Stability, Control, and Power Effects on Configuration Design Robert Stengel, Aircraft Flight Dynamics MAE 331, 2008 Preliminary layout of the plane Mission Payload requirements Propulsion system Wing design Tail shape and sizing Balance and neutral point Stability and trim Aerodynamic coefficient estimates Control surfaces Avionics and feedback control requirements Shape of the airplane determined by its purpose Handling, performance, functioning, and comfort Agility vs. sedateness Control surfaces adequate to produce needed moments Center of mass location too far forward increases unpowered control-stick forces too far aft degrades static stability Goals for Design Copyright 2008 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/~stengel/mae331.html http://www.princeton.edu/~stengel/flightdynamics.html 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 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 c.m. envelope Grumman X-29 Northrop N-9M McDonnell-Douglas X-36 Douglas DC-3
Wing Design Parameters Planform Aspect ratio Sweep Taper Complex geometries Shape at root Shape at tip Chord section Airfoils Twist Movable surfaces Leading- and trailing-edge devices Ailerons Spoilers Interfaces Fuselage Powerplants Wing Design Effects Planform Aspect ratio Sweep Taper Complex geometries Shape at root Shape at tip Inertial and aerodynamic effects Performance Short period damping Phugoid damping Roll damping North American F-100 Short Period Transient Response Roll Mode Transient Response Variable sweep Wing Design Effects High aspect ratio for lowspeed flight Landing and takeoff Loiter Low aspect ratio for highspeed flight Reduction of transonic and supersonic drag Variable incidence Improve pilot!s line of sight for carrier landing General Dynamics F-111 Sweep Effect on Thickness Ratio Grumman F-14 LTV F-8 from Asselin
Sweep Effect on Wing Subsonic Lift Distribution Sweep Effect on Wing Center of Pressure Planform Aspect ratio Sweep Taper Complex geometries Shape at root Shape at tip Sweep moves subsonic lift distribution toward the wing tips Sweep also increases the dihedral effect of the wing (TBD) Planform Aspect ratio Sweep Taper Complex geometries Shape at root Shape at tip Sweep moves subsonic lift distribution toward the wing tips Center of pressure of straight wing moves aft with increasing! Swept outboard wing stalls before inboard wing ( tip stall ) Center of pressure moved forward Static margin is reduced as angle of attack increases C L (!) vs. C m (!) 30 swept wing exhibits pitch-up instability Pitch Up Crossplot C L vs. C m to obtain plots such as those shown on previous slide Positive break in C m is due to forward movement of net center of pressure, decreasing static margin Shortal-Maggin Longitudinal Stability Boundary for Swept Wings F-100 crashes due to tip stall http://www.youtube.com/watch?v=rmlynu5yopm http://www.youtube.com/watch?v=nyjkkcxyqsu&feature=related Stable or unstable pitch break at the stall Stability boundary is expressed as a function of Aspect ratio Sweep angle of the quarter chord Taper ratio http://en.wikipedia.org/wiki/f-100_super_sabre
Mach Number Effect on Wing Center of Pressure P-38 Compressibility Limit on Allowable Airspeed Straight Wing Subsonic center of pressure (c.p.) at ~1/4 mean aerodynamic chord (m.a.c.) Transonicsupersonic c.p. at ~1/2 m.a.c. Delta Wing Subsonicsupersonic c.p. at ~2/3 m.a.c. Mach number increases the static margin of conventional configurations Has less effect on delta wing static margin C m (!) vs. C L (!) Static margin increase with Mach number increases control stick force required to maintain pitch trim produces pitch down from P-38 Pilot!s Manual Pilots warned to stay well below speed of sound in steep dive Wing Design Effects Strakes or leading edge extensions Maintain lift at high! McDonnell Douglas F-18 Reduce c.p. shift at high Mach number General Dynamics F-16 Wing Design Effects Vortex generators, fences, vortilons, notched or dog-toothed wing leading edges Boundary layer control Maintain attached flow with increasing! Avoid tip stall McDonnell-Douglas F-4 LTV F-8 Sukhoi Su-22
