2.1 Airfoil geometry

Airfoil geometry is crucial in aerodynamics, shaping how wings and blades interact with air. The design impacts lift, drag, and overall performance. Key components include the leading edge, trailing edge, camber line, chord line, and thickness distribution.

Various airfoil types exist, each optimized for specific conditions. Parameters like angle of attack, camber, and thickness-to-chord ratio influence performance. Understanding these elements helps engineers design efficient wings for different aircraft and applications.

Airfoil components

• The airfoil is the cross-sectional shape of a wing or blade that generates lift when moving through a fluid
• Consists of several key components that contribute to its aerodynamic properties and performance

Leading edge

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• The front-most point of the airfoil where the flow first encounters the surface
• Plays a crucial role in determining the stall characteristics and the maximum lift coefficient
• Shape affects the pressure distribution and the formation of the boundary layer
• Typically rounded to promote smooth flow attachment and delay flow separation (NACA 0012)

Trailing edge

• The rear-most point of the airfoil where the flow leaves the surface
• Influences the lift and drag characteristics, as well as the stall behavior
• Shape affects the pressure recovery and the wake formation behind the airfoil
• Can be sharp (NACA 4412) or blunt (Supercritical airfoils) depending on the design requirements

Camber line

• The curve that passes through the midpoints between the upper and lower surfaces of the airfoil
• Determines the amount of lift generated by the airfoil at zero angle of attack
• Positive camber produces lift even at zero angle of attack, while symmetric airfoils generate zero lift
• Can be designed to optimize lift distribution along the span (NACA 2412)

Chord line

• The straight line connecting the leading edge and the trailing edge of the airfoil
• Serves as a reference for measuring the angle of attack and other geometric parameters
• Length is used to non-dimensionalize airfoil parameters and performance coefficients
• Typically normalized to a unit length for comparison between different airfoils (NACA 0015)

Thickness distribution

• The variation of the airfoil thickness along the chord, measured perpendicular to the camber line
• Affects the structural strength, weight, and internal volume of the wing or blade
• Influences the pressure distribution, drag, and critical Mach number of the airfoil
• Can be designed to optimize the trade-off between aerodynamic and structural performance (NACA 63-415)

Airfoil classifications

Symmetrical vs asymmetrical

• Symmetrical airfoils have identical upper and lower surface shapes, resulting in zero lift at zero angle of attack (NACA 0012)
• Asymmetrical airfoils have different upper and lower surface shapes, generating lift even at zero angle of attack (NACA 4412)
• Symmetrical airfoils are often used for vertical stabilizers, while asymmetrical airfoils are used for wings and horizontal stabilizers

Laminar flow vs conventional

• Laminar flow airfoils are designed to maintain laminar boundary layer over a significant portion of the chord (NACA 6-series)
• Conventional airfoils have a shorter laminar flow region and rely on a turbulent boundary layer for most of the chord (NACA 4-series)
• Laminar flow airfoils can achieve lower drag coefficients but are more sensitive to surface roughness and off-design conditions

Low-speed vs high-speed

• Low-speed airfoils are designed for subsonic flow conditions, typically with thicker profiles and higher camber (Clark Y)
• High-speed airfoils are optimized for transonic or supersonic flow, with thinner profiles and reduced camber (NACA 64-series)
• Low-speed airfoils prioritize high lift and gentle stall characteristics, while high-speed airfoils focus on minimizing wave drag and delaying shock formation

Airfoil parameters

Angle of attack

• The angle between the chord line and the incoming flow direction, measured in degrees
• Determines the lift and drag forces acting on the airfoil, as well as the stall behavior
• Increasing angle of attack generally increases lift up to the stall angle, beyond which lift decreases abruptly
• Typical stall angles range from 10 to 20 degrees, depending on the airfoil design (NACA 0012: 15°)

