3.3 Drag Components: Parasite, Profile & Induced Drag

Aerodynamic Drag Breakdown

Drag is the retarding force acting parallel and opposite to the flight path direction. Every vehicle moving through a fluid experiences resistance. In EASA Part-66 aerodynamic theory, total aircraft drag ($D_{\text{total}}$) is categorized into two fundamental components: Parasite Drag ($D_p$) and Induced Drag ($D_i$).

$D_{\text{total}} = D_p + D_i = (D_{\text{skin}} + D_{\text{form}} + D_{\text{interference}}) + D_i$

Parasite Drag ($D_p$)

Parasite Drag is drag caused by moving a solid body through a fluid medium, unrelated to the generation of lift. It comprises three distinct physical mechanisms: Skin Friction Drag, Form (Pressure) Drag, and Interference Drag.

1. Skin Friction Drag ($D_{\text{skin}}$)

Skin friction drag is generated by the viscous shearing stresses between air molecules and the aircraft's outer skin within the boundary layer.

• Boundary Layer Mechanics: As air flows over a surface, the microscopic layer directly touching the skin comes to zero velocity relative to the aircraft (the no-slip condition). Flow velocity increases outward through the boundary layer until reaching 99% of freestream velocity.
• Laminar vs. Turbulent Flow:
  • Laminar Boundary Layer: Smooth, thin layer with parallel streamlines. Produces extremely low skin friction, but has low kinetic energy and is highly prone to separation under adverse pressure gradients.
  • Turbulent Boundary Layer: Thicker, highly energetic layer with swirling eddies. Produces significantly higher skin friction drag, but resists separation much better than laminar flow.
• Reynolds Number ($Re$): Dimensionless ratio of inertial forces to viscous forces: $Re = \frac{\rho \cdot V \cdot c}{\mu}$ Higher Reynolds numbers push the transition point forward toward the leading edge, converting laminar flow into turbulent flow.

2. Form (Pressure) Drag ($D_{\text{form}}$)

Form drag arises from the static pressure differential between the front and rear of a body caused by boundary layer separation.

• When airflow separates from a surface, a low-pressure turbulent wake forms behind the body.
• The high static pressure at the front stagnation point combined with the low static pressure in the rear wake creates a net backward pressure force.
• Streamlining: Refining body geometry (e.g., tapering the trailing edge with a fineness ratio of approximately $3:1$ to $4:1$) delays separation, drastically reducing wake size and form drag.

3. Interference Drag ($D_{\text{interference}}$)

Interference drag occurs when airflows over adjacent aircraft components (e.g., wing root junctions, engine nacelles, fuselage joints, landing gear struts) merge and collide. The mixing of intersecting boundary layers creates localized turbulence and separation greater than the sum of the individual parts.

• Mitigation: Smooth curved fillets and fairings are installed at structural intersections to transition airflow smoothly.

Profile Drag & The Parasite Drag Equation

In aerodynamic terminology:

$\text{Profile Drag } (D_{\text{profile}}) = D_{\text{skin friction}} + D_{\text{form drag (of the wing section)}}$

Profile drag represents the total basic drag of the 2D aerofoil section itself operating in isolation.

The Parasite Drag Equation

Parasite drag for an entire aircraft is calculated using a dynamic pressure formula analogous to the lift equation:

$D_p = C_{Dp} \cdot \frac{1}{2}\rho V^2 \cdot S$

Where $C_{Dp}$ is the non-dimensional parasite drag coefficient.

Because parasite drag is directly proportional to $V^2$, parasite drag is small at low speeds but grows exponentially as flight velocity increases, dominating total drag at high cruise speeds.

Induced Drag ($D_i$) Mechanics

Induced Drag ($D_i$) is an inevitable byproduct of lift generation on a 3D finite wing. It originates from the static pressure differential between the lower and upper wing surfaces.

Wingtip Vortex Formation & Downwash

1. Spanwise Flow: High static pressure air on the lower wing surface naturally leaks around the wingtips toward the low static pressure region on the upper surface. This sets up an outward spanwise flow on the bottom surface and an inward spanwise flow on the top surface.
2. Wingtip Vortices: At the wingtip and trailing edge, these opposing spanwise currents merge, producing powerful rotating helical trailing vortices that roll up behind the wing.
3. Induced Downwash Field ($w$): The trailing vortex system induces a strong downward velocity component ($w$) across the entire wing planform and downstream airflow field.
4. Apparent Relative Wind Tilt: This downwash vector combines vectorially with the freestream relative wind ($V_{\infty}$), rotating the local effective relative wind downward through an induced angle of attack ($\alpha_i$).
5. Backward Tilt of Lift Vector: Because aerodynamic lift ($L_{\text{effective}}$) is defined as perpendicular to the local effective relative wind, the total lift vector is tilted backward through the angle $\alpha_i$.

Resolving this tilted force vector relative to the freestream direction yields:

• True vertical force = $L = L_{\text{effective}} \cos \alpha_i \approx L_{\text{effective}}$
• Retarding horizontal force = Induced Drag ($D_i$) = $L_{\text{effective}} \sin \alpha_i \approx L \cdot \alpha_i$

Mathematical Formulation & Induced Drag Reduction

The induced drag coefficient ($C_{Di}$) is expressed mathematically as:

$C_{Di} = \frac{C_L^2}{\pi \cdot AR \cdot e}$

Where:

• $C_L$ is the lift coefficient.
• $AR = \frac{b^2}{S}$ is the Wing Aspect Ratio ($b$ = wingspan, $S$ = wing area).
• $e$ is the Oswald Wing Efficiency Factor ($e \le 1.0$, where $1.0$ corresponds to an ideal elliptical lift distribution).

Airspeed Dependency of Induced Drag

In unaccelerated level flight, total lift equals aircraft weight ($L = W = \text{constant}$):

$C_L = \frac{W}{\frac{1}{2}\rho V^2 S} \implies C_L \propto \frac{1}{V^2}$

Substituting $C_L$ into the induced drag equation:

$D_i = C_{Di} \cdot q \cdot S = \left( \frac{C_L^2}{\pi \cdot AR \cdot e} \right) \left( \frac{1}{2}\rho V^2 \right) S \implies D_i \propto \frac{(1/V^2)^2}{1} \cdot V^2 = \frac{1}{V^2}$

Thus, Induced Drag varies inversely with the square of True Airspeed ($D_i \propto \frac{1}{V^2}$). At low airspeeds (e.g., during takeoff, climb, or landing flare where $C_L$ is high), induced drag dominates total aircraft drag.

Design Mitigation Strategies for EASA Engineers