✈️Aerodynamics Unit 2 – Airfoils and wing theory

Basic Airfoil Concepts

• Airfoils are the cross-sectional shapes of wings, propeller blades, and other aerodynamic surfaces that generate lift when moving through a fluid (air)
• Lift is generated by the pressure difference between the upper and lower surfaces of the airfoil, resulting from the airfoil's shape and angle of attack
• The angle of attack is the angle between the airfoil's chord line and the oncoming airflow
• As the angle of attack increases, lift increases up to a certain point called the critical angle of attack, beyond which the airflow separates from the airfoil's surface, causing a sudden decrease in lift (stall)
• The Bernoulli principle states that as the velocity of a fluid increases, its pressure decreases, contributing to the lift generation on an airfoil
• The Kutta condition ensures that the airflow leaves the trailing edge of the airfoil smoothly, preventing flow separation and maintaining lift
• Circulation, a measure of the rotation of the airflow around the airfoil, plays a crucial role in lift generation according to the Kutta-Joukowski theorem

Airfoil Geometry and Nomenclature

• The chord line is a straight line connecting the leading edge (front) and trailing edge (back) of the airfoil
• The mean camber line is the curve that lies halfway between the upper and lower surfaces of the airfoil
• Camber refers to the asymmetry between the upper and lower surfaces of the airfoil, with positive camber indicating a curved upper surface and negative camber indicating a curved lower surface
  • Camber affects the lift and moment characteristics of the airfoil
  • Symmetric airfoils have no camber and produce zero lift at zero angle of attack
• The thickness of an airfoil is the distance between the upper and lower surfaces, typically expressed as a percentage of the chord length
  • Thicker airfoils generally have higher structural strength and can accommodate larger internal structures (fuel tanks, landing gear)
• The leading edge radius is the curvature of the airfoil's front portion, affecting the airfoil's stall characteristics and low-speed performance
• The trailing edge angle is the angle formed by the upper and lower surfaces at the rear of the airfoil, influencing the airfoil's lift and drag characteristics

Aerodynamic Forces on Airfoils

• Lift is the upward force generated by the airfoil perpendicular to the oncoming airflow, enabling flight
• Drag is the force acting parallel to the oncoming airflow, opposing the aircraft's motion
  • Drag consists of parasitic drag (form drag, skin friction drag) and induced drag (due to lift generation)
• The moment about the aerodynamic center is the torque acting on the airfoil, affecting the aircraft's pitch stability
• The lift coefficient ($C_L$) is a dimensionless number that represents the lift generated by an airfoil, normalized by the dynamic pressure and the airfoil's planform area
• The drag coefficient ($C_D$) is a dimensionless number that represents the drag generated by an airfoil, normalized by the dynamic pressure and the airfoil's planform area
• The moment coefficient ($C_M$) is a dimensionless number that represents the moment about the aerodynamic center, normalized by the dynamic pressure, the airfoil's planform area, and the chord length
• The lift-to-drag ratio ($L/D$) is a measure of the airfoil's aerodynamic efficiency, indicating the amount of lift generated per unit of drag

Airfoil Performance Characteristics

• The lift curve shows the relationship between the lift coefficient and the angle of attack, typically linear up to the stall angle
• The drag polar is a graph showing the relationship between the lift coefficient and the drag coefficient, useful for determining the airfoil's optimal operating conditions
• The pitching moment curve depicts the variation of the moment coefficient with the lift coefficient or angle of attack, providing insight into the airfoil's pitch stability
• The maximum lift coefficient ($C_{L,max}$) is the highest lift coefficient an airfoil can achieve before stalling, a critical parameter for low-speed performance and landing
• The lift-to-drag ratio curve shows the variation of $L/D$ with the angle of attack or lift coefficient, helping to identify the most efficient operating point for the airfoil
• The endurance parameter ($C_L^{3/2}/C_D$) is a measure of an airfoil's efficiency in terms of the distance it can travel per unit of fuel consumed, relevant for long-range aircraft
• The range parameter ($C_L/C_D$) is a measure of an airfoil's efficiency in terms of the distance it can travel per unit of fuel consumed at a given velocity, relevant for transport aircraft

