Delta Wing & Vortex Lift

How vortex lift works

On a conventional wing at moderate angle of attack, air flows smoothly over the upper surface (attached flow) and the wing produces lift via a familiar pressure differential. Push the angle of attack past the critical value and the boundary layer separates chaotically — stall, lift loss, recovery only by reducing alpha.

A delta wing turns that picture inside out. The sharp, highly-swept leading edge forces flow to separate at the leading edge from the moment alpha exceeds about 5°. But because the edge is swept, the separation doesn't form a chaotic wake — it rolls up into a tightly organised conical vortex spinning along the leading edge from apex to tip. Underneath that vortex, on the upper wing surface, pressure drops dramatically because the rotating fluid creates strong centripetal suction. The wing experiences this suction as additional lift.

The contributions add. Polhamus' leading-edge suction analogy splits total lift into two terms:

C_L = K_p · sin(α) · cos²(α)        [potential-flow lift]
    + K_v · sin²(α) · cos(α)        [vortex lift]

For a 70° swept delta, K_p ≈ 1.3 and K_v ≈ 3.0. At α = 20°:

C_L,p = 1.3 · sin(20°) · cos²(20°)
      = 1.3 · 0.342 · 0.883
      ≈ 0.392

C_L,v = 3.0 · sin²(20°) · cos(20°)
      = 3.0 · 0.117 · 0.940
      ≈ 0.330

C_L_total ≈ 0.722

Vortex lift adds 84% on top of attached-flow theory. By α = 30°, the vortex term dominates outright. There is no equivalent on a conventional wing — at α = 30°, a 737's wing is fully stalled and producing no useful lift.

Why deltas exist

• Supersonic flight: high sweep keeps the leading edge inside the Mach cone.
• One wing for all regimes: same planform from takeoff to Mach 2+.
• High maximum lift coefficient through vortex augmentation (C_L,max as high as 1.7 on F-16-class deltas).
• Soft, gradual stall ("departure") instead of an abrupt drop in lift — the vortex breaks down progressively.
• Large internal volume for fuel and structure with a single deep spar.
• Stealth: the sharp leading edge and few discontinuities reduce radar cross-section.

Delta variants compared

	Pure delta	Cropped delta	Ogival delta	Double delta	Tailless delta	Tailed delta
Planform	Triangle to point	Tip cut off	Curved leading edge, varying sweep	Two kinked sweep sections	Delta + no horizontal tail	Delta + horizontal tail
Leading-edge sweep	50°–75° constant	50°–60° constant	~80° inboard, ~55° outboard	80° inboard, 60° outboard	varies	varies
Pitch control	Elevons (combined)	Elevons	Elevons + droop nose	Elevons	Elevons only	Stabilator
Examples	Avro Vulcan, Convair F-102	Mirage III, F-15 (modified)	Concorde, Tu-144	Saab Draken, SR-71	Mirage 2000, Vulcan	F-16XL, MiG-21 (canard'd variants)
Trim drag	High (no separate tail)	High	Moderate (curved planform helps)	Lower (kink balances)	High	Lower
Cruise efficiency	Modest at subsonic	Better than pure	Excellent at M 2.0	Excellent across Mach	Acceptable	Best of both

Geometry variants in detail

• Pure (simple) delta. Constant leading-edge sweep all the way to the wingtip apex. Avro Vulcan, Convair F-102, dart-like and clean. The penalty is large untrimmed pitching moment and high subsonic drag.
• Cropped delta. The tip is cut off, replaced by a short trailing edge — easier to mount ailerons, lower wave drag, and softens the apex's structural concentration. Mirage III, MiG-21 (modified), F-15 (modified delta-trapezoidal hybrid).
• Ogival delta. Leading edge is curved, with sweep varying smoothly along the span. Concorde and Tu-144 used this shape: ~80° at the apex and ~55° at the tip, blending high-sweep transonic efficiency with lower-sweep slow-flight lift. Generates a strong, well-controlled vortex that travels predictably across the span.
• Double delta. Two distinct sweep angles meeting at a span-wise kink: high sweep inboard, lower sweep outboard. The inboard section sheds a strong vortex that flows over the outboard section, energising its boundary layer and delaying stall. Saab 35 Draken (1955) was the first; the SR-71 chines work on the same principle.
• Tailless delta. No horizontal stabiliser; pitch and roll control come from elevons (combined elevators-ailerons) on the trailing edge. Lighter, simpler, lower drag, but limited pitch authority and high trim drag.
• Tailed delta. A delta wing with a separate horizontal stabilator (MiG-21 with later canards, F-16XL prototype). Combines delta volume with conventional pitch authority.
• Compound (hybrid) delta with strakes. A trapezoidal main wing with a sharp delta-like leading-edge extension (LEX) inboard. The LEX sheds a vortex that energises the main wing's boundary layer. F-16, F-18, F-22 all use this — strictly not a delta but it relies on the same vortex-lift physics.