Wing Design Effects Wing Design Effects Planform Aspect ratio Sweep Taper Complex geometries Shape at root Shape at tip Chord section Airfoils Twist Elliptical lift distribution Tip stall Bending stress Republic XF-91 Planform Aspect ratio Sweep Taper Complex geometries Shape at root Shape at tip Chord section Airfoils Twist Camber increases zero-! lift coefficient Thickness increases transonic drag Wing Design Effects Planform Aspect ratio Sweep Taper Complex geometries Shape at root Shape at tip Chord section Airfoils Twist Washout twist reduces tip angle of attack reduces likelihood of tip stall Wing Design 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
Wing tips Wing Design Effects Winglets and rake reduce induced drag Chamfer produces favorable roll w/ sideslip (spiral mode) B-747-400 Boeing P-8A Yankee AA-1 Tail Design Effects Longitudinal stability Horizontal stabilizer Short period natural frequency and damping Directional stability Vertical stabilizer (fin) Ventral fins Strakes Leading-edge extensions Multiple surfaces Butterfly (V) tail Dutch roll natural frequency and damping Stall or spin prevention/ recovery Avoid rudder lock (TBD) North American P-51 Tail Design Effects Ventral fins Increase directional stability at high Mach Number Increase directional stability due to design change LTV F8U-3 North American X-15 Horizontal Tail Location and Size 15-30% of wing area~ wing semi-span behind the c.m. Requirement to trim neutrally stable airplane at maximum lift in ground effect Effect on short period mode Horizontal Tail Volume: Average value = 0.48 V H = S ht S l ht c l ht S "C mtail = "C ht Ltail S c = "C L tail V H where "C Ltail is referenced to horizontal tail area Learjet 60 Beechcraft 1900D Curtiss SB2C North American F-86
Vertical Tail Location and Size Analogous to horizontal tail volume Effect on Dutch roll mode Powerful rudder for spin recovery Full-length rudder located behind the elevator High horizontal tail so as not to block the flow over the rudder Vertical Tail Volume: Average value = 0.18 Tail Location and Size Short-coupled designs have stability problems V H = S ht S V V = S vt S l ht c l vt b McDonnell Douglas XF-85 V V = S vt S l vt b l vt S "C ntail = "C vt Ltail S c = "C L tail V V where "C Ltail is referenced to vertical tail area Curtiss SB2C Piper Tomahawk Twin and Triple Vertical Tails Increased tail area with no increase in vertical height End-plate effect for horizontal tail improves effectiveness Proximity to propeller slipstream Consolidated B-24 North American B-25 Handbook Approach to Aerodynamic Estimation Build estimates from component effects USAF Stability and Control DATCOM (download from Course Blackboard) USAF Digital DATCOM (see Wikipedia page) ESDU Data Sheets (see Wikipedia page) Ilan Kroo!s web page (http://adg.stanford.edu/aa241/aircraftdesign.html) UIUC Applied Aerodynamics Group(http://www.ae.uiuc.edu/m-selig/) Lockheed C-69 Fairchild-Republic A-10
Wind Tunnel Data 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 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, flowthrough effects, aeroelastic deformation, surface distortions Tested virtually every US airplane used in World War II, when it was operating 24/7 Artifices to improve reduced/fullscale correlation, e.g., boundary layer trips and vortex generators 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 Design for Control Elevator/stabilator: pitch control Rudder: yaw control Ailerons: roll control Trailing-edge flaps: low-angle lift control Leading-edge flaps: High-angle lift control Spoilers: Roll, lift, and drag control Thrust: speed/altitude control
Critical Issues for Control Effect of control surface deflections on aircraft motions Generation of control forces and rigid-body moments on the aircraft Rigid-body dynamics of the aircraft "E is an input Control Flap Carryover Effect on Lift Produced By Total Surface from Schlichting & Truckenbrodt C L"E C L# c f vs. x f + c f " =L Command and control of the control surfaces Displacements, forces, and hinge moments within the control mechanisms Dynamics of control linkages "E is a state C L"E C L# " E =L c f ( x f + c f ) Aerodynamic Moments on Control Surfaces Increasing size and speed of aircraft leads to increased hinge moments This leads to need for mechanical or aerodynamic reduction of hinge moments Need for aerodynamically balanced surfaces Control surface hinge moment H elevator = C H elevator 1 2 "V 2 Sc Hinge-moment coefficient, C H Linear model of dynamic effects C H = C H" " + C H" " + C H# # + C H pilot input +... C H" : aerodynamic damping moment C H" : aerodynamic spring moment C H# : floating tendency C H pilot input : pilot input " V! Dynamic Model of a Control Surface Control mechanism dynamics 1 " = H C H elevator elevator = 2 #V 2 Sc I elevator I elevator [ " ] = C H " + C H" " + C H$ $ + C H pilot input +... % H " + H " " + H $ $ + H pilot input +... " " # H " # H " " = H $ $ + H pilot input +... " 1 2 #V 2 Sc I elevator Second-order model of control-deflection dynamics mechanism dynamics = external forcing I elevator = effective inertia of surface, linkages, etc. H " = # ( H elevator I elevator ) # ; H " = # ( H elevator I elevator ) " #" H $ = # ( H elevator I elevator ) #$