Types of Airfoils and Their Applications

• Symmetric airfoils have no camber and are often used for vertical stabilizers, helicopter rotor blades, and some supersonic applications
• Flat plate airfoils are the simplest type of airfoil, used for initial aerodynamic studies and some high-speed applications (supersonic fins)
• Cambered airfoils have asymmetric upper and lower surfaces, generating lift even at zero angle of attack, commonly used for subsonic aircraft wings
• Laminar flow airfoils are designed to maintain extensive regions of laminar flow over the surface, reducing skin friction drag and improving efficiency (gliders, high-altitude aircraft)
• Supercritical airfoils are designed to delay the formation of shock waves at transonic speeds, reducing wave drag and improving performance (commercial airliners, business jets)
• High-lift airfoils are designed to generate high lift coefficients at low speeds, enabling shorter takeoff and landing distances (STOL aircraft, cargo planes)
• Rotorcraft airfoils are designed specifically for helicopter rotor blades, accounting for the unique flow conditions and structural requirements (variable pitch, high Mach numbers)

Wing Theory Fundamentals

• Wings are three-dimensional lifting surfaces formed by extending airfoils in the spanwise direction
• The aspect ratio (AR) is the ratio of the wing's span to its mean chord, affecting the wing's lift, drag, and stall characteristics
  • Higher aspect ratio wings generally have better lift-to-drag ratios but are more prone to aeroelastic effects (flutter, divergence)
• The wing planform is the shape of the wing as viewed from above, influencing the wing's lift distribution and stall behavior
  • Common planforms include rectangular, tapered, swept, and delta wings
• Winglets are vertical extensions added to the wing tips to reduce induced drag by minimizing wingtip vortices
• The lift distribution along the wing's span affects the overall lift, drag, and structural loads on the wing
  • Elliptical lift distribution is theoretically optimal for minimizing induced drag but is difficult to achieve in practice
• The wing's angle of incidence is the angle between the wing's chord line and the aircraft's longitudinal axis, setting the wing's angle of attack relative to the fuselage
• Wing twist refers to the variation of the airfoil's angle of incidence along the wing's span, used to optimize the lift distribution and stall characteristics

Wing Design Considerations

• The choice of airfoil sections along the wing's span depends on the desired performance characteristics and operating conditions (high lift, low drag, structural efficiency)
• The wing's structural design must account for the aerodynamic loads, aeroelastic effects, and fatigue life requirements
  • Common structural configurations include monospar, multi-spar, and box beam designs
• High-lift devices such as flaps and slats are used to increase the wing's maximum lift coefficient during takeoff and landing
  • Flaps (plain, split, slotted, Fowler) increase the wing's camber and area, while slats extend from the leading edge to delay flow separation
• Sweep angle is the angle between the wing's leading edge and the perpendicular to the aircraft's longitudinal axis, used to delay the onset of compressibility effects at high speeds
  • Forward sweep can improve low-speed handling qualities but may introduce aeroelastic instabilities
• Dihedral is the upward angle of the wing relative to the horizontal plane, providing lateral stability and roll control
• Wing-fuselage integration considers the aerodynamic interference effects between the wing and the fuselage, as well as structural attachment points and fuel tank locations

Advanced Airfoil and Wing Concepts

• Laminar flow control techniques, such as boundary layer suction and active flow control, are used to maintain laminar flow over the airfoil surface and reduce drag
• Morphing airfoils and wings can adapt their shape to optimize performance for different flight conditions (variable camber, variable thickness)
• Biomimetic airfoil and wing designs draw inspiration from nature to improve aerodynamic efficiency and maneuverability (bird wings, insect wings)
• Nonplanar wing configurations, such as box wings and joined wings, offer potential improvements in lift-to-drag ratio and structural efficiency compared to conventional planar wings
• Blended wing body (BWB) designs integrate the fuselage and wing into a single lifting surface, offering improved aerodynamic efficiency and reduced fuel consumption
• Plasma actuators and other active flow control devices can manipulate the airflow over the airfoil surface to enhance lift, reduce drag, or delay flow separation
• Multidisciplinary optimization (MDO) techniques are used to simultaneously optimize the aerodynamic, structural, and control aspects of airfoil and wing design, considering multiple objectives and constraints