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Configuration
Aerodynamics - 1
Robert Stengel, Aircraft Flight Dynamics,
MAE 331, 2012
!
•  Configuration Variables"
•  Lift"
Description of Aircraft
Configuration
–  Effects of shape, angle, and
Mach number"
–  Stall"
•  Parasitic Drag"
–  Skin friction"
–  Base drag"
Copyright 2012 by Robert Stengel. All rights reserved. For educational use only.!
http://www.princeton.edu/~stengel/MAE331.html!
http://www.princeton.edu/~stengel/FlightDynamics.html!
Wing Planform Variables"
A Few Definitions"
• 
Aspect Ratio"
b
AR =
c
• 
rectangular wing
λ=
2
=
• 
Republic F-84F"
Taper Ratio"
b×b b
=
c×b S
Rectangular Wing"
• 
any wing
Delta Wing"
• 
ctip
tip chord
=
croot root chord
Swept Trapezoidal Wing"
Mean Aerodynamic Chord and
Wing Center of Pressure"
• 
Medium to High Aspect Ratio Configurations"
Cessna 337!
DeLaurier Ornithopter!
Mean aerodynamic chord (m.a.c.) ~ mean geometric chord"
Vtakeoff = 82 km/h!
hcruise = 15 ft!
b2
1
c = ∫ c 2 ( y ) dy
S −b 2
Vcruise = 144 mph!
hcruise = 10 kft!
2
# 2& 1+ λ + λ
=% (
croot
$ 3' 1 + λ
Schweizer 2-32!
[for trapezoidal wing]
Trapezoidal Wing"
• 
Mtypical = 75 mph!
hmax = 35 kft!
Axial location of the wing s subsonic
aerodynamic center (a.c.)"
–  Determine spanwise location of m.a.c."
–  Assume that aerodynamic center is at
25% m.a.c."
Mcruise = 0.84!
hcruise = 35 kft!
• 
Midchord !
line!
Typical for subsonic aircraft"
Elliptical Wing"
from Raymer!
Boeing 777-300!
from Sunderland!
Low Aspect Ratio Configurations"
Variable Aspect Ratio Configurations"
North American B-1!
General Dynamics F-111!
North American A-5A Vigilante"
Mmax = 2!
hceiling = 52 kft!
Mmax = 1.25!
hceiling = 53 kft!
• 
Typical for supersonic aircraft"
Lockheed F-104 Starfighter"
Mcruise = 1.4!
hcreiling= 50 kft!
Mmax = 2.5!
hceiling = 65 kft!
• 
Mcruise = 0.9!
Mmax = 1.25!
hcruise = 50 kft!
Aerodynamic efficiency at sub- and supersonic speeds"
Reconnaissance Aircraft"
Sweep Effect on Thickness Ratio"
Lockheed U-2 (ER-2)"
Lockheed SR-71 Trainer"
Grumman F-14!
Vcruise = 375 kt!
hcruise = 70 kft!
Mcruise = 3!
hcruise = 85 kft!
from Asselin!
• 
Uninhabited Air Vehicles"
Northrop-Grumman/Ryan Global Hawk"
General Atomics Predator"
Subsonic, high-altitude flight"
• 
Supersonic, high-altitude flight"
Stealth and Small UAVs"
Lockheed-Martin RQ-170"
Northrop-Grumman X-47B"
Vcruise = 70-90 kt!
hcruise = 25 kft!
Vcruise = 310 kt!
hcruise = 50 kft!
http://en.wikipedia.org/wiki/Stealth_aircraft!
General Atomics Predator-C (Avenger)"
InSitu/Boeing ScanEagle"
Lifting Body Re-Entry Vehicles"
Subsonic Biplane"
Northrop HL-10"
•  Compared to monoplane"
Martin Marietta X-24A"
–  Structurally stiff (guy wires)"
–  Twice the wing area for the same
span"
–  Lower aspect ratio than a single
wing with same area and chord"
–  Mutual interference"
–  Lower maximum lift"
–  Higher drag (interference, wires)"
Northrop M2-F2"
JAXA ALFLEX"
NASA X-38"
•  Interference effects of two wings"
– 
– 
– 
– 
Martin Marietta X-24B"
Gap"
Aspect ratio"
Relative areas and spans"
Stagger"
http://www.youtube.com/watch?v=K13G1uxNYks!
http://www.youtube.com/watch?v=YCZNW4NrLVY!
Longitudinal Aerodynamic Forces
and Moment of the Airplane"
Aerodynamic
Lift and Drag
• 
Non-dimensional force
coefficients are dimensionalized
by "
–  dynamic pressure, q"
–  reference area, S"
• 
Non-dimensional moment
coefficients also
dimensionalized by "
–  reference length, c!
