0. RWDC Background Discussion
Harold Youngren
AeroCraft
129 Pitt St
Portland, ME
cell

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

2. 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

3. 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)

4. RWDC - Resources Aircraft Design Resources
Online material on aircraft design (free!)
Aircraft Design, Synthesis and Analysis
Aerodynamics Design Resources
Online aero design textbook (free!)
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
Online structural mechanics material

5. 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”

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

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

8. 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

9. 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

10. 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

11. 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

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

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

14. 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

15. 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

16. 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

17. 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)

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

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

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

21. 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

22. 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

23. 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

24. 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

25. 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)

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

27. 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

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

29. 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

30. 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 * [ CDwing ]
Where q = 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

31. 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!!!

32. 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

33. 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

34. 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)

35. 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

36. 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)

37. 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

38. 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

39. RWDC Aero – Blank Slide
Blank slide