Swept Wing

How sweep delays the shock

Picture an aircraft cruising at Mach 0.85. Air over the curved upper surface of an unswept wing accelerates locally and reaches Mach 1 before the freestream does — a shock wave forms, drag spikes, and the wing buffets. The aircraft hits a wall.

Now angle the wing back by 30°. The freestream still hits the wing at Mach 0.85, but the airfoil section only "sees" the velocity component normal to its leading edge. That normal component is V·cos(Λ):

M_normal = M_freestream · cos(Λ)
M_normal = 0.85 · cos(30°)
M_normal = 0.85 · 0.866
M_normal ≈ 0.74

The airfoil thinks the air is flowing at M 0.74 — well below the section's critical Mach number where shocks form. The wing does its lift-generating job in subsonic flow even though the aircraft is moving transonically. Increase sweep, and the freestream can climb higher before the section's normal Mach hits the critical value.

This was first formalised by Adolf Busemann in 1935 and independently by Robert Jones at NACA in 1945. The Messerschmitt Me 262, Boeing B-47, and every jet transport since has carried the idea forward.

When sweep pays

• Cruise Mach above 0.7 — below that, sweep costs more than it saves.
• Long-range transport, where every percent of cruise speed and fuel efficiency compounds.
• Supersonic flight, where high sweep keeps the leading edge inside the shock cone.
• Stealth shaping, where matching leading and trailing edge angles minimises radar return spikes.

Wing planforms compared

	Straight	Swept-back	Delta	Forward-swept	Variable-sweep
Cruise speed	Up to ~M 0.6	M 0.7–0.95	M 0.9–2.2	Subsonic / transonic	M 0.5–2.5
Stall behavior	Root first, predictable	Tip first, pitch-up	Vortex lift, no hard stall	Root first, predictable	Depends on sweep angle
Low-speed handling	Excellent	Poor without slats	Poor — high AoA	Excellent at root	Excellent (wings forward)
Structural challenge	Standard	Root bending; spanwise flow	Large spar carry-through	Aeroelastic divergence	Pivot pin loads, complexity
Examples	Cessna 172, P-51	737, A350, F-15	Mirage, Concorde, B-2	X-29, Su-47, HFB 320	F-14, F-111, B-1B, Tornado
Sweep angle	0°	15°–45°	50°–75°	−25° to −35°	Variable, e.g. 20°→68°
Drag at design point	Lowest at low M	Lowest at transonic	Tolerable at supersonic	Low-induced drag	Optimal across regimes

The price of sweep

Sweep is not free. The same geometry that delays shock formation also introduces aerodynamic and structural problems:

• Spanwise flow. Air on a swept wing tends to drift outboard along the span. The boundary layer thickens toward the tip, where it separates earlier than at the root.
• Tip stall. Because the tip's boundary layer is thicker, the wing tip stalls before the root. Ailerons sit near the tip, so the pilot loses roll control just when they need it.
• Pitch-up. When the tip stalls first, the lift centroid shifts forward (toward the unstalled root), producing a nose-up moment that worsens the stall.
• Reduced lift slope. The 2D lift curve slope is multiplied by cos(Λ), so a swept wing produces less lift per degree of angle of attack. Designers compensate with larger area, more camber, or high-lift devices.
• Heavier structure. Bending moments at the wing root grow with span and sweep. Sweeping the spar back complicates the wing-fuselage joint.
• Poor low-speed handling. Without slats and large flaps, swept wings have terrible takeoff and landing characteristics. Every airliner uses leading-edge slats and Fowler flaps to recover the C_L it loses to sweep.

The fix is a stack of aerodynamic countermeasures: washout (less geometric twist at the tip so it stalls last), wing fences (vertical plates that block spanwise flow), vortilons (small flow strakes), saw-tooth leading edges (kinks that shed boundary-layer-energising vortices), and full-span slats.

Sweep variants

• Swept-back (positive sweep). The dominant choice for transports and most fighters. Easy to engineer, well-understood failure modes.
• Forward-swept (negative sweep). Tip is forward of root. Stalls at the root first — preserving aileron authority and avoiding pitch-up. But the wing has divergent aeroelasticity: a gust deflects the tip up, which increases its local angle of attack, which deflects it more. Aluminium can't take it. Aeroelastic-tailored carbon-fibre layups (Grumman X-29 in 1984, Sukhoi Su-47 in 1997) made it structurally possible, but neither aircraft entered production.
• Variable-sweep (swing wing). Hinged at the wing root, swept aft for high speed and forward for low speed. F-14 Tomcat, F-111 Aardvark, B-1B Lancer, Panavia Tornado, Tu-160. Heavy, complex, expensive to maintain — no new design has used variable sweep since 1990.
• Cranked / yehudi. Inboard section is swept differently from the outboard. Used to balance structural mounting, fuel volume, and aerodynamic optimum at different span stations. Visible on the F-117 and several missile fins.
• Oblique wing. Single wing skewed across the fuselage — one side forward, the other back. Theoretically optimal for transonic cruise, demonstrated by NASA's AD-1, never adopted in production.

Failure modes

• Tip stall and pitch-up. The signature swept-wing failure. F-104 Starfighter, B-47, and early 707s suffered fatal departures. Modern transports prevent it with stick-shakers, stick-pushers, and fly-by-wire angle-of-attack limiters.
• Transonic shock-induced separation at the root. Air piles up where the wing meets the fuselage and a strong shock forms there. The Whitcomb area rule (necking the fuselage where the wing joins) and the supercritical airfoil are the responses.
• Mach tuck. As shocks form on the upper surface, the centre of pressure shifts aft, producing a nose-down pitching moment. The aircraft tucks under and accelerates further — a runaway dive. Mach trim systems counter automatically.
• Aeroelastic divergence (forward sweep only). The reason every X-29 had carbon-fibre spar caps with the fibres aligned to redirect bending into wash-out, not wash-in.
• Wing-pivot wear (variable sweep). The F-14's wing-glove seals leaked hydraulic fluid; the F-111's pivot bearings developed cracks that grounded fleets. Variable-sweep maintenance burdens are why nobody builds them anymore.
• Spanwise icing. Ice accumulates on the leading edge and disrupts the spanwise flow control. Boots, hot-air anti-icing, and electric heaters along the leading edge are mandatory.

Real-world specs

• Boeing 737. 25° quarter-chord sweep. M 0.785 long-range cruise. Has not changed planform fundamentally since 1967.
• Boeing 787. 32.2° quarter-chord. M 0.85 cruise. Carbon-fibre wing with significant aeroelastic tailoring and raked tips for induced-drag reduction.
• Airbus A350. 31.9° quarter-chord. M 0.85 cruise. Curved trailing edge for better high-speed performance.
• B-2 Spirit. 33° flying-wing sweep, no tail. Sweep also serves as the radar-cross-section reduction angle that aligns leading and trailing edges with major design facets.
• F-14 Tomcat. Variable from 20° (loiter) to 68° (Mach 2.4 dash). Wing-sweep program automatically schedules with Mach.
• SR-71 Blackbird. Modified delta with leading-edge sweep ~60° and chines blending into the fuselage for vortex lift at high Mach. Cruised at M 3.2.
• Concorde. 55° leading-edge sweep on a complex ogival delta. The wing was so highly swept it generated lift through stable leading-edge vortices instead of attached flow at high alpha during landing.