Configuration Aerodynamics - 1

Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2012!

•  Configuration Variables"•  Lift"

–  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!

Description of Aircraft Configuration�

Republic F-84F"

A Few Definitions" Wing Planform Variables"•  Aspect Ratio" •  Taper Ratio"

λ =ctipcroot

=tip chord

root chord

AR = bc

rectangular wing

=b×bc×b

=b2

Sany wing

•  Rectangular Wing" •  Delta Wing" •  Swept Trapezoidal Wing"

Mean Aerodynamic Chord and Wing Center of Pressure"

c =1S

c2 y( )dy−b 2

b 2

∫

=23

#$%

&'(

1+ λ + λ2

1+ λcroot [for trapezoidal wing]

from Raymer!

•  Mean aerodynamic chord (m.a.c.) ~ mean geometric chord"

•  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."

from Sunderland!

Trapezoidal Wing"

Elliptical Wing"

Mid-chord !line!

Medium to High Aspect Ratio Configurations"Cessna 337! DeLaurier Ornithopter! Schweizer 2-32!

•  Typical for subsonic aircraft"

Boeing 777-300!

Mtypical = 75 mph!hmax = 35 kft!

Mcruise = 0.84!hcruise = 35 kft!

Vtakeoff = 82 km/h!hcruise = 15 ft!

Vcruise = 144 mph!hcruise = 10 kft!

Low Aspect Ratio Configurations"North American A-5A Vigilante"

•  Typical for supersonic aircraft" Lockheed F-104 Starfighter"

Mmax = 1.25!hceiling = 53 kft!

Mmax = 2!hceiling = 52 kft!

Mcruise = 1.4!hcreiling= 50 kft!

Variable Aspect Ratio Configurations"General Dynamics F-111!

North American B-1!

•  Aerodynamic efficiency at sub- and supersonic speeds"

Mcruise = 0.9!Mmax = 1.25!hcruise = 50 kft!Mmax = 2.5!

hceiling = 65 kft!

Sweep Effect on Thickness Ratio"

Grumman F-14!

from Asselin!

Reconnaissance Aircraft"Lockheed U-2 (ER-2)" Lockheed SR-71 Trainer"

•  Subsonic, high-altitude flight" •  Supersonic, high-altitude flight"

Mcruise = 3!hcruise = 85 kft!

Vcruise = 375 kt!hcruise = 70 kft!

Uninhabited Air Vehicles"Northrop-Grumman/Ryan Global Hawk" General Atomics Predator"

Vcruise = 70-90 kt!hcruise = 25 kft!

Vcruise = 310 kt!hcruise = 50 kft!

Stealth and Small UAVs"Lockheed-Martin RQ-170" General Atomics Predator-C (Avenger)"

InSitu/Boeing ScanEagle"

http://en.wikipedia.org/wiki/Stealth_aircraft!

Northrop-Grumman X-47B"

Lifting Body Re-Entry Vehicles"Northrop HL-10"

Martin Marietta X-24A"

Northrop M2-F2"

Martin Marietta X-24B"

JAXA ALFLEX" NASA X-38"

http://www.youtube.com/watch?v=K13G1uxNYks!

http://www.youtube.com/watch?v=YCZNW4NrLVY!

Subsonic Biplane"

•  Compared to monoplane"–  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)"

•  Interference effects of two wings"–  Gap"–  Aspect ratio"–  Relative areas and spans"–  Stagger"

Aerodynamic �Lift and Drag�

Longitudinal Aerodynamic Forces and Moment of the Airplane"

Lift = CLq SDrag = CDq SPitching Moment = Cmq Sc

•  Non-dimensional force coefficients are dimensionalized by "

–  dynamic pressure, q"–  reference area, S"

•  Non-dimensional moment coefficients also dimensionalized by "

–  reference length, c!

Typical subsonic lift, drag, and pitching moment variations with angle of attack"

Circulation of Incompressible Air Flow About a 2-D Airfoil"

•  Bernoulli�s equation (inviscid, incompressible flow)"

pstatic +12ρV 2 = constant along streamline = pstagnation

•  Vorticity" Vupper (x) = V∞ + ΔV (x) 2Vlower (x) = V∞ − ΔV (x) 2

γ 2−D (x) =ΔV (x)Δz(x)

•  Circulation"

Γ2−D = γ 2−D (x)dx0

c

∫ Lower pressure on upper surface"

What Do We Mean by 2-Dimensional Aerodynamics?"

•  Finite-span wing –> finite aspect ratio"

AR = bc

rectangular wing

=b × bc × b

=b2

Sany wing

•  Infinite-span wing –> infinite aspect ratio"

What Do We Mean by 2-Dimensional Aerodynamics?"