Camber

• The maximum distance between the camber line and the chord line, typically expressed as a percentage of the chord length
• Positive camber increases lift at a given angle of attack, while negative camber decreases lift
• Higher camber also results in a more positive zero-lift angle of attack and a higher pitching moment
• Typical camber values range from 0% for symmetric airfoils to 6% for high-lift airfoils (NACA 4412: 4%)

Thickness-to-chord ratio

• The maximum thickness of the airfoil divided by the chord length, expressed as a percentage
• Affects the structural strength, weight, and internal volume of the wing or blade
• Higher thickness-to-chord ratios increase drag but improve the stall characteristics and maximum lift coefficient
• Typical values range from 6% for high-speed airfoils to 18% for low-speed airfoils (NACA 0015: 15%)

Leading edge radius

• The radius of curvature at the leading edge, normalized by the chord length
• Larger leading edge radii promote smooth flow attachment and delay stall, but increase drag
• Smaller radii result in sharper pressure peaks and earlier flow separation, but reduce drag
• Typical values range from 0.5% to 2.5% of the chord length, depending on the airfoil design (NACA 0012: 1.58%)

Airfoil shapes

NACA 4-digit series

• Defined by a 4-digit code: first digit represents maximum camber as a percentage of chord, second digit represents the position of maximum camber along the chord, and last two digits represent the maximum thickness as a percentage of chord (NACA 2412)
• Widely used for general aviation and low-speed applications due to their simple geometry and predictable performance
• Examples include NACA 0012 (symmetric), NACA 2412 (moderate camber), and NACA 4412 (high camber)

NACA 5-digit series

• Designed to maintain laminar flow over a larger portion of the chord compared to the 4-digit series
• The first digit represents the camber line shape, the second and third digits represent the position of maximum camber, and the last two digits represent the maximum thickness (NACA 23012)
• Commonly used for high-performance sailplanes and low-drag applications

Supercritical airfoils

• Developed to delay the formation of shock waves and reduce wave drag in transonic flow conditions
• Characterized by a flattened upper surface, a highly cambered aft section, and a blunt trailing edge (NASA SC(2)-0714)
• Used for transonic and supersonic aircraft wings, as well as helicopter rotor blades

Laminar flow airfoils

• Designed to maintain laminar boundary layer over a significant portion of the chord, reducing skin friction drag
• Typically have a favorable pressure gradient on the upper surface and a carefully controlled shape to prevent premature transition (NACA 6-series)
• Used for high-performance sailplanes, low-drag fuselage sections, and wind turbine blades

Airfoil selection considerations

Reynolds number effects

• The Reynolds number (Re) represents the ratio of inertial forces to viscous forces in a fluid flow
• Airfoil performance depends on Re, with low-Re airfoils prioritizing laminar flow and high-Re airfoils focusing on turbulent flow characteristics
• Increasing Re generally improves the maximum lift coefficient and stall angle, while reducing the drag coefficient
• Typical Re ranges from 10^4 for model aircraft to 10^7 for commercial airliners

Mach number effects

• The Mach number (M) represents the ratio of the flow velocity to the speed of sound
• Airfoil performance is affected by compressibility effects at high subsonic (M > 0.6) and supersonic (M > 1) speeds
• Increasing M leads to the formation of shock waves, which cause a rapid increase in drag and a change in the pressure distribution
• Supercritical airfoils are designed to delay shock formation and minimize wave drag at transonic speeds

Stall characteristics

• The stall behavior of an airfoil determines its safety and controllability at high angles of attack
• Desirable stall characteristics include a gradual loss of lift beyond the stall angle, minimal lift hysteresis, and a gentle pitch break
• Airfoils with sharp leading edges or highly cambered sections may exhibit abrupt stall and post-stall behavior
• Stall characteristics can be improved through the use of leading edge devices (slats) or vortex generators

