2.3 Aerofoil Geometry & Design Parameters

2.3 Aerofoil Geometry & Design Parameters

The aerodynamic characteristics of a wing are dictated by the two-dimensional cross-sectional shape—the aerofoil profile—and the overall three-dimensional wing planform geometry. For certifying and maintaining aircraft under EASA Part-66 standards, engineers must master the geometric nomenclature, structural parameters, and reference centers governing aerofoil design.

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Geometric Terminology of an Aerofoil Section

An aerofoil profile is designed to produce lift efficiently while minimizing drag. Its shape is defined by standard geometric reference lines and dimensions.

                          Max Camber
                             v
                 Upper Surface Contour (Suction Side)
                /-------------*-----------------------\
               /     Mean Camber Line                  \
  Leading Edge* - - - - - - - - - - - - - - - - - - - - * Trailing Edge
    (LE)       \          Chord Line                   /   (TE)
                \-------------------------------------/
                 Lower Surface Contour (Pressure Side)
                             ^
                       Max Thickness (t)

Core Geometric Definitions

1. Leading Edge (LE): The forwardmost point of the aerofoil profile, usually designed with a rounded contour (leading-edge radius) to prevent early flow separation over a range of angles of attack.
2. Trailing Edge (TE): The aftmost point of the aerofoil contour where upper and lower airflow streams rejoin. It is typically drawn as a sharp or slightly blunted point.
3. Chord Line: The straight reference line drawn directly from the leading edge to the trailing edge. The distance between the LE and TE along this line is the chord length ($c$).
4. Mean Camber Line (MCL): The locus of points located exactly halfway between the upper and lower surfaces, measured perpendicular to the chord line. The MCL starts at the leading edge and ends at the trailing edge.
5. Maximum Camber: The maximum distance between the mean camber line and the chord line, expressed as a percentage of chord length ($c$). Camber measures the curvature of the aerofoil.
   • Zero Camber: The mean camber line lies directly on top of the chord line (Symmetrical Aerofoil).
   • Positive Camber: The mean camber line curves upward above the chord line (Asymmetrical / Cambered Aerofoil).
6. Maximum Thickness ($t$): The maximum distance between the upper and lower surfaces measured perpendicular to the chord line. It is expressed as a thickness-to-chord ratio ($t/c$):

$\text{Thickness Ratio} = \frac{t}{c} \times 100\%$

Typical Thickness Ratios across Flight Regimes

• Subsonic Transport Aircraft Wings: $t/c = 12% - 15%$ (Provides high structural depth for wing spars and internal fuel tanks while maintaining high $C_{L,max}$).
• High-Speed Transonic Wings: $t/c = 9% - 11%$ (Reduces wave drag rise near Mach 1.0).
• Supersonic Fighter Aircraft Wings: $t/c = 3% - 6%$ (Sharp leading edges and ultra-thin profiles to minimize supersonic wave drag).

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Aerodynamic Reference Points: Center of Pressure vs. Aerodynamic Center

Understanding where aerodynamic forces act along an aerofoil chord is critical for aircraft flight stability and flight control trim.

1. Center of Pressure (CP)

The Center of Pressure (CP) is the single point along the chord line where the resultant of all distributed static pressure and shear stress forces acts. If all aerodynamic forces were concentrated into a single total force vector, it would pass through the CP with zero net pitching moment at that point.

• Movement on Cambered Aerofoils (Unstable Movement): On a positively cambered aerofoil, the position of the CP moves as the angle of attack ($\alpha$) changes:
  • As $\alpha$ increases, suction over the forward upper surface intensifies, causing the CP to shift forward toward the leading edge.
  • As $\alpha$ decreases, upper surface suction shifts aft, causing the CP to move backward toward the trailing edge.
  • This forward/aft movement creates aerodynamic instability because a pitch-up nose displacement moves CP forward, increasing the pitch-up moment further.
• Movement on Symmetrical Aerofoils: On a symmetrical aerofoil, the CP remains virtually stationary at approximately 25% chord ($0.25c$) across all normal operational angles of attack.

