope, !Cm/!#, varieswith static margin
Control deflectionaffects Cmo and trimangle of attack
MB = Cmo + Cm!! + Cm"E"E( )q Sc
-
Subsonic Pitching Coefficient
vs. Angle of Attack (0 < # < 90) Pitch Up and Deep Stall
Possibility of 2 stable equilibrium(trim) points with same control setting
Low #
High #
High-angle trim is called deep stall
Low lift
High drag
Large control moment required toregain low-angle trim
Pitch Up andDeep Stall
Possibility of 2stable equilibrium(trim) points withsame controlsetting Low #
High #
High-angle trim iscalled deep stall Low lift
High drag
Large controlmoment requiredto regain low-angle trim
Air Midwest 5481, Beechcraft 1900Dhttp://www.youtube.com/watch?v=2pVBN9cLVuc
Colgan Flight 3407, Bombardier, Dash 8 Q400http://www.youtube.com/watch?v=lxywEE1kK6I&feature=fvw
Next Time:Aircraft Performance