Drag characteristics

• The drag characteristics of an airfoil determine its efficiency and performance over a range of operating conditions
• Desirable drag characteristics include low minimum drag coefficient, a wide low-drag bucket, and gradual drag rise at high lift coefficients
• Airfoil drag can be reduced through the use of laminar flow designs, shock-free shapes, and boundary layer control devices
• Trade-offs between drag and other performance parameters (lift, stall, structural) must be considered in airfoil selection

Airfoil modifications

Leading edge devices

• Devices attached to the leading edge of an airfoil to improve its high-lift performance and stall characteristics
• Slats are retractable surfaces that create a slot between the main airfoil and the slat, delaying flow separation at high angles of attack
• Krueger flaps are hinged surfaces that extend forward and downward from the leading edge, increasing camber and lift
• Leading edge devices can increase the maximum lift coefficient by up to 50% and delay stall by 5-10 degrees

Trailing edge devices

• Devices attached to the trailing edge of an airfoil to increase lift, reduce drag, or control the pitching moment
• Plain flaps are hinged surfaces that deflect downward, increasing camber and lift (NACA 23012 with 20% plain flap)
• Split flaps are similar to plain flaps but have a gap between the main airfoil and the flap, reducing the hinge moment
• Fowler flaps extend aft and downward, increasing both camber and chord length for high lift (Boeing 727 with triple-slotted Fowler flaps)

Boundary layer control

• Techniques used to manipulate the boundary layer on an airfoil to improve its performance
• Suction is applied through small holes or slots to remove the low-energy boundary layer, delaying flow separation (Griffith airfoil)
• Blowing involves injecting high-velocity air into the boundary layer to energize it and prevent separation (Circulation Control Wing)
• Vortex generators are small protrusions that create streamwise vortices, mixing high-energy flow with the boundary layer (Boeing 737 with vortex generators)

Airfoil performance analysis

Lift coefficient vs angle of attack

• The lift coefficient (Cl) represents the normalized lift force generated by an airfoil at a given angle of attack (α)
• The Cl vs α curve shows the variation of lift with angle of attack, including the linear region, the maximum lift coefficient, and the stall angle
• The slope of the linear region (dCl/dα) is typically around 2π per radian for thin airfoils, but can be lower for thick or highly cambered airfoils
• The maximum lift coefficient (Cl_max) and stall angle (α_stall) depend on the airfoil shape, Reynolds number, and Mach number (NACA 0012: Cl_max ≈ 1.5, α_stall ≈ 15°)

Drag polar

• The drag polar is a plot of the lift coefficient (Cl) versus the drag coefficient (Cd) for an airfoil
• It shows the relationship between lift and drag over a range of angles of attack or operating conditions
• The minimum drag coefficient (Cd_min) occurs at zero lift for symmetric airfoils, and at a slightly positive lift coefficient for cambered airfoils
• The drag polar can be used to determine the best lift-to-drag ratio, the maximum lift coefficient, and the drag divergence Mach number

Lift-to-drag ratio

• The lift-to-drag ratio (L/D) represents the aerodynamic efficiency of an airfoil, with higher values indicating better performance
• The maximum L/D ratio ((L/D)_max) occurs at a specific angle of attack and lift coefficient, depending on the airfoil design
• Typical (L/D)_max values range from 20 for low-speed airfoils to 200 for high-performance sailplane airfoils (NACA 0012: (L/D)_max ≈ 60)
• The L/D ratio is an important parameter for determining the glide ratio, the power required, and the range of an aircraft

Pitching moment characteristics

• The pitching moment coefficient (Cm) represents the normalized torque acting on an airfoil about a reference point (usually the quarter-chord point)
• The Cm vs α curve shows the variation of pitching moment with angle of attack, including the zero-lift pitching moment (Cm_0) and the slope (dCm/dα)
• Positive camber typically results in a negative Cm_0, which requires a downward tail force to trim the aircraft
• The pitching moment characteristics affect the longitudinal stability and control of an aircraft, as well as the trim drag penalty
• Supercritical airfoils are designed to have a more positive Cm_0 to reduce the trim drag and improve the overall efficiency