2. Aerodynamic Center (AC)

The Aerodynamic Center (AC) is defined as the specific point along the aerofoil chord about which the pitching moment coefficient ($C_m$) remains constant regardless of changes in angle of attack:

$\frac{dC_m}{d\alpha} = 0$

• Subsonic Flow: For thin aerofoils in subsonic flow ($M < 0.8$), thin aerofoil theory proves that the Aerodynamic Center is fixed at the quarter-chord point (25% chord, $0.25c$) behind the leading edge.
• Supersonic Flow: When flow accelerates to supersonic speeds ($M > 1.0$), pressure distribution shifts aft, moving the Aerodynamic Center to approximately mid-chord (50% chord, $0.50c$).

Subsonic Flow (M < 0.8)                 Supersonic Flow (M > 1.0)
Aerodynamic Center (AC) at 0.25c        Aerodynamic Center (AC) shifts to 0.50c

LE |----*-------------------------| TE   LE |--------------------*----| TE
      0.25c                                                 0.50c

Summary Comparison: Center of Pressure vs. Aerodynamic Center

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Symmetrical vs. Cambered (Asymmetrical) Aerofoils

Aerofoil profiles are divided into two main structural categories based on mean camber line shape.

Comparison Matrix

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Standard NACA 4-Digit Aerofoil Designation System

The National Advisory Committee for Aeronautics (NACA) developed standardized numerical systems to describe aerofoil geometry. The NACA 4-digit series directly encodes geometric parameters into a four-digit number: NACA M P TT.

$\text{NACA } \mathbf{M} \mathbf{P} \mathbf{T T}$

1. First Digit (M): Maximum camber as a percentage of chord length ($c$).
   • Example: In NACA 2412, the first digit 2 = 2% maximum camber ($0.02c$).
2. Second Digit (P): Distance from leading edge to maximum camber location in tenths of chord ($0.1c$).
   • Example: In NACA 2412, the second digit 4 = maximum camber located at 40% chord from leading edge ($0.4c$).
3. Last Two Digits (TT): Maximum thickness as a percentage of chord length ($c$).
   • Example: In NACA 2412, the last two digits 12 = 12% maximum thickness-to-chord ratio ($0.12c$).

Decoding Example: NACA 0015

• First digit 0: 0% maximum camber (No camber).
• Second digit 0: Maximum camber location undefined.
• Last two digits 15: 15% maximum thickness-to-chord ratio ($0.15c$).
• Conclusion: NACA 0015 is a symmetrical aerofoil with a 15% thickness ratio.

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3D Wing Planform Design Parameters

When cross-sectional aerofoils are assembled into a three-dimensional wing, several planform parameters dictate overall aerodynamic performance.

1. Wingspan ($b$) and Wing Area ($S$)

• Wingspan ($b$): The tip-to-tip straight-line distance across the aircraft span.
• Wing Area ($S$): The total projected planform area of the wing, including the section projected through the fuselage centerline.

2. Aspect Ratio ($AR$)

Aspect Ratio is the ratio of wingspan to mean geometric chord ($\bar{c}$), or span squared to wing area:

$AR = \frac{b^2}{S} = \frac{b}{\bar{c}}$

• High Aspect Ratio ($AR > 10$): Found on sailplanes and long-range reconnaissance aircraft (e.g., U-2). Produces high lift-to-drag ratio ($L/D$) and low induced drag.
• Low Aspect Ratio ($AR < 4$): Found on supersonic fighters (e.g., F-16). Yields high structural strength, rapid roll rates, but high induced drag at low speeds.

3. Taper Ratio ($\lambda$)

Taper Ratio is the ratio of tip chord ($c_t$) to root chord ($c_r$):

$\lambda = \frac{c_t}{c_r}$

• Rectangular Wing ($\lambda = 1.0$): Constant chord; easy to manufacture, but aerodynamically inefficient due to strong tip vortices.
• Elliptical Wing: Uniform downwash distribution across span; yields minimum induced drag ($e = 1.0$), but expensive to manufacture (e.g., Supermarine Spitfire).
• Tapered Wing ($\lambda \approx 0.45$): Practical structural compromise that closely approximates elliptical lift distribution.