Lift3−D = CL3−D

12ρV 2 S = CL3−D

12ρV 2 bc( ) [Rectangular wing]

Δ Lift3−D( ) = CL3−D

12ρV 2 cΔy

limΔy→0

Δ Lift3−D( ) = limΔy→0

CL3−D

12ρV 2 cΔy%

&'()*⇒ "2-D Lift" = CL2−D

12ρV 2 c

•  Assuming constant chord section, the �2-D Lift��is the same at any y station of the infinite-span wing"

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"

CL2−D=α

∂CL

∂α

$

%&

'

()

2−D

=α CLα( )2−D= 2π( )α [Lifting-line Theory]

•  Swept wing, 2-D lift slope coefficient"–  Inviscid, incompressible flow"

CL2−D= CLα( )

2−Dα = 2π cosΛ( )α

Classic Airfoil Profiles"

•  NACA 4-digit Profiles (e.g., NACA 2412)"–  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"

NACA Airfoils!http://en.wikipedia.org/wiki/NACA_airfoil!

•  Clark Y (1922): Flat lower surface, 11.7% thickness"

–  GA, WWII aircraft"–  Reasonable L/D"–  Benign computed stall characteristics, but

experimental result is more abrupt"

Fluent, Inc, 2007!

Clark Y Airfoil!http://en.wikipedia.org/wiki/Clark_Y!

Relationship Between Circulation and Lift"

•  2-D Lift (inviscid, incompressible flow)"

Lift( )2−D = ρ∞V∞ Γ( )2−D

12ρ∞V∞

2c 2πα( ) thin, symmetric airfoil[ ] + ρ∞V∞ Γcamber( )2−D

12ρ∞V∞

2c CLα( )2−D

α + ρ∞V∞ Γcamber( )2−D

Talay, NASA SP-367!

•  Positive camber"

•  Neutral camber"

•  Negative camber"

Göttingen 387!

NACA 0012!

Whitcomb!Supercritical!

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"Aero L-39 Albatros!

dL = CL2−Dy( )c y( )qdy

•  3-D wing lift"

L3−D = CL2−Dy( )c y( )q dy

−b /2

b /2

∫

Effect of Aspect Ratio on Wing Lift Slope Coefficient (Incompressible Flow)"

•  Airfoil section lift coefficients and lift slopes near wingtips are lower than their estimated 2-D values"

Talay, NASA SP-367!

Effect of Aspect Ratio on 3-Dimensional Wing Lift

Slope Coefficient (Incompressible Flow)!

•  High Aspect Ratio (> 5) Wing"

CLα

∂CL

∂α

#

$%

&

'(3−D

=2πARAR+2

= 2π ARAR+2#

$%

&

'(

•  Low Aspect Ratio (< 2) Wing"

CLα=πAR2

= 2π AR4

#

$%

&

'(

All wings at M = 1!

Bombardier Dash 8!

Handley Page HP.115! Effect of Aspect Ratio on 3-D Wing Lift Slope Coefficient

(Incompressible Flow)"•  All Aspect Ratios (Helmbold equation)"

CLα=

πAR

1+ 1+ AR2

#

$%

&

'(2)

*++

,

-..

HL-10!Q400!

For Small Angles, Lift is Proportional to Angle of Attack"

Lift = CL12ρV 2S ≈ CL0

+∂CL

∂αα%

&'(

)*12ρV 2S ≡ CL0

+ CLαα%& ()12ρV 2S

where CLα= lift slope coefficient

•  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!

•  Build estimates from component effects"–  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)"

InterferenceEffects

InterferenceEffects

Wing Aerodynamics

Fuselage Aerodynamics

TailAerodynamics

InterferenceEffects

•  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"

Wind Tunnel Data!

Blended Wing-Body Model in Free Flight!http://www.youtube.com/watch?v=B7zMkptajMQ!

Full-Scale P-38!

Sub-Scale Learjet!

Sub-Scale F/A-18!

http://crgis.ndc.nasa.gov/historic/30_X_60_Full_Scale_Tunnel!

Wind Tunnel Force and Moment Data!Three-Strut Mount! Single-Strut Mount!

Sting Balance!High-Angle-of-Attack !

Sting Balance!

Texas A&M!

NACA Free Flight Wind Tunnels"•  Test section angle and airspeed adjusted to gliding flight

path angle and airspeed"

12-ft Free Flight Wind Tunnel!

http://crgis.ndc.nasa.gov/historic/12-Foot_Low_Speed_Tunnel!

5-ft Free Flight Wind Tunnel!

Model in 12-ft Free-Flight Tunnel!http://www.nasa.gov/multimedia/videogallery/index.html?collection_id=16538&media_id=17245841!

Interpreting Wind Tunnel Data!•  Wall corrections, uniformity of the

flow, turbulence, flow recirculation, temperature, external winds (open circuit)"

•  Open-throat tunnel equilibrates pressure"

•  Tunnel mounts and balances: struts, wires, stings, magnetic support"

•  Simulating power effects, flow-through effects, aeroelastic deformation, surface distortions"

•  Artifices to improve reduced/full-scale correlation, e.g., boundary layer trips and vortex generators"

Full-Scale F-84!

