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