AircrAircraft Flight Dynamics Robert F. Stengel Lecture5 Configuration Aerodynamics 1

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" 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 ! Description of Aircraft Configuration Republic F-84F" A Few Definitions" Wing Planform Variables" •  Aspect Ratio" •  Taper Ratio" λ = c tip c root = tip chord root chord AR = b c rectangular wing = b × b c × b = b 2 S any wing •  Rectangular Wing" •  Delta Wing" •  Swept Trapezoidal Wing" Mean Aerodynamic Chord and Wing Center of Pressure" c = 1 S c 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! h cruise = 10 kft! 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! h ceiling = 52 kft! 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! h cruise = 50 kft! M max = 2.5! h ceiling = 65 kft! 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! h cruise = 85 kft! V cruise = 375 kt! h cruise = 70 kft! Uninhabited Air Vehicles" Northrop-Grumman/Ryan Global Hawk" General Atomics Predator" V cruise = 70-90 kt! h cruise = 25 kft! V cruise = 310 kt! h cruise = 50 kft! 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" Lifting Body Re-Entry Vehicles" Northrop HL-10" Martin Marietta X-24A" Northrop M2-F2" Martin Marietta X-24B" JAXA ALFLEX" NASA X-38" http://www.youtube.com/watch?v=K13G1uxNYks! http://www.youtube.com/watch?v=YCZNW4NrLVY! Subsonic Biplane" •  Compared to monoplane" –  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 m 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" Circulation of Incompressible Air Flow About a 2-D Airfoil" •  Bernoullis equation (inviscid, incompressible flow)" p static + 1 2 ρ V 2 = constant along streamline = p stagnation •  Vorticity" V upper (x) = V ∞ + ΔV (x) 2 V lower (x) = V ∞ − ΔV (x) 2 γ 2− D (x) = ΔV (x) Δz(x) •  Circulation" Γ 2− D = γ 2− D (x)dx 0 c ∫ Lower pressure on upper surface" What Do We Mean by 
 2-Dimensional Aerodynamics?" •  Finite-span wing –> finite aspect ratio" AR = b c rectangular wing = b × b c × b = 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−D 1 2 ρ V 2 S = C L 3−D 1 2 ρ V 2 bc ( ) [Rectangular wing] Δ Lift 3− D ( ) = C L 3−D 1 2 ρ V 2 cΔy lim Δy→ 0 Δ Lift 3− D ( ) = lim Δy→ 0 C L 3−D 1 2 ρ V 2 cΔy % & ' ( ) * ⇒ "2-D Lift" = C L 2− D 1 2 ρ V 2 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" C L 2−D = α ∂C L ∂ α $ % & ' ( ) 2−D = α C L α ( ) 2−D = 2 π ( ) α [Lifting-line Theory] •  Swept wing, 2-D lift slope coefficient" –  Inviscid, incompressible flow" C L 2−D = C L α ( ) 2 − D α = 2 π cos Λ ( ) α 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 ∞ Γ ( ) 2 −D  1 2 ρ ∞ V ∞ 2 c 2 πα ( ) thin, symmetric airfoil [ ] + ρ ∞ V ∞ Γ camber ( ) 2 −D  1 2 ρ ∞ V ∞ 2 c C L α ( ) 2 −D α + ρ ∞ V ∞ Γ camber ( ) 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 (Incompressible Flow)" •  Airfoil section lift coefficients and lift slopes near wingtips are lower than their estimated 2-D values" Talay, NASA SP-367! Effect of Aspect Ratio on 3-Dimensional Wing Lift Slope Coefficient (Incompressible Flow)! •  High Aspect Ratio (> 5) Wing" C L α  ∂C L ∂ α # $ % & ' ( 3−D = 2 π AR AR + 2 = 2 π AR AR + 2 # $ % & ' ( •  Low Aspect Ratio (< 2) Wing" C L α = π AR 2 = 2 π AR 4 # $ % & ' ( All wings at M = 1! Bombardier Dash 8! Handley Page HP.115! Effect of Aspect Ratio on 3-D Wing Lift Slope Coefficient (Incompressible Flow)" •  All Aspect Ratios (Helmbold equation)" C L α = π AR 1+ 1+ AR 2 # $ % & ' ( 2 ) * + + , - . . HL-10!Q400! For Small Angles, Lift is Proportional to Angle of Attack" Lift = C L 1 2 ρ V 2 S ≈ C L 0 + ∂ C L ∂α α % & ' ( ) * 1 2 ρ V 2 S ≡ C L 0 + C L α α % & ( ) 1 2 ρ V 2 S where C L α = lift slope coefficient •  At higher angles, " –  flow separates" –  wing loses lift" •  Flow separation produces stall" http://www.youtube.com/watch?v=RgUtFm93Jfo! Aerodynamic Estimation and Measurement Handbook Approach to Aerodynamic Estimation! •  Build estimates from component effects" –  USAF Stability and Control DATCOM (download at http://www.pdas.com/datcomb.html )" –  USAF Digital DATCOM (see Wikipedia page)" –  ESDU Data Sheets (see Wikipedia page)" Interference Effects Interference Effects Wing Aerodynamics Fuselage Aerodynamics Tail Aerodynamics Interference Effects •  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" Wind Tunnel Data! 