Failure modes & design challenges

• Vortex breakdown. The leading-edge vortex sustains itself only against limited adverse pressure gradient. Beyond α ≈ 30–40° (depending on sweep), the vortex bursts into turbulent recirculation. When breakdown moves over the wing, the lift collapses on that side. Asymmetric breakdown causes wing rock: alternating roll oscillations of ±20° at 1–2 Hz, classic on F-18s and Mirages. Modern fighters with fly-by-wire damp it actively.
• High induced drag at low alpha. The same low aspect ratio that gives high sweep also gives high induced drag. Deltas burn fuel quickly during subsonic loiter — Concorde's 100 t fuel load was largely consumed by transonic acceleration and supersonic cruise, not gentle subsonic flight.
• Trim drag. The aerodynamic centre of a delta shifts substantially with Mach number. Subsonic, it sits roughly at quarter-chord; supersonic, it shifts back toward mid-chord. To trim out the resulting nose-down moment, the aircraft pumps fuel between forward and aft tanks (Concorde, SR-71) or applies sustained elevon deflection (which itself produces drag).
• High landing speeds and AoA. Vortex lift only exists at substantial alpha. Concorde's 11° landing AoA blocked forward visibility; the droop nose was the fix. F-16 pilots lift the nose to about 13° on touchdown.
• Pitch-up at vortex burst. When breakdown moves forward, the lift centre also moves forward, producing nose-up pitching just when the wing is losing lift. Departure-resistant control laws are mandatory.
• Buffet and structural fatigue. Strong leading-edge vortices oscillate and shed turbulent wakes that buffet the vertical tails downstream. F-18 vertical fins have repeatedly cracked from LEX-vortex-induced fatigue and require periodic reinforcement.
• Tip flutter. Long, low-aspect-ratio deltas are torsionally flexible. SR-71 outer wing panels were stiffened with corrugated skin specifically to manage flutter at Mach 3 cruise.

Real-world specs

• Concorde. 55° leading-edge sweep on an ogival delta planform, 358 m² wing area, M 2.04 cruise at 60,000 ft. Landing α ≈ 11°, approach speed 165 knots. Without leading-edge vortices it could not have landed at any reasonable speed.
• Mirage III. 60° cropped delta, 35 m² wing area, M 2.2 dash. Tailless; pitch control via elevons. The aircraft that proved the operational delta in combat (Six-Day War, 1967).
• Avro Vulcan. ~50° pure delta, 368 m² wing area, M 0.96 cruise. The bomber that demonstrated a delta could be benign at high subsonic cruise.
• Saab 35 Draken. 80°/57° double delta. M 2.0. The kink and its resulting vortex pair gave the Draken a margin of low-speed lift that pure deltas couldn't match.
• SR-71 Blackbird. Modified delta, ~60° leading-edge sweep, fuselage chines blending forward to generate body vortices. M 3.2 cruise; vortices kept the wing flying despite the thin, sharp airfoils required for supersonic efficiency.
• F-16 Fighting Falcon. Cropped trapezoidal wing with a strong forebody/wing-root LEX. The LEX vortex energises the main wing, allowing sustained controlled flight to α ≈ 26°.
• HFB-320 Hansa Jet. Forward-swept variant; not a delta but used negative sweep to delay tip stall — a design philosophy that complements delta vortex behaviour.