RWDC Background Discussion Harold Youngren AeroCraft 129 Pitt St Portland, ME 207-671-7350 cell 207-871-0552 harold.youngren@gmail.com

Background Aerospace engineer (MIT, Lockheed-Martin, consultant) Work on design of aircraft, wings, propellers, helicopters, CFD, aeroelastic analysis

RWDC Background Talk Overview of design problem (how the pieces relate) Aero Structure Aeroelastic Optimization Wing aerodynamics lift, drag as they affect wings airfoils and compressible drag   vortex drag due to lift   drag reduction approaches for wing basic info on materials beams and torsion boxes   wing structures, examples of likely wing structures Aeroelasticity  what this is, static aeroelastics vs flutter   static deflection with load  mass distribution    flutter how to design a wing to eliminate flutter

RWDC Key Design Issues Overall Problem Focus is transonic airliner wing with specified flight conditions and load Metric (objective function) for wing optimization driven by weight and drag Design for cruise metric and max loading condition at 3.75g Aerodynamics -> lift and drag Challenging operating point (Mach=0.7, CL~0.7) will involve transonic effects Lift must support the aircraft weight Design to reduce drag rise using combination of sweep and airfoil selection or thickness Structure -> weight Structure must be optimized for high load condition (avoid static divergence) Minimize weight for objective function metric Flutter free to max velocity (mostly involves control of stiffness and mass centers)

RWDC - Resources Aircraft Design Resources Online material on aircraft design (free!) Aircraft Design, Synthesis and Analysis http://adg.stanford.edu/aa241/AircraftDesign.html Aerodynamics Design Resources Online aero design textbook (free!) http://www.desktop.aero/appliedaero/preface/welcome.html Somewhat aircraft design oriented, but has technical focus Very good introduction for aerodynamics with lots of background, plots, examples Discussion of background issues for wing, airfoil design Structural Design Resources Limited simple resources Online beam calculation http://www.engapplets.vt.edu/statics/BeamView/BeamView.html Online structural mechanics material http://web.mst.edu/~mecmovie/

RWDC Aero – Flight Conditions Flight condition nomenclature Altitude - sets temperature (T), density (r), pressure (p), speed of sound (a) Speed = V Mach number, M = V/a = ratio of speed to speed of sound Dynamic pressure, q = ½ * r * V2, is pressure of oncoming “wind”

RWDC Aero – Aircraft Nomenclature Wingspan Leading edge (LE) Trailing edge (TE) LE sweep Root chord, tip chord ¼ chord sweep Dihedral

RWDC Aero – Wing Nomenclature Wing outer mold line (outer shape) specified by: Span Chord (root, tip) Sweep Taper Dihedral Airfoils and twist

Airfoils come in thousands of shapes for special purposes RWDC Aero - Airfoils Airfoil nomenclature Chord length Leading edge Trailing edge Thickness Camber Angle of attack Airfoils come in thousands of shapes for special purposes

RWDC Aero – Airfoil Forces Airfoils refer to the 2D sections of a wing Airfoil Force Nomenclature CL = lift coefficient CD = drag coefficient CM = pitching moment coefficient Angle of attack = a determines forces CL,CD,CM Characteristics are also a function of Mach number and other factors to a smaller degree

RWDC Aero – Airfoil Aerodynamics Lift (CL) is linearly proportional to angle of attack (CL~2p*a) with lift slope Cla=2p until stall Drag (CD) is low up until stall Moment (CM) about ¼ chord is nearly constant

RWDC Aero – Airfoil Aerodynamics Airfoil drag comes from three sources: Viscous drag CDv Pressure drag CDp Compressible drag CDc Viscous and pressure drag lumped into CDo

RWDC Aero - Airfoil Transonic Drag Rise Airfoils develop strong shock waves with increasing speed (NACA 0012 12% thick airfoil shown) Mach 0.6 Mach 0.7 Mach 0.8 Strong Shock Wave Shock Wave Higher drag Pressure indicated by color

RWDC Aero - Airfoil Compressible Drag Airfoil drag increases rapidly beyond critical Mach number, Mcrit~0.65 for this airfoil

RWDC Aero - Wing Transonic Drag Rise Optimized wing at transonic speed operates with (mild) shock wave Thicker airfoils and/or higher lift increase shock strength and drag Drag Rise

RWDC Aero – Wing Aerodyamics Wings characteristics include lift, drag and moment (about aircraft CG) Wing drag includes airfoil drag across wing Airfoil section drag Cdv+Cdp+Cdc Induced drag Cdi

RWDC Aero – Wing Aerodyamics Induced drag is a function of loading of wing along span Loading goes to zero at tips Optimal spanloading is elliptical (minimum Cdi) Small changes from elliptical loading possible without excessive penalty

RWDC Aero – Wing Spanwise Load Distribution Wing loads are modified by airfoil incidence angles Tip wash-out decreases outboard loading Lower outboard loading reduces high bending moments at wing root Lower outboard loading and root bending moment with tip wash-out Wing angle adjusted for constant total lift Tip wash-in (higher incidence) Tip wash-out (lower incidence)