C H " C H# # + C H$ $ + C H pilot input Stick-free case Control surface free to float Normally C H " C H# # + C H$ $ C H" < 0 : reduces short # period stability C H$ < 0 : required for mechanical stability Inertial and aerodynamic effects Control surface in front of hinge line Increasing C H" improves pitch stability, to a point Too much area Degrades restoring moment Increases possibility of mechanical instability Increases possibility of destabilizing coupling to short-period mode Horn Balance Overhang or Leading-Edge Balance Effect is similar to that of horn balance Varying gap and protrusion into airstream with deflection angle C H " C H# # + C H$ $ + C H pilot input Trailing-Edge Bevel Balance See discussion in Abzug and Larrabee C H " C H# # + C H$ $ + C H pilot input B-52 application Control-surface fin with flexible seal moves within an internal cavity in the main surface Differential pressures reduce control hinge moment Internally Balanced Control Surface C H " C H# # + C H$ $ + C H pilot input
Shorts SB.4 All-Moving Control Surfaces Particularly effective at supersonic speed (Boeing Bomarc wing tips, North American X-15 horizontal and vertical tails, Grumman F-14 horizontal tail) SB.4!s aero-isoclinic wing Sometimes used for trim only (e.g., Lockheed L-1011 horizontal tail) Hinge moment variations with flight condition X-15 F-14 L-1011 Bomarc Aft Flap vs. All-Moving Control Surface Carryover effect Aft-flap deflection can be almost as effective as full surface deflection at subsonic speeds Negligible at supersonic speed Aft flap Mass and inertia lower, reducing likelihood of mechanical instability Aerodynamic hinge moment is lower Can be mounted on structurally rigid main surface Ailerons Spoilers When one aileron goes up, the other goes down Average hinge moment affects stick force Frise aileron Asymmetric contour, with hinge line at or below lower aerodynamic surface Reduces hinge moment Cross-coupling effects can be adverse or favorable, e.g. yaw rate with roll Up travel of one > down travel of other to control yaw effect Spoiler reduces lift, increases drag Speed control Differential spoilers Roll control Avoid twist produced by outboard ailerons on long, slender wings free trailing edge for larger high-lift flaps Plug-slot spoiler on P-61 Black Widow: low control force Hinged flap has high hinge moment North American P-61
Rudder Rudder provides yaw control Turn coordination Countering adverse yaw Crosswind correction Countering yaw due to engine loss Strong rolling effect, particularly at high! Only control surface whose nominal aerodynamic angle is zero Possible nonlinear effect at low deflection angle Insensitivity at high supersonic speed Wedge shape, all-moving surface on X-15 Martin B-57 Bell X-2 Control Tabs Balancing or geared tabs Tab is linked to the main surface in opposition to control motion, reducing the hinge moment with little change in control effect Flying tabs Pilot's controls affect only the tab, whose hinge moment moves the control surface [BAC 1-11 deep stall flight test accident] Linked tabs divide pilot's input between tab and main surface Spring tabs put a spring in the link to the main surface BAC 1-11 Control Mechanization Effects Fabric-covered control surfaces (e.g., DC-3, Spitfire) subject to distortion under air loads, changing stability and control characteristics Control cable stretching Elasticity of the airframe changes cable/pushrod geometry Nonlinear control effects friction breakout forces backlash Instabilities Due To Control Mechanization Aileron buzz (aero-mechanical instability; P-80 test, Avro CF-105) Rudder snaking (Dutch roll/mechanical coupling; Meteor, He-162, X-1) Aeroelastic coupling (B-47, Boeing 707 yaw dampers)