Full-Scale P-51 Fuselage!

Sub-Scale !Supersonic Transport!

Computational Fluid Dynamics!•  Strip theory"

–  Sum or integrate 2-D airfoil force and moment estimates over wing and tail spans"

•  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"

Aerodynamic Stall, Theory and Experiment"

Anderson et al, 1980!

•  Flow separation produces stall"•  Straight rectangular wing, AR = 5.536, NACA 0015"•  Hysteresis for increasing/decreasing α!

Angle of Attack for

CL max!

Maximum Lift of Rectangular Wings"

Schlicting & Truckenbrodt, 1979!

Aspect Ratio"

Maximum"Lift "

Coefficient,"CL max!

ϕ : Sweep angleδ : Thickness ratio

Maximum Lift of Delta Wings with Straight Trailing Edges"

δ : Taper ratioAspect Ratio"

Angle of Attack for CL max!

Maximum Lift "Coefficient, CL max!

Aspect Ratio"

Schlicting & Truckenbrodt, 1979!

Large Angle Variations in Subsonic Lift Coefficient (0° < α < 90°)"

Lift = CL12ρV 2S

•  All lift coefficients have at least one maximum (stall condition)"

•  All lift coefficients are essentially Newtonian at high !"

•  Newtonian flow: TBD"

Flap Effects on Aerodynamic Lift"

•  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)"

Subsonic Air Compressibility and Sweep Effects on 3-D Wing Lift Slope"

•  Subsonic 3-D wing, with sweep effect"

CLα=

πAR

1+ 1+ AR2cosΛ1 4

$

%&&

'

())

2

1−M 2 cosΛ1 4( )+

,

---

.

/

000

€

Λ1 4 = sweep angle of quarter chord

Supersonic Compressibility Effects on Triangular Wing Lift Slope"

•  Supersonic delta (triangular) wing"

CLα=

4M 2 −1

Supersonic leading edge"

CLα=2π 2 cotΛπ + λ( )

where λ = m 0.38 + 2.26m − 0.86m2( )m = cotΛLE cotσ

Subsonic leading edge"

€

ΛLE = sweep angle of leading edge

Supersonic Effects on Arbitrary Wing and Wing-Body 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"

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"

Drag = CD12ρV 2S ≈ CD0

+ εCL2( ) 12 ρV

2S

≈ CD0+ ε CLo

+ CLαα( )2%

&'()*12ρV 2S

Parasitic Drag"

•  Pressure differential, viscous shear stress, and separation"

Parasitic Drag = CD0

12ρV 2S

Talay, NASA SP-367!

Reynolds Number and Boundary Layer"

Reynolds Number = Re = ρVlµ

=Vlν

whereρ = air densityV = true airspeedl = characteristic lengthµ = absolute (dynamic) viscosityν = kinematic viscosity

Reynolds Number, Skin Friction, and Boundary Layer"•  Skin friction coefficient for a flat plate"

Cf =Friction Drag

qSwetwhere Swet = wetted area

Cf ≈ 1.33Re−1/2 laminar flow[ ]

≈ 0.46 log10 Re( )−2.58 turbulent flow[ ]

•  Boundary layer thickens in transition, then thins in turbulent flow"

Wetted Area: Total surface area of the wing or aircraft, subject to skin friction"

Typical Effect of Reynolds Number on Parasitic Drag"

from Werle*!

* See Van Dyke, M., An Album of Fluid Motion, Parabolic Press, Stanford, 1982"

•  Flow may stay attached farther at high Re, reducing the drag"

Effect of Streamlining on Parasitic Drag"

Talay, NASA SP-367!

Some Videos"•  Flow over a narrow airfoil, with

downstream vortices"http://www.youtube.com/watch?v=zsO5BQA_CZk!

http://www.youtube.com/watch?v=0z_hFZx7qvE!

•  Flow over transverse flat plate, with downstream vortices"

http://www.youtube.com/watch?v=WG-YCpAGgQQ&feature=related!

•  Laminar vs. turbulent flow"

http://www.youtube.com/watch?v=iNBZBChS2YI!

•  Supersonic wind tunnel Schlieren imaging demonstration"

More Videos"•  YF-12A supersonic flight past the sun"

•  Supersonic flight, sonic booms"

•  Smoke flow visualization, wing with flap"

•  1930s test in NACA wind tunnel"

http://www.youtube.com/watch?v=atItRcfFwgw&feature=related!

http://www.youtube.com/watch?v=gWGLAAYdbbc&list=LP93BKTqpxbQU&index=1&feature=plcp!

http://www.youtube.com/watch?feature=fvwp&NR=1&v=eBBZF_3DLCU/!

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 