Lift = C L q S
Drag = C D q S
Pitching Moment = Cm q Sc
Typical subsonic lift, drag, and pitching
moment variations with angle of attack"
Circulation of Incompressible Air Flow
About a 2-D Airfoil"
• 
pstatic +
• 
What Do We Mean by 2-Dimensional Aerodynamics?"
Bernoulli s equation (inviscid, incompressible flow)"
1 2
ρV = constant along streamline = pstagnation
2
Vorticity"
• 
Finite-span wing –> finite aspect ratio"
Vupper (x) = V∞ + ΔV (x) 2
b
rectangular wing
c
b × b b2
=
any wing
=
c×b S
AR =
Vlower (x) = V∞ − ΔV (x) 2
γ 2 − D (x) =
• 
Circulation"
ΔV (x)
Δz(x)
• 
Infinite-span wing –> infinite aspect ratio"
c
Γ 2 − D = ∫ γ 2 − D (x)dx
Lower pressure on upper surface"
0
What Do We Mean by 2Dimensional Aerodynamics?"
For Small Angles, Lift is
Proportional to Angle of Attack"
• 
Unswept wing, 2-D lift slope coefficient"
–  Inviscid, incompressible flow"
–  Referenced to chord length, c, rather than wing area"
• 
Assuming constant chord section, the 2-D Lift is
the same at any y station of the infinite-span wing"
1 2
1
ρV S = C L3− D ρV 2 ( bc ) [Rectangular wing]
2
2
1 2
Δ ( Lift 3− D ) = C L3− D ρV cΔy
2
1
1
%
(
lim Δ ( Lift 3− D ) = lim ' C L3− D ρV 2 cΔy* ⇒ "2-D Lift" = C L2− D ρV 2 c
Δy→0
Δy→0 &
)
2
2
Lift 3− D = C L3− D
$ ∂C '
C L2−D = α & L ) = α (C Lα )2−D = ( 2 π ) α [Lifting-line Theory]
% ∂α (2−D
• 
Swept wing, 2-D lift slope coefficient"
–  Inviscid, incompressible flow"
( )
C L2− D = C Lα
2− D
α = ( 2π cos Λ )α
Relationship Between
Circulation and Lift"
Classic Airfoil
Profiles"
• 
NACA 4-digit Profiles (e.g., NACA 2412)"
• 
NACA Airfoils!
http://en.wikipedia.org/wiki/NACA_airfoil!
( Lift )2 − D = ρ∞V∞ ( Γ )2 − D
–  Maximum camber as percentage of chord (2)"
–  Distance of maximum camber from leading
edge, (4) = 40%"
–  Maximum thickness as percentage of chord (12)"
–  See NACA Report No. 460, 1935, for lift and drag
characteristics of 78 airfoils"
• 
2-D Lift (inviscid, incompressible flow)"
1
ρ∞V∞2 c ( 2πα ) [ thin, symmetric airfoil ] + ρ∞V∞ ( Γ camber )2 − D
2
1
 ρ∞V∞2 c C Lα
α + ρ∞V∞ ( Γ camber )2 − D
2− D
2

( )
Clark Y (1922): Flat lower surface, 11.7%
thickness"
–  GA, WWII aircraft" Clark Y Airfoil!
http://en.wikipedia.org/wiki/Clark_Y!
–  Reasonable L/D"
–  Benign computed stall characteristics, but
experimental result is more abrupt"
• 
Positive camber"
• 
Neutral camber"
• 
Negative camber"
Göttingen 387!
NACA 0012!
Whitcomb!
Supercritical!
Fluent, Inc, 2007!
Talay, NASA SP-367!
Effect of Aspect Ratio on Wing
Lift Slope Coefficient
(Incompressible Flow)"
Aerodynamic Strip Theory"
• 
Airfoil section may vary from tip-to-tip"
– 
– 
– 
– 
Chord length"
Airfoil thickness"
Airfoil profile"
Airfoil twist"
• 
Lift of a 3-D wing is found by integrating 2-D lift
coefficients of airfoil sections across the finite span"
• 
Incremental lift along span"
dL = C L2− D ( y ) c ( y ) qdy
• 
3-D wing lift"
Aero L-39 Albatros!
• 
Airfoil section lift
coefficients and
lift slopes near
wingtips are lower
than their
estimated 2-D
values"
b /2
L3− D =
∫
−b /2
C L2− D ( y ) c ( y ) q dy
Talay, NASA SP-367!
Bombardier
Dash 8!
Effect of Aspect Ratio on
3-Dimensional Wing Lift
Slope Coefficient
Handley Page HP.115!
(Incompressible Flow)!