RWDC Structure – Example Wing Structure RWDC rules specify wing box for structural elements (mid-chord region of wing)

RWDC Structure – Wing Box Wing box is key element of structural design, also holds fuel mass

RWDC Structure – Wing Box Layout Wing box is made up of: Skin Spars (spar cap + web) Stringers Ribs

RWDC Structure – Basic Loads Loads are forces applied to structure Loads take three main forms: Tension (pulling) Compression (pushing) Shear (sideways forces) Torsion (another shear force) Materials are measured and specified with respect to these three loadings

RWDC Structure – Aero Loads Loads on wing consist primarily of: Lift loads Torsion loads Inertial loads or gravity (weight) Key focus in design is controlling the spanwise loading of the wing with incidence angles of the airfoil sections

Beams resist bending and shear forces RWDC Structure – Beams Beams resist bending and shear forces Caps resist bending by tension and compression Webs resist shear forces from side loads and bending “I” beam shape comes from large caps needed to resist bending of long, slender wings

RWDC Structure – Elastic Axis Beams have a natural axis for bending without twist – the elastic axis Forces applied at the elastic axis will not twist the beam Forces applied away from the elastic axis will cause the beam to twist Aerodynamic forces act at AC Inertial forces (due to acceleration at at CG

RWDC Structure – Material Properties Materials have strength properties specified by stress (force/unit area) and strain (relative change in size or length) Modulus “springiness” of material (how much it moves with applied stress) Yield stress (when material starts to fail) Ultimate stress (failure and beyond)

RWDC Structure – Materials Materials list for RWDC (gives material properties)

RWDC Structure – Material Properties Materials for RWDC include knocked down properties for strength Aluminum (traditional aerospace material, also lists steel, titanium) Glass/epoxy <- small improvement from aluminum Carbon/epoxy <- best overall for weight and strength Kevlar/epoxy <- good in tension, poor in compression

RWDC Structure – Composite Materials Composites (carbon, glass, kevlar) Fibers embedded as layers in epoxy matrix Can be tailored by fiber orientation

RWDC Structure – Finite Element Analysis Structure is analyzed with finite elements using NASTRAN (or similar) computer code Requires division of structure into small “bricks” or plates or rods Each element is assigned properties (material, thickness, etc) Computer solves for stresses in elements so that designer can check to ensure that stresses do not exceed material limits

RWDC Optimization Optimization for wing design seeks best solution for weight and drag using objective function that blends these to produce a “psuedo weight” number OF = [145,360 + Wwing ] + 19 * q * S * [ 0.01819 + CDwing ] Where q = 162.92 lb/ft^2, and S = 1,400 ft^2 Weight of wing strongly driven by sweep, airfoil thickness and loading (airfoil incidence) Drag of wing driven by sweep, thickness at specified Mach 0.7

RWDC Optimization – Objective Function Space Optimization by changing design parameters to find lower OF values in design space Direction from gradient search or steepest descent Design space may not be as simple as this, it have local minima!!!

RWDC Optimization - Wing Design Parameters Key wing design parameters Sweep (more sweep reduces effective Mach number) Airfoil thickness (thicker wing is lighter) Structural stiffness for bending and torsion (tailors twist under load to shift loading inboard and reduce structural weight) RWDC rules specify: Span Area Taper Ratio (tip chord/root chord) Dihedral Material properties

RWDC Aeroelastics – Background Aeroelastic effects are static (aerostatic) or dynamic (flutter) Aerostatic deflections are due to airloads deflecting the structure in bending and twist Changes to structural shape (particularly twist) will change airloads Predicting aerostatic deflections may require iteration of aero loads analysis and structural analysis Flutter is a dynamic instability where the airloads force motions of the structure that grow with time Indicated by dynamic analysis of aero/mass/structural system (one or more characteristic roots go unstable) Flutter is almost always destructive and is avoided by design

RWDC Aeroelastics – Aerostatic Divergence Example of aerostatics - NASA HELIOS Solar Airplane Very flexible structure Encounter with gust drastically deflected wing upwards leading to failure of flight control system (was not designed to cope with highly bent wing) NASA Helios Solar Airplane (2003)

RWDC Aeroelastics – Aerostatic Divergence NASA HELIOS Solar Airplane Gust caused tips to rise over 50 ft (increasing dihedral) leading to loss of control and catastrophic overload of structure Gust raised wingtips 50’ and twisted wing

RWDC Aeroelastics – Flutter Flutter of swept flying wing Unstable pitching and bending motions of wing at critical speed Torsion no involved with this flutter (unusual)

RWDC Aeroelastics – Flutter Flutter is found by examining behavior of dynamic system Root locus shows behavior of system roots (characteristic modes, such as wing 1st bending) as velocity of aircraft is increased When complex root crosses real axis then system becomes unstable Modal analysis like this done by NASTRAN using structural FEM and mass distribution with unsteady airloads from ZAERO

RWDC Aeroelastics – Flutter Wing flutter can be cured (delayed) by: Increasing wing stiffness (adds weight) This could mean increasing bending stiffness and/or torsional stiffness Moving mass center closer to or forward of the elastic axis Moving elastic axis of the wing closer to the mass centers

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