Aircraft Flight Dynamics Robert F. Stengel Lecture24 Configuration and Power Effects on Flight Stability

Configuration and Power Effects Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2012" • Wing design" • Empennage design" • Aerodynamic coefficient estimation and measurement" • Powe

Configuration and Power Effects

Robert Stengel, Aircraft Flight Dynamics, MAE 331,

2012"

•   Wing design"

•   Empennage design"

•   Aerodynamic coefficient

estimation and measurement"

•   Power Effects"

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 !

Loss of Engine"

(and sometimes rolling) moment(s), requiring major application of controls "

especially during takeoff, for both propeller and jet aircraft"

graduating from single-engine aircraft"

Beechcraft Baron! Learjet 60!

Solutions to the

Engine-Out Problem"

•  Engines on the centerline (Cessna

337 Skymaster)"

•  More engines (B-36)"

•  Cross-shafting of engines (V-22)"

•  Large vertical tail (Boeing 737)"

NASA TCV (Boeing 737)!

Cessna 337!

Convair B-36!

Boeing/Bell V-22!

Airplane Balance "

–  c.m near wing's aerodynamic center (point at which wing's

pitching moment coefficient is invariant with angle of attack

~25% mac)"

Northrop N-9M!

Airplane Balance "

•   Canard configuration : "

–  Neutral point moved forward by canard surfaces"

–  Center of mass may be behind the neutral point, requiring

closed-loop stabilization"

•   Fly-by-wire feedback control can expand envelope

of allowable center-of-mass locations (e.g.,

open-loop instability"

Grumman X-29!

McDonnell-Douglas X-36!

Configuration Effects Can Be Evaluated via Approximate Dynamic Models"

λRoll ≈ L p ≈ C l ˆp

ρV N

4I xx

$

%&

' ()Sb

2

ωn ≈ − Mα+ M q

Lα

V N

%

&'

( )* ; ζ ≈

Lα

V N − M q

%

&' ( )*

2 − Mα+ M q

Lα

V N

%

&'

( )*

ωnDR ≈ Nβ1 −Y r

V N

( )+ N r Yβ V

N

ζDR ≈ − N r+Yβ

V N

&

'(

)

*+ 2 Nβ 1 −Y r

V N

( )+ N r

Yβ

V N

•  Phugoid Mode"

•  Short-Period Mode"

•  Dutch Roll Mode"

•  Roll Mode"

ωn ≈ gL V / V N; ζ≈D V

2 gL V / V N

λSpiral≈ 0

•  Spiral Mode"

However, important mode-coupling terms, e.g., M V and L!,

are neglected "

•   Straight Wing "

–  Subsonic center of

pressure (c.p.) at ~1/4

mean aerodynamic

chord (m.a.c.) "

–  Transonic-supersonic

c.p at ~1/2 m.a.c "

•   Delta Wing "

–  Subsonic-supersonic

c.p at ~2/3 m.a.c."

Planform Effect on Center of

Pressure Variation with Mach

Number"

•   Mach number "

–   increases the static margin of conventional configurations -> Short Period "

–   Has less effect on delta wing static margin "

C m

α

Sweep Reduces Subsonic Lift Slope "

C L

1 + 1 + AR

2 cos Λ 1 4

$

% ' (

2

1 − M2 cos Λ 1 4

+ ,

- / 0 0

1 + 1 + AR

2 cos Λ 1 4

$

% ' (

2

+ ,

- / 0 0 [Incompressible flow]

C L

α =2π

2 cot ΛLE

where λ= m 0.38 + 2.26m − 0.86m2

m = cot Λ LE cotσ

Λ ,σ: measured from y axis

Swept Wing"

Triangular Wing"

Effects of Wing Aspect Ratio "

λRoll ≈ L p ≈ C l ˆp

ρV N

4I xx

$

%&

' ()Sb

2

ωn = − Mα+ M q Lα

V N

$

%&

' () ; ζ =

Lα

V N − M q

$

%&

' ()

2 − Mα+ M q Lα

V N

$

%&

' ()

ωn≈ 2g V

2 L / D( )N

Short Period"

Phugoid"

Roll"

Effects of Wing Aspect Ratio and

Sweep Angle "

•   Lift slope"

•   Pitching moment slope"

•   Lift-to-drag ratio"

•   All contribute to"

–   Phugoid damping"

–   Short period natural frequency and damping"

–   Roll damping"

p,C l

β

•  !c/4 = sweep

angle of

quarter-chord"

•  Sweep moves lift

distribution

toward wing tips"

•  Sweep increases

dihedral effect of

wing!

CL

α,Cm

α,Cl p,Cl

β

Sweep Effect on

wings induces rolling motion "

•  Lateral-directional ( spiral mode ) stability effect (TBD)" C l

β

Modes Strongly Affected

By The Empennage "

ωn ≈ − Mα+ M q Lα

V N

%

&'

( )*

ζ ≈ Lα

V N − M q

%

&'

( )* 2 − Mα+ M q Lα

V N

%

&'

( )*

ωn DR ≈ Nβ+ N r

Yβ

V N

ζDR ≈ − N r+ β

V N

&

'(

)

*+ 2 Nβ+ N r Yβ

V N

•  Short-Period Mode (horizontal tail)"

•  Dutch Roll Mode (vertical tail)"

C m

α,C m q ,C m

α,C n

β,C n r ,C n

β

•  Increased tail area with no increase in vertical height"

•  Proximity to propeller slipstream"

Twin and Triple Vertical Tails "

North American B-25!

Lockheed C-69!

Consolidated B-24!

Fairchild-Republic A-10!

•  Increase directional stability"

•  Counter roll due to sideslip of the dorsal fin

""

LTV F8U-3!

Ventral Fin Effects "

North American X-15!

Learjet 60!

Beechcraft 1900D!

Cn

β,Cn r,Cnβ,Cl

β

Ground Attack Aircraft"

•  Maneuverability, payload, low-speed/subsonic performance, ruggedness"

General Aviation Aircraft"

•  Low cost, safety, comfort, ease of handling"

Approaches to Stealth"

•  Low radar cross-section"

•  Open-loop instability"

•  Need for closed-loop control"

Supersonic Flight"

•  Transient vs cruising flight"

•  Hypersonic performance"

•  Resistance to aerodynamic heating"

Commercial Transport"

•  Safety, fuel economy, cost/passenger-mile,

maintenance factors"

•  Regional vs long-haul flight segments"

Business Aircraft"

•  Segment between personal and commercial transport"

Long-Range/-Endurance

Surveillance Aircraft"

•  Subsonic performance"

Propeller Effects "

•  Slipstream over wing, tail, and fuselage"

–  Increased dynamic pressure "

–   Swirl of flow"

–   Downwash and sidewash at the tail"

•  Propeller fin effect: Visualize lateral/

horizontal projections of the propeller

as forward surfaces"

torque and swirl"

Westland Wyvern!

DeHavilland DH-2! DeHavilland DHC-6!

Cmα,Cm q,Cmα,Cl o,Cn o,Cnβ,Cn r,Cnβ

Jet Effects on Rigid-Body Motion"

•  Angular momentum of rotating machinery"

North American F-86! McDonnell Douglas F/A-18!

C m o ,C mα,C m q ,C n o ,C nβ,C n r ,C nβ

Next Time:

Problems of High Speed

and Altitude

Reading