•  High Aspect Ratio (> 5) Wing"
Effect of Aspect Ratio on 3-D
Wing Lift Slope Coefficient
(Incompressible Flow)"
•  All Aspect Ratios (Helmbold equation)"
# ∂C &
# AR &
2 π AR
C Lα  % L ( =
= 2π %
(
$ ∂α '3−D AR + 2
$ AR + 2 '
C Lα =
•  Low Aspect Ratio (< 2) Wing"
# AR &
π AR
C Lα =
= 2π %
(
$ 4 '
2
Q400!
π AR
2,
)
+1+ 1+ #% AR &( .
$ 2 ' .+*
HL-10!
All wings at M = 1!
For Small Angles, Lift is
Proportional to Angle of Attack"
1 2
∂C ( 1
1
%
ρV S ≈ 'C L0 + L α * ρV 2 S ≡ %&C L0 + C Lα α () ρV 2 S
2
2
∂α
2
&
)
where C Lα = lift slope coefficient
Lift = C L
•  At higher angles, "
–  flow separates"
–  wing loses lift"
•  Flow separation
produces stall"
http://www.youtube.com/watch?v=RgUtFm93Jfo!
Aerodynamic Estimation
and Measurement
Handbook Approach to
Aerodynamic Estimation!
NASA 30 x 60 Tunnel"
Full-scale aircraft on balance"
Sub-scale aircraft on sting"
Sub-scale aircraft in free flight"
Maximum airspeed = 118 mph"
Constructed in 1931 for $37M (~
$500M in today s dollars)"
–  Two 4000-hp electric motors"
–  USAF Stability and Control DATCOM (download at
http://www.pdas.com/datcomb.html)"
–  USAF Digital DATCOM (see Wikipedia page)"
–  ESDU Data Sheets (see Wikipedia page)"
Interference
Effects
• 
– 
– 
– 
– 
– 
•  Build estimates from component effects"
Interference
Effects
Wind Tunnel Data!
Sub-Scale Learjet!
Tail
Aerodynamics
Fuselage
Aerodynamics
Wing
Aerodynamics
Full-Scale P-38!
Interference
Effects
Sub-Scale F/A-18!
Blended Wing-Body Model in Free Flight!
http://www.youtube.com/watch?v=B7zMkptajMQ!
Wind Tunnel Force and Moment Data!
Three-Strut Mount!
Single-Strut Mount!
NACA Free Flight Wind Tunnels"
• 
Test section angle and airspeed adjusted to gliding flight
path angle and airspeed"
5-ft Free Flight Wind Tunnel!
Sting Balance!
http://crgis.ndc.nasa.gov/historic/30_X_60_Full_Scale_Tunnel!
12-ft Free Flight Wind Tunnel!
High-Angle-of-Attack!
Sting Balance!
Model in 12-ft Free-Flight Tunnel!
http://www.nasa.gov/multimedia/videogallery/index.html?collection_id=16538&media_id=17245841!
Texas A&M!
http://crgis.ndc.nasa.gov/historic/12-Foot_Low_Speed_Tunnel!
Interpreting Wind Tunnel Data!
• 
Wall corrections, uniformity of the
flow, turbulence, flow recirculation,
temperature, external winds (open
circuit)"
Full-Scale F-84!
Computational Fluid Dynamics!
• 
–  Sum or integrate 2-D airfoil force
and moment estimates over wing
and tail spans"
• 
• 
Open-throat tunnel equilibrates
pressure"
• 
Tunnel mounts and balances: struts,
wires, stings, magnetic support"
• 
Simulating power effects, flowthrough effects, aeroelastic
deformation, surface distortions"
• 
Artifices to improve reduced/fullscale correlation, e.g., boundary layer
trips and vortex generators"
Strip theory"
Full-Scale P-51 Fuselage!
3-D calculations at grid points"
–  Finite-element or finite-difference
modeling"
–  Pressures and flow velocities (or
vorticity) at points or over panels of
aircraft surface"
–  Euler equations neglect viscosity"
–  Navier-Stokes equations do not"
Sub-Scale !
Supersonic Transport!
Aerodynamic Stall, Theory and Experiment"
•  Flow separation produces stall"
•  Straight rectangular wing, AR = 5.536, NACA 0015"
•  Hysteresis for increasing/decreasing α!
Maximum Lift of
Rectangular Wings"
Maximum"
Lift "
Coefficient,"
CL max!
Schlicting & Truckenbrodt, 1979!
Angle of
Attack for
CL max!
Anderson et al, 1980!
Aspect Ratio"
ϕ : Sweep angle
δ : Thickness ratio
Maximum Lift of Delta Wings with
Straight Trailing Edges"
Maximum Lift"
Coefficient, CL max!
Large Angle Variations in Subsonic
Lift Coefficient (0° < α < 90°)"
Angle of Attack
for CL max!
Lift = C L
Aspect Ratio"
Aspect Ratio"
δ : Taper ratio
1 2
ρV S
2
•  All lift coefficients
have at least one
maximum (stall
condition)"
•  All lift coefficients
are essentially
Newtonian at high
!"
