Three-Dimensional Airflow and Wing Design

5.1 Wing Terminology

•  Wing Area (S): The plan surface area of the wing, including the part covered by the
• fuselage.
•  Wing Span (b): The distance from wingtip to wingtip.
•  Aspect Ratio (AR): The ratio of the wing span squared to the wing area (AR = b²/S). It
• defines the "slenderness" of a wing.
• High AR wings (long and thin) are found on sailplanes (AR ~35).
• Medium AR wings are found on transport jets (AR ~12).

• Low AR wings (short and stubby) are found on fighter jets (AR ~3).
•  Taper Ratio: The ratio of the tip chord to the root chord (Taper = Cₜ / Cᵣ).
•  Sweep Angle: The angle between the line of 25% chord and a line perpendicular to the root
• chord.

5.2 Wing Tip Vortices

• On a finite wing, the air from the high-pressure area below the wing's surface will always try
• to flow around the wingtip to the low-pressure area on the upper surface. This flow creates
• a powerful swirling vortex at each wingtip.
•  Spanwise Flow: This pressure differential creates a secondary flow pattern on the wing's
• surface: an outward flow on the bottom surface and an inward flow on the top surface.
•  Vortex Strength: These vortices are strongest when the pressure differential is highest,
• which occurs at high angles of attack (i.e., when flying slowly).

5.3 Induced Downwash and Induced Drag

•  The powerful wingtip vortices create a large field of downward-moving air behind the wing,
• known as
• downwash.
•  This downwash alters the direction of the relative airflow experienced by the wing,
• effectively reducing the wing's angle of attack.
•  This change tilts the total lift vector rearward. The horizontal component of this tilted lift
• vector is a drag force known as
• induced drag.
•  Induced drag is an unavoidable by-product of lift generation on a finite wing. The stronger
• the vortices, the greater the induced drag.

5.4 Wake Turbulence

•  The trailing vortices from a large aircraft can be extremely powerful and hazardous to other
• aircraft, a phenomenon known as wake turbulence.
•  Generation: Wake vortex generation begins when the nose wheel lifts off on takeoff
• (rotation) and ends when the nose wheel touches down on landing.
•  Vortex Characteristics: Vortex strength is determined by:
• Gross Weight: Heavier aircraft produce stronger vortices.
• Airspeed: Slower aircraft produce stronger vortices.
• Configuration: Aircraft in a "clean" configuration (flaps and gear up) produce stronger
• vortices for a given speed.
•  Vortex Behavior: The two vortices drift downwards and outwards, separating by about 3/4
• f the aircraft's wingspan. They can descend 500-1000 ft and persist for several minutes.

•  Avoidance:
• Landing: Stay above the preceding aircraft's flight path and land beyond its touchdown
• point.
• Takeoff: Rotate prior to the preceding aircraft's rotation point and climb above its flight path.