Configuration and Power Effects on Flight Stability 
 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" •  Loss of engine produces large yawing (and sometimes rolling) moment(s), requiring major application of controls " •  Engine-out training can be as hazardous, especially during takeoff, for both propeller and jet aircraft" •  Acute problem for general-aviation pilots 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" •  Conventional aft-tail configuration " –  c.m. near wing's aerodynamic center (point at which wing's pitching moment coefficient is invariant with angle of attack ~25% mac)" •  Tailless airplane: c.m. ahead of the neutral point" Douglas DC-3! 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 " λ Roll ≈ L p ≈ C l ˆ p ρ V N 4 I xx $ % & ' ( ) Sb 2 ω n ≈ − M α + M q L α V N % & ' ( ) * ; ζ ≈ L α V N − M q % & ' ( ) * 2 − M α + M q L α V N % & ' ( ) * ω n DR ≈ N β 1 − Y r V N ( ) + N r Y β V N ζ DR ≈ − N r + Y β V N & ' ( ) * + 2 N β 1 − Y r V N ( ) + N r Y β V N •  Phugoid Mode" •  Short-Period Mode" •  Dutch Roll Mode" •  Roll Mode" ω n ≈ gL V / V N ; ζ ≈ D V 2 gL V / V N λ Spiral ≈ 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 α = π AR 1 + 1 + AR 2 cos Λ 1 4 $ % & ' ( ) 2 1 − M 2 cos Λ 1 4 ( ) + , - - - . / 0 0 0 = π AR 1 + 1 + AR 2 cos Λ 1 4 $ % & ' ( ) 2 + , - - - . / 0 0 0 [Incompressible flow] C L α = 2 π 2 cot Λ LE π + λ ( ) where λ = m 0.38 + 2.26m − 0.86m 2 ( ) m = cot Λ LE cot σ Λ LE , σ : measured from y axis Swept Wing" Triangular Wing" Effects of Wing Aspect Ratio" •  Wing lift slope has direct effect on" –  Phugoid damping" –  Short period natural frequency and damping" –  Roll damping" λ Roll ≈ L p ≈ C l ˆ p ρ V N 4 I xx $ % & ' ( ) Sb 2 ω n = − M α + M q L α V N $ % & ' ( ) ; ζ = L α V N − M q $ % & ' ( ) 2 − M α + M q L α V N $ % & ' ( ) ω n ≈ 2 g V N ; ζ ≈ 1 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" C L α ,C m α ,C l p ,C l β •  ! c/4 = sweep angle of quarter- chord" •  Sweep moves lift distribution toward wing tips" –  Roll damping" –  Static margin" •  Sweep increases dihedral effect of wing! C L α ,C m α ,C l p ,C l β Sweep Effect on Lift Distribution " Wing Location and Angle Effects" •  Vertical location of the wing, dihedral angle, and sweep" –  Sideslip induces yawing motion" –  Unequal lift on left and right wings induces rolling motion" •  Lateral-directional (spiral mode) stability effect (TBD)" C l β Modes Strongly Affected By The Empennage " ω n ≈ − M α + M q L α V N % & ' ( ) * ζ ≈ L α V N − M q % & ' ( ) * 2 − M α + M q L α V N % & ' ( ) * ω n DR ≈ N β + N r Y β V N ζ DR ≈ − N r + Y β V N & ' ( ) * + 2 N β + N r Y β V N •  Short-Period Mode (horizontal tail)" •  Dutch Roll Mode (vertical tail)" •  Weathervane and damping effects" 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" •  End-plate effect for horizontal tail improves effectiveness" •  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! C n β ,C n r ,C n  β ,C l 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" •  Low parasitic drag, high supersonic L/D" Hypersonic 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" •  DH-2 unstable with engine out" •  Single- and multi-engine effects" •  Design factors: fin offset (correct at one airspeed only), c.m. offset" •  Propeller fin effect: Visualize lateral/ horizontal projections of the propeller as forward surfaces" •  Counter-rotating propellers minimize torque and swirl" Westland Wyvern! DeHavilland DH-2! DeHavilland DHC-6! C m α ,C m q ,C m  α ,C l o ,C n o ,C n β ,C n r ,C n  β Jet Effects on Rigid-Body Motion" •  Normal force at intake (analogous to propeller fin effect) (F-86)" •  Deflection of airflow past tail due to entrainment in exhaust (F/A-18)" •  Pitch and yaw damping due to internal exhaust flow" •  Angular momentum of rotating machinery " North American F-86! McDonnell Douglas F/A-18! C m o ,C m α ,C m q ,C n o ,C n β ,C n r ,C n  β Next Time: Problems of High Speed and Altitude  Reading Flight Dynamics, Aircraft Stability and Control, Virtual Textbook, Part 22  . Configuration and Power Effects on Flight Stability 
 Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2012" •  Wing design" • . on Lift Distribution " Wing Location and Angle Effects& quot; •  Vertical location of the wing, dihedral angle, and sweep" –  Sideslip induces yawing motion" –  Unequal lift on. 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