Downsprings and Bobweights Downspring Long mechanical spring with low spring constant Exerts a trailing-edge down moment on the elevator Bobweight Weight on control column that affects feel or basic stability Mechanical stability augmentation Beechcraft B-18 Mechanical and Augmented Control Systems Mechanical system Push rods, bellcranks, cables, pulleys On almost all aircraft currently flying Power boost Pilot's input augmented by hydraulic servo that lowers manual force Fully powered (irreversible) system No direct mechanical path from pilot to controls Mechanical linkages from cockpit controls to servo actuators Mechanical, Power-Boosted Systems Advanced Control Systems McDonnell Douglas F-15 Grumman A-6 Artificial-feel systems Restores the pilot's control forces to those of an "honest" airplane "q-feel" modifies force gradient Variation with trim stabilizer angle Bobweight responds to gravity and to normal acceleration Fly-by-wire/light systems Minimal mechanical runs through the airplane Command input and feedback signals drive servo actuators Fully powered systems Move toward electric rather than hydraulic power
Boeing 767 Elevator Control System Boeing 777 Fly-By-Wire Control System Control-Configured Vehicles Command/stability augmentation Lateral-directional response Bank without turn Turn without bank Yaw without lateral translation Lateral translation without yaw Velocity-axis roll (i.e., bank) Longitudinal response Pitch without heave Heave without pitch Normal load factor Pitch-command/attitude-hold Flight path angle USAF AFTI/F-16 USAF F-15 IFCS Princeton Variable-Response Research Aircraft Power Effects on Stability and Control Gee Bee R1 Racer: an engine with wings and almost no tail During W.W.II, the size of fighters remained about the same, but installed horsepower doubled (F4F vs. F8F) Use of flaps means high power at low speed, increasing relative significance of thrust effects (AD) Douglas AD-1 GB R1 Grumman F4F Grumman F8F
Multi-Engine Aircraft of World War II Large W.W.II aircraft (e.g., B-17, B-24, and B-29) had unpowered controls: High foot-pedal force Rudder stability problems arising from balancing to reduce pedal force Severe engine-out problem for twin-engine aircraft, e.g., A-26, B-25, and B-26 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 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) Boeing/Bell V-22 Cessna 337 Convair B-36 Direct Thrust Effect on Speed Stability In powered, steady, level flight, nominal thrust balances nominal drag 1 T N " D N = C TN 2 #V 2 1 N S " C DN 2 #V 2 N S = 0 Effect of velocity change # < 0, for propeller aircraft!t %!V = $ " 0, for turbojet aircraft & % > 0, for ramjet aircraft "D > 0 for most flight regimes "V Small velocity perturbation grows if!t!v "!D!V > 0 Therefore, propeller is stabilizing for velocity change, turbojet has neutral effect, and ramjet is destabilizing
Pitching Moment Due to Thrust Thrust line above or below center of mass induces a pitching moment XB-51, PBY, MD-11, A-10 Martin XB-51 Consolidated PBY Velocity-Dependent Thrust- Induced Pitching Moment "M thrust "V # "T "V $ Moment Arm Negative " M/" V (Pitch-down effect) tends to increase velocity Positive " M/" V (Pitch-up effect) tends to decrease velocity With propeller thrust line above the c.m., increased velocity decreases thrust, producing a pitch-up moment Tilting the propeller thrust line can have benefits (Lake Amphibian, F6F Hellcat, F8F Bearcat, and AD Skyraider) McDonnell Douglas MD-11 Fairchild-Republic A-10 Lake Amphibian Grumman F6F Grumman F8F Douglas AD-1 Propeller Effects Slipstream washing over wing, tail, and fuselage Increased dynamic pressure Swirl of flow Downwash and sidewash at the tail DH-2 unstable with engine out Difference between 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 to minimize torque and swirl DeHavilland DH-2 Westland Wyvern 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
United Flight 232, DC-10, Sioux City, IA, 1989 Uncontained engine failure damaged all three flight control hydraulic systems (http://en.wikipedia.org/wiki/united_airlines_flight_232) Crew resource management (http://en.wikipedia.org/wiki/crew_resource_management) Propulsion Controlled Aircraft Proposed backup attitude control in event of flight control system failure Differential throttling of engines to produce control moments Requires feedback control for satisfactory flying qualities Proposed retrofit to McDonnell- Douglas (Boeing) C-17 NASA MD-11 PCA Flight Test 296 people onboard 185 survived due to pilot!s differential control of engines NASA F-15 PCA Flight Test Next Time: Linearized Equations and Modes of Motion