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! http://crgis.ndc.nasa.gov/historic/30_X_60_Full_Scale_Tunnel! Wind Tunnel Force and Moment Data! Three-Strut Mount! Single-Strut Mount! 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! 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! 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" 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 Maximum Lift of Delta Wings with Straight Trailing Edges" δ : Taper ratio Aspect Ratio" Angle of Attack for C L max ! Maximum Lift " Coefficient, C L max ! Aspect Ratio" Schlicting & Truckenbrodt, 1979! Large Angle Variations in Subsonic Lift Coefficient (0° < α < 90°)" Lift = C L 1 2 ρ V 2 S •  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" •  Camber modification" •  Trailing-edge flap deflection shifts C L up and down" •  Leading-edge flap (slat) deflection increases stall α " •  Same effect applies for 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" C L α = π AR 1+ 1+ AR 2 cos Λ 1 4 $ % & & ' ( ) ) 2 1− M 2 cos Λ 1 4 ( ) + , - - - . / 0 0 0 € Λ 1 4 = sweep angle of quarter chord [...]... http://www.youtube.com/watch?feature=fvwp&NR =1& v=eBBZF_3DLCU/! •  19 30s test in NACA wind tunnel" http://www.youtube.com/watch?v=3_WgkVQWtno&feature=related ! Next Time: Configuration Aerodynamics – 2 Reading Flight Dynamics, 84 -10 3 Virtual Textbook, Part 4,5 ... from Werle*! •  Boundary layer thickens in transition, then thins in turbulent flow" C f ≈ 1. 33Re 1/ 2 ≈ 0.46 ( log10 [laminar flow ] Re ) [turbulent −2.58 flow ] Wetted Area: Total surface area of the wing or aircraft, subject to skin friction" * See Van Dyke, M., An Album of Fluid Motion, Parabolic Press, Stanford, 19 82" Effect of Streamlining on Parasitic Drag " Some Videos " •  Flow over a narrow airfoil,... http://www.youtube.com/watch?v=iNBZBChS2YI! More Videos " •  YF -12 A supersonic flight past the sun" http://www.youtube.com/watch?v=atItRcfFwgw&feature=related! •  Supersonic flight, sonic booms" http://www.youtube.com/watch? v=gWGLAAYdbbc&list=LP93BKTqpxbQU&index =1& feature=plcp! •  Smoke flow visualization, wing with flap" http://www.youtube.com/watch?feature=fvwp&NR =1& v=eBBZF_3DLCU/! •  19 30s test in NACA wind tunnel" http://www.youtube.com/watch?v=3_WgkVQWtno&feature=related... upwash on the wing, canard, and tail" from Etkin! Aerodynamic Drag " 1 2 2 1 ρV S ≈ C D0 + ε C L ρV 2 S 2 2 2 1 + ε C Lo + C Lα α ( ρV 2 S *2 ) ( Drag = C D ≈ %C D0 ' & ( ) ) Parasitic Drag " Reynolds Number and Boundary Layer " Reynolds Number = Re = •  Pressure differential, viscous shear stress, and separation" Parasitic Drag = C D0 1 2 ρV S 2 ρVl Vl = µ ν where ρ = air density V = true airspeed l... •  No simple equations for lift slope" •  Supersonic delta (triangular) wing" Supersonic leading edge" C Lα = 4 M2 1 Subsonic 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 Λ LE = sweep angle of leading edge Schlicting & Truckenbrodt, 19 79! € Wing-Fuselage Interference Effects " •  Wing lift induces" –  Upwash in front of the wing" –  Downwash behind . Aerodynamics Fuselage Aerodynamics Tail Aerodynamics Interference Effects •  NASA 30 x 60 Tunnel" –  Full-scale aircraft on balance" –  Sub-scale aircraft on sting" –  Sub-scale. 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 =16 538&media_id =17 2458 41! Interpreting. on 3-D Wing Lift Slope" •  Subsonic 3-D wing, with sweep effect" C L α = π AR 1+ 1+ AR 2 cos Λ 1 4 $ % & & ' ( ) ) 2 1 M 2 cos Λ 1 4 ( ) + , - - - . / 0 0 0 € Λ 1 4 =