Subsonic Aerodynamics | 3D Flow Around Wings | PPL(A) Principles of Flight

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3D Airflow Around a Finite Wing

In two-dimensional theory, a wing is assumed to have infinite span — there are no wingtips, no vortices, and no spanwise pressure effects. This is a useful simplification for studying airfoil profiles in isolation, but it does not reflect reality.

All real aircraft wings are finite. The moment a wing has tips, the airflow around it becomes fully three-dimensional — and that changes everything about how lift and drag behave.

The 3D relative airflow around an aircraft is the vector sum of two components:

Component	Description
Undisturbed freestream vector	The undisturbed airflow approaching the aircraft from ahead
Induced velocity vector	The downward airflow (downwash) caused by lift generation — this alters the surrounding airflow direction

The vector sum of these two determines the local airflow the wing actually experiences — and it is this local flow that governs the lift and drag forces produced.

2D vs 3D — Why It Matters

In 2D flow (infinite wing), there are no wingtip effects. In 3D flow (finite wing), wingtip vortices form, downwash is created, the effective angle of attack is reduced, and induced drag appears. Understanding 3D effects is essential for predicting real aircraft performance — 2D theory alone is not sufficient.

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Wingtip Vortices

How They Form

Lift generation creates a pressure difference between the wing surfaces — low pressure above, high pressure below. Along the span of the wing, this pressure difference is maintained by the wing surface itself. But at the wingtips, the wing ends — and there is nothing to prevent the high-pressure air beneath from curling around the tip toward the low-pressure region above.

This spillage of air around each wingtip creates a rotating mass of air — the wingtip vortex. The vortex alters the streamline pattern near the wingtips, changing the local airflow direction and velocity distribution across the outer portion of the wing. This is why wingtip vortices are central to predicting induced drag and real aircraft performance — they are not just a curiosity, they fundamentally change how the wing behaves.

• Vortex rotation is strongest right at the wingtips
• Vortices trail behind the aircraft and descend after formation — typically 500–1000 ft below the original flight path
• Dissipation rate depends on aircraft size, weight, and atmospheric conditions
• Calm air prolongs vortex persistence; wind or turbulence speeds up dissipation

Rotation Direction

Viewed from the cockpit looking forward:

• Left wing vortex rotates clockwise
• Right wing vortex rotates counter-clockwise

Between the two vortices, both rotation directions drive air downward — this downward airflow behind the wing is called downwash.

Vortex Rotation — Exam Tip

Left wing vortex = clockwise (viewed from cockpit).
Right wing vortex = counter-clockwise (viewed from cockpit).
Both vortices combine to push air downward between them — that downward flow is downwash.

Downwash and the Effective Angle of Attack

The downwash produced by wingtip vortices tilts the local airflow downward in the region around and behind the wing. This has two important consequences:

1. Reduces the effective angle of attack — the wing no longer “sees” the geometric angle of attack set by the pilot. Instead, it sees a slightly lower effective AoA, because the incoming airflow is already angled downward by the vortex-induced downwash before it reaches the wing
2. Tilts the lift vector rearward — because lift always acts perpendicular to the local airflow (which is now tilted downward), a component of the lift force now points rearward — in the drag direction

The practical result: lift per unit span is lower near the wingtips than 2D theory predicts. To generate enough total lift to support the aircraft’s weight in straight and level flight, the pilot must set a higher geometric angle of attack than 2D theory alone would suggest.

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Induced Angle of Attack

The induced angle of attack (αᵢ) is the angular difference between:

• The wing’s geometric angle of attack — the angle the pilot sets via pitch input
• The effective (local) airflow angle — the actual direction of airflow at the wing, tilted downward by vortex-induced downwash

Think of it this way: the pilot sets a geometric AoA of, say, 5°. But because downwash is already tilting the incoming air downward by 1°, the wing only “experiences” an effective AoA of 4°. That 1° difference is the induced angle of attack.

The Chain of Cause and Effect

• Lift is generated → pressure difference between upper and lower surfaces
• Pressure difference → air spills around wingtips → vortices form
• Vortices induce rotational motion in surrounding air → airflow is deflected downward
• Downward deflection changes the local airflow angle relative to the chord line
• The angular difference between geometric AoA and local flow direction = induced angle of attack
• Induced AoA tilts the lift vector aft → a rearward drag component appears → this is induced drag

Induced Angle of Attack — Key Point

The induced angle of attack is not set by the pilot — it is an unavoidable consequence of generating lift on a finite wing. The only way to eliminate it entirely would be to have an infinitely long wing — which is impossible in practice.

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Induced Drag

Induced drag is the drag cost of generating lift on a finite wing. It exists because the lift vector is tilted rearward by the induced angle of attack — meaning part of the force that should be acting upward is instead acting backward, opposing the aircraft’s motion.

Formula

CDi = cL² ÷ (π × AR)

Symbol	Meaning
CDi	Induced drag coefficient (dimensionless)
cL	Lift coefficient
AR	Wing aspect ratio (wingspan² ÷ wing area)

Induced Drag Formula — Exam Essential

CDi = cL² ÷ (π × AR)

Two things to remember:

• cL is squared — so doubling the lift coefficient quadruples the induced drag coefficient
• AR is in the denominator — so a higher aspect ratio directly reduces induced drag

This is why gliders have very long, narrow wings — high AR minimises induced drag for efficient soaring.