4. Wing Sweep Angle ($\Lambda$)

The angle between the 25% chord line (or leading edge) and the aircraft lateral axis. Swept wings delay transonic wave drag rise by reducing the normal velocity component ($V_n = V_\infty \cos \Lambda$).

5. Dihedral Angle ($\Gamma$)

The upward angle of the wings relative to the lateral axis. Dihedral produces lateral stability: when an aircraft rolls into a sideslip, the lower wing experiences a higher effective angle of attack, creating a restoring rolling moment.

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Aerodynamic Twist and Washout Mechanics

If a tapered wing stalled uniformly across its entire span, the wingtips would stall simultaneously with the root. This would cause catastrophic loss of aileron roll control and potentially enter a spin.

To prevent tip stall, aircraft designers incorporate washout (aerodynamic or geometric twist).

Wing Root Section                                   Wingtip Section
High Angle of Incidence (i_root)                    Lower Angle of Incidence (i_tip)
(Stalls First -> Warning Buffet)                    (Stalls Last -> Retains Aileron Control)

       /-----\                                             /-----\
======(=======)===========================================(=======)======
       \-----/                                             \-----/

Geometric vs. Aerodynamic Washout

1. Geometric Washout: The physical wing structure is twisted along the span such that the tip chord line is rotated nose-down relative to the root chord line. The angle of incidence at the tip is less than at the root ($i_{tip} < i_{root}$).
2. Aerodynamic Washout: The physical incidence angle remains constant, but aerofoil profile shapes vary along the span—using a high-camber profile at the root (stalls at lower $\alpha$) and a low-camber/thinner profile at the tip (stalls at higher $\alpha$).

Operational Purpose of Washout

• Preserves Roll Control at Stall: Washout ensures that the wing root stalls first while attached airflow is maintained over the outboard wingtips. Because the ailerons are located at the wingtips, the pilot retains positive roll control throughout the stall entry.
• Stall Warning Buffet: Separated turbulent wake from the stalled wing root flows downstream and strikes the horizontal tailplane, providing a physical aerodynamic buffet warning to the flight crew before full wing stall occurs.

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Wash-In (Opposite of Washout)

Wash-in is the reverse geometric twist: tip incidence is higher than root incidence ($i_{tip} > i_{root}$). Wash-in tends to stall the tip first, which is undesirable for aileron authority and is generally avoided on conventional transport wings. Part-66 exams test the vocabulary contrast:

If an exam question asks which twist preserves roll control at the stall, the answer is washout, not wash-in.

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Aerofoil Contamination: Ice, Snow, and Frost

Aerofoil contamination — including ice, snow, and frost — is an explicit EASA Part-66 Module 08 Appendix I topic because even thin roughness can destroy lift margin long before the wing looks "blocked."

Why Contamination Matters Aerodynamically

Lift and stall behaviour assume a clean surface that sustains a favourable boundary layer. Contamination:

1. Trips the boundary layer early — roughness elements (frost crystals, ice nodules, packed snow) promote premature laminar-to-turbulent transition and can provoke early separation.
2. Reduces $C_{L,max}$ — published flight-test data show that even light frost can cut maximum lift by 20–30% or more, depending on location and thickness.
3. Lowers critical angle of attack — stall occurs earlier; the aircraft may stall in a configuration that felt normal when clean.
4. Increases parasite drag — takeoff ground roll lengthens and climb gradient falls.

Ice vs Snow vs Frost (Exam Distinctions)

Critical Exam Trap

Contamination need not be thick to be dangerous. A frost layer of only a few millimetres on the upper wing can stall an aircraft on rotation. Part-66 candidates must associate contamination with boundary-layer disruption and loss of $C_{L,max}$, not merely with "extra weight."

Operational Link to Washout and Stall

Washout assumes the clean tip remains attached while the root stalls first. Upper-surface ice concentrated outboard can reverse that progression — tip stall first — destroying aileron authority. This is why cold-weather dispatch procedures treat wing contamination as a hard no-go, not a performance footnote.