•  Newtonian flow:
TBD"
Schlicting & Truckenbrodt, 1979!
Flap Effects on
Aerodynamic Lift"
Subsonic Air Compressibility and
Sweep Effects on 3-D Wing Lift Slope"
•  Subsonic 3-D wing, with sweep effect"
C Lα =
• 
• 
• 
• 
Camber modification"
Trailing-edge flap deflection
shifts CL up and down"
Leading-edge flap (slat)
deflection increases stall α"
Same effect applies for
other control surfaces"
–  Elevator (horizontal tail)"
–  Ailerons (wing)"
–  Rudder (vertical tail)"
π AR
2
+
.
-1+ 1+ $& AR ') 1− M 2 cos Λ 0
(
)
1
4
& 2 cos Λ )
0
14 (
%
-,
0/
Λ1 4 = sweep angle of quarter chord
Supersonic Effects on Arbitrary Wing
and Wing-Body Lift Slope"
Supersonic Compressibility Effects on
Triangular Wing Lift Slope"
•  Impinging shock waves"
•  Discrete areas with differing M and
local pressure coefficients, cp!
•  Areas change with α!
•  No simple equations for lift slope"
•  Supersonic delta (triangular) wing"
Supersonic leading edge"
C Lα =
4
M2 −1
Subsonic leading edge"
C Lα =
2π 2 cot Λ
(π + λ )
(
where λ = m 0.38 + 2.26m − 0.86m 2
)
m = cot Λ LE cot σ
Λ LE = sweep angle of leading edge
Schlicting & Truckenbrodt, 1979!
€
Wing-Fuselage Interference Effects"
• 
Wing lift induces"
–  Upwash in front of the wing"
–  Downwash behind the wing, having major effect on the tail"
–  Local angles of attack over canard and tail surface are modified,
affecting net lift and pitching moment"
• 
Flow around fuselage induces upwash on the wing, canard,
and tail"
from Etkin!
Aerodynamic Drag"
1 2
1
ρV S ≈ C D0 + ε C L2 ρV 2 S
2
2
2 1
+ ε C Lo + C Lα α (* ρV 2 S
)2
(
Drag = C D
≈ %'C D0
&
(
)
)
Parasitic Drag"
Reynolds Number and Boundary Layer"
Reynolds Number = Re =
•  Pressure differential,
viscous shear stress,
and separation"
Parasitic Drag = C D0
1 2
ρV S
2
ρVl Vl
=
µ
ν
where
ρ = air density
V = true airspeed
l = characteristic length
µ = absolute (dynamic) viscosity
ν = kinematic viscosity
Talay, NASA SP-367!
Typical Effect of Reynolds
Number on Parasitic Drag"
Reynolds Number,
Skin Friction, and
Boundary Layer"
• 
Flow may stay attached
farther at high Re,
reducing the drag"
•  Skin friction coefficient for a flat plate"
Friction Drag
qSwet
where Swet = wetted area
Cf =
from Werle*!
•  Boundary layer thickens in transition,
then thins in turbulent flow"
C f ≈ 1.33Re −1/2
≈ 0.46 ( log10
[laminar flow ]
Re )
[turbulent
−2.58
flow ]
Wetted Area: Total surface area of the
wing or aircraft, subject to skin friction"
* See Van Dyke, M., An Album of Fluid Motion,
Parabolic Press, Stanford, 1982"
Effect of Streamlining on Parasitic Drag"
Some Videos"
•  Flow over a narrow airfoil, with
downstream vortices"
http://www.youtube.com/watch?v=zsO5BQA_CZk!
•  Flow over transverse flat plate, with
downstream vortices"
http://www.youtube.com/watch?v=0z_hFZx7qvE!
•  Laminar vs. turbulent flow"
http://www.youtube.com/watch?v=WG-YCpAGgQQ&feature=related!
•  Supersonic wind tunnel Schlieren
imaging demonstration"
Talay, NASA SP-367!
http://www.youtube.com/watch?v=iNBZBChS2YI!
More Videos"
•  YF-12A supersonic flight past the sun"
http://www.youtube.com/watch?v=atItRcfFwgw&feature=related!
•  Supersonic flight, sonic booms"
http://www.youtube.com/watch?
v=gWGLAAYdbbc&list=LP93BKTqpxbQU&index=1&feature=plcp!
•  Smoke flow visualization, wing with flap"
http://www.youtube.com/watch?feature=fvwp&NR=1&v=eBBZF_3DLCU/!
•  1930s test in NACA wind tunnel"
http://www.youtube.com/watch?v=3_WgkVQWtno&feature=related!
Next Time:
Configuration
Aerodynamics – 2
Reading
Flight Dynamics, 84-103
Virtual Textbook, Part 4,5