Key Relationships

Factor	Effect on induced drag	Reason
Higher AoA	Increases	More lift → stronger vortices → more induced drag
Higher weight	Increases	More lift required → higher AoA → stronger vortices
Higher speed	Decreases	Lower AoA needed for same lift → weaker vortices
Higher aspect ratio	Decreases	Weaker vortices → less downwash → smaller induced AoA
Lower aspect ratio	Increases	Stronger vortices → more downwash → larger induced AoA
Winglets fitted	Decreases	Limit tip vortex formation → reduce downwash and induced drag

Winglets

Winglets are the upturned (or downturned) tips seen on many modern airliners and business jets. They work by blocking the spanwise spillage of air around the wingtip, reducing the strength of the vortex that forms there. Weaker vortex → less downwash → smaller induced angle of attack → less induced drag. The fuel savings on a long-haul airliner are significant.

Stronger wingtip vortices always produce higher induced drag. Anything that reduces vortex strength — higher AR, winglets, higher speed — reduces induced drag.

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Wingtip Vortex Strength

Vortex strength is not fixed — it varies with several aircraft and flight parameters. Understanding what makes vortices stronger or weaker is important both for aerodynamic efficiency and for wake turbulence awareness.

Weight

Heavier aircraft require more lift. More lift means a greater pressure difference between upper and lower surfaces — which drives a stronger spillage of air around the wingtip and a more powerful vortex.

Heavier aircraft → stronger vortices

Wing Aspect Ratio

Higher aspect ratio wings (long and narrow) spread the lift generation over a greater span. The pressure equalisation at each wingtip is less intense because the tip is further from the concentrated lift region, producing weaker vortices.

Higher AR → weaker vortices
Lower AR → stronger vortices

Speed and Angle of Attack

At lower speeds, a higher angle of attack is required to generate sufficient lift. A higher AoA increases the pressure differential across the wing, which strengthens the vortices.

Lower speed + higher AoA → stronger vortices
Higher speed + lower AoA → weaker vortices

Aircraft Configuration

Flaps, slats, landing gear, and speed brakes all alter the spanwise pressure distribution and modify how vortices form. Importantly, a clean configuration (no high-lift devices deployed) can actually produce stronger vortices than a configured aircraft — because the pressure distribution is more concentrated and the effective span loading is higher.

This is why wake turbulence is often strongest from a heavy aircraft in a clean configuration — such as a large jet that has just rotated and retracted its flaps.

Summary Table

Factor	Stronger vortices	Weaker vortices
Weight	Heavier	Lighter
Aspect ratio	Lower AR	Higher AR
Speed	Lower	Higher
Angle of attack	Higher	Lower
Configuration	Clean	Flaps/devices deployed

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Wake Turbulence

What It Is

Wake turbulence is the disturbed, turbulent airflow left behind a flying aircraft — generated primarily by its wingtip vortices. It is not the same as engine exhaust or propwash. Wake turbulence is a direct consequence of lift generation — any aircraft producing lift produces wake turbulence.

Hazards to Following Aircraft

Wake turbulence is one of the most serious hazards in aviation, particularly when a smaller aircraft follows a larger one:

• Can cause sudden, violent, uncommanded rolls — potentially exceeding the following aircraft’s full roll control authority
• Can cause severe disruption to airflow over the following aircraft’s wings and control surfaces
• Most dangerous during approach and landing — the aircraft is slow, low, and has very little altitude margin for recovery
• The vortices from the leading aircraft can sit directly on the approach path, invisible to the following crew
• Separation rules and pilot awareness are the primary defences

Factors Affecting Vortex Persistence and Strength

Weight of the preceding aircraft:

• Heavier aircraft produce stronger vortices — vortex strength is directly proportional to the lift being generated, which is directly proportional to weight in level flight
• A fully-loaded heavy jet on approach produces the most dangerous wake

Separation distance:

• Smaller separation means less time for vortices to dissipate or drift clear
• ATC separation standards are specifically designed to ensure vortices have dissipated or moved away before the following aircraft arrives at the same point

Altitude:

• At higher altitudes, lower air density means vortices dissipate faster
• At lower altitudes (on approach and departure), vortices persist longer and their impact is greater — this is where the hazard is highest

Atmospheric conditions:

• In calm conditions, vortices can persist for several minutes and remain close to the flight path
• Wind and turbulence accelerate dissipation and cause vortices to drift laterally away from the centreline
• A crosswind can hold one vortex stationary over the runway while drifting the other clear — a critical hazard for landing aircraft

Wake Turbulence — Critical Points for PPL Students

• Wake turbulence is strongest behind heavy, slow, clean-configured aircraft — e.g. a large jet just after rotation with flaps retracting
• Vortices sink after generation — typically 500–1000 ft below the original flight path — so flying slightly above the preceding aircraft’s flight path gives some protection
• In calm conditions, vortices can persist for several minutes
• A crosswind can hold a vortex stationary over the runway threshold — do not assume it has drifted clear
• Always respect wake turbulence separation — never close up on a heavy aircraft on approach, even if you can see it clearly ahead
• On departure, rotate before the preceding aircraft’s rotation point and climb above their flight path to avoid their wake