AircrAircraft Flight Dynamics Robert F. Stengel Lecture5 Configuration Aerodynamics 1

~ 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...

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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"

http://www.princeton.edu/~stengel/MAE331.html !

http://www.princeton.edu/~stengel/FlightDynamics.html !

Description of Aircraft

Configuration

Republic F-84F"

•   Aspect Ratio "

•   Taper Ratio "

λ = c tip

c root =

tip chord root chord

AR = b

c rectangular wing

=b × b

c × b=

b2

S any wing

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

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Mean Aerodynamic Chord and

Wing Center of Pressure"

c =1

2

y

( )dy

−b 2

b 2

∫

= 2 3

#

$%

&

'(

1 + λ + λ 2

1 + λ c root [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!

M typical = 75 mph!

h max = 35 kft!

M cruise = 0.84!

h cruise = 35 kft!

V takeoff = 82 km/h!

h cruise = 15 ft!

V cruise = 144 mph!

Low Aspect Ratio Configurations"

North American A-5A Vigilante"

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

M max = 1.25!

h ceiling = 53 kft!

M max = 2!

M cruise = 1.4!

h creiling= 50 kft!

Variable Aspect Ratio Configurations"

General Dynamics F-111!

North American B-1!

•   Aerodynamic efficiency at sub- and supersonic speeds "

M cruise = 0.9!

M max = 1.25!

M max = 2.5!

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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 "

M cruise = 3!

V cruise = 375 kt!

Uninhabited Air Vehicles"

Northrop-Grumman/Ryan Global Hawk" General Atomics Predator"

V cruise = 70-90 kt!

V cruise = 310 kt!

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"

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Lifting Body Re-Entry Vehicles"

Northrop HL-10"

Martin Marietta X-24A"

Northrop M2-F2"

Martin Marietta X-24B"

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

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

Subsonic Biplane"

–   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 = C L q S Drag = C D q S Pitching Moment = C q 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"

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Circulation of Incompressible Air Flow

•   Bernoulli s equation (inviscid, incompressible flow)"

p static+1

2ρV

2

= constant along streamline = p stagnation

•   Vorticity" V upper (x) = V∞+ ΔV (x) 2

V lower (x) = V∞− ΔV (x) 2

γ2 − D (x) = ΔV (x)

Δz(x)

•   Circulation"

Γ2 − D = γ2 − D (x)dx

0

c

What Do We Mean by   2-Dimensional Aerodynamics?"

•   Finite-span wing –> finite aspect ratio"

AR = b

c rectangular wing

=b × b

c × b=

2

S any wing

•   Infinite-span wing –> infinite aspect ratio"

What Do We Mean by

2-Dimensional Aerodynamics?"

Lift 3− D = C L 3− D1

2ρV2

S = C L 3− D

1

2ρV2

bc

( ) [Rectangular wing]

Δ Lift( 3− D)= C L 3− D1

2ρV2

cΔy

lim

Δy→0 Δ Lift( 3− D) = lim

Δy→0 C L 3− D1

2ρV2

cΔy

%

&'

( )*⇒ "2-D Lift"= C L 2− D

1

2ρV2

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 "

2−D= α ∂C L

∂α

$

%

& ' (

)

2−D

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

•   Swept wing, 2-D lift slope coefficient"

–   Inviscid, incompressible flow "

2− D = C( )Lα 2 − Dα = 2π cos Λ ( ) α

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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∞ ( ) Γ2 − D

1

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

1

2ρ∞V∞ 2

c C( )Lα 2 − Dα + 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 = C L 2− D( )y c y( )qdy

•   3-D wing lift"

L 3− D= C L

2− D( )y c y( )q dy

−b /2

b /2

∫

Effect of Aspect Ratio on Wing

Lift Slope Coefficient

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

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Effect of Aspect Ratio on 3-Dimensional Wing Lift Slope Coefficient

(Incompressible Flow)!

•   High Aspect Ratio (> 5) Wing "

C L

∂α

#

$

'

(

3−D

AR + 2 = 2π

AR

AR + 2

#

$

' (

•   Low Aspect Ratio (< 2) Wing "

C Lα = πAR

AR

4

#

$

' (

All wings at M = 1!

Dash 8!

Wing Lift Slope Coefficient

•   All Aspect Ratios (Helmbold equation)"

2

#

$

% &

' (

2

)

*

+ +

,

- .

HL-10!

Q400!

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

Lift = C L1

2ρV

2

S ≈ C L0+∂C L

∂α α

%

&'

( )*

1

2ρV

2

S ≡ C%& L0 +C Lαα ()12ρV2S where C L

α = lift slope coefficient

•   At higher angles, "

•   Flow separation

produces stall "

http://www.youtube.com/watch?v=RgUtFm93Jfo!

Aerodynamic Estimation and Measurement

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Handbook Approach to

•  Build estimates from component effects"

http://www.pdas.com/datcomb.html)"

Interference Effects Interference

Effects Wing Aerodynamics

Fuselage Aerodynamics

Tail Aerodynamics

Interference Effects

–   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 "

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!

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 !

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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!

•  Strip theory"

and moment estimates over wing

•  3-D calculations at grid points"

modeling"

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

C L max !

Maximum Lift of Rectangular Wings"

Schlicting & Truckenbrodt, 1979!

Aspect Ratio"

Maximum"

Lift "

Coefficient,"

C L max !

ϕ : Sweep angle δ: Thickness ratio

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Maximum Lift of Delta Wings with

Straight Trailing Edges"

δ: Taper ratio

Aspect Ratio"

Angle of Attack for CL max !

Maximum Lift "

Coefficient, CL max !

Aspect Ratio"

Large Angle Variations in Subsonic

•   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"

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 "

2 cos Λ 1 4

$

%

&& '

( ))

2

1−M2

cos Λ 1 4

+ ,

- /

0 0 0

€

Λ1 4 = sweep angle of quarter chord

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Supersonic Compressibility Effects on

Triangular Wing Lift Slope"

•   Supersonic delta (triangular) wing "

− 1

Supersonic 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

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, c p !

•   Areas change with α!

•   No simple equations for lift slope "

Wing-Fuselage Interference Effects"

–   Upwash in front of the wing"

–   Downwash behind the wing, having major effect on the tail"

and tail"

from Etkin!

Aerodynamic Drag"

Drag = C D 1

2

S ≈ C D0 + εC L2

S

≈ C D0 + ε(C L o + C Lαα)2

%

1

2

S

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Parasitic Drag"

•   Pressure differential, viscous shear stress, and separation "

2ρV

2

S

Reynolds Number and Boundary Layer"

Reynolds Number = Re = ρVl

Vl

ν

where

ρ = air density

V = true airspeed

l = characteristic length

µ = absolute (dynamic) viscosity

ν = kinematic viscosity

Reynolds Number,

Skin Friction, and

Boundary Layer"

•  Skin friction coefficient for a flat plate"

C f = Friction Drag

qS wet where S wet = wetted area

C f ≈ 1.33Re−1/2 [laminar flow]

≈ 0.46 log( 10 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*!

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

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Effect of Streamlining on Parasitic Drag"

Some Videos"

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!

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

Tiêu đề	Configuration Aerodynamics - 1
Tác giả	Robert Stengel
Trường học	Princeton University
Chuyên ngành	Aircraft Flight Dynamics
Thể loại	lecture
Năm xuất bản	2012
Thành phố	Princeton

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Số trang	13
Dung lượng	1,65 MB