High-lift devices: flaps and slats

Why it matters

A wing sized for efficient cruise has too little area to land at a reasonable speed. High-lift devices raise the maximum lift coefficient from about 1.5 to 2.5–3.5, cutting stall speed by a quarter or more and take-off and landing distances by a third or more. Their design decides runway requirements, approach attitude and a large share of wing weight and cost.

Key ideas

What limits C_L,max. The lift of a clean wing is capped by boundary-layer separation, which starts either at the trailing edge (thick sections) or just behind the leading-edge suction peak (thin sections). High-lift devices work by one or more of:

• increasing camber — shifts the lift curve up (α_L=0 more negative), so more lift at the same α;
• increasing area — extending the chord rearward (Fowler action) gives more lift for the same C_L based on the original area;
• controlling the boundary layer — slots feed high-energy air from the lower surface over the upper surface, and leading-edge devices reduce the suction peak, both delaying separation and raising the stall angle.

Trailing-edge flaps.

• Plain flap: the rear part of the section hinges down. Pure camber increase; ΔC_L,max ≈ 0.5–0.9.
• Split flap: only the lower surface hinges down; slightly more ΔC_L but much more drag (useful on approach).
• Slotted flap (single, double, triple): a gap lets lower-surface air energise the flap's boundary layer, so larger deflections stay attached; ΔC_L,max up to about 1.5–2.
• Fowler flap: moves aft on tracks, then deflects — increases area and camber and usually has slots; the most effective and most complex. Trailing-edge flaps raise C_L at a given α but slightly reduce the stalling angle, and they give a strong nose-down pitching moment that the tail must trim.

Leading-edge devices.

• Slat: a small auxiliary airfoil ahead of the leading edge, opening a slot. It takes over part of the suction peak and lets the main wing's boundary layer start fresh. Slats mainly raise the stall angle (by 5–10°), extending the lift curve rather than shifting it; ΔC_L,max ≈ 0.5–1.
• Krueger flap: hinges forward from the lower leading edge; used inboard on many jets.
• Drooped leading edge: increases leading-edge camber and reduces the suction peak.

Combined systems. Leading-edge devices extend the curve upward; trailing-edge flaps shift it upward. Used together (as on airliners: slats plus double-slotted Fowler flaps), C_L,max of 2.5–3.5 based on the clean wing area is typical. The price is drag, weight, complexity and noise. Powered-lift schemes (blown flaps, circulation control) go further by adding jet momentum.

Thin-airfoil estimate for a plain flap. A flap of chord fraction E = c_f/c deflected by δ acts like extra camber. Thin airfoil theory gives Δc_l = 2(π − θ_h + sin θ_h)·δ, with cos θ_h = 2E − 1. Real flaps reach only 60–80 % of this because of viscous effects at the hinge, so use empirical factors from your data book for design.

Operational points. Flaps are retracted for cruise because the extra drag and nose-down moment far outweigh the benefit; each flap setting has a placard speed above which structural loads are excessive. Take-off uses moderate settings (good L/D for climb); landing uses full settings (high C_L and high drag help the approach).

Formulas

• V_s = √(2W/(ρ∞·S·C_L,max)) — stall speed (m/s); W weight (N), S reference area (m²).
• V_s,2/V_s,1 = √(C_L,max,1/C_L,max,2) — same weight, area and density.
• Landing or take-off distance ∝ V² ∝ 1/C_L,max (for given weight, area, deceleration).
• Δc_l = 2(π − θ_h + sin θ_h)·δ with cos θ_h = 2E − 1 — thin-airfoil plain flap; δ in rad.
• Δα_L=0 = −Δc_l/(2π) — equivalent shift of zero-lift angle.
• C_L = L/(½ρ∞V∞²S) — always based on the clean reference area unless stated.

Worked examples

Example 1 (standard). An aircraft of weight 180 kN has a wing area of 40 m². C_L,max is 1.5 clean and 2.4 with slats and flaps. Find the sea-level stall speed (ρ = 1.225 kg/m³) in each case and the ratio of landing distances.

1. Clean: V_s = √(2 × 180 000/(1.225 × 40 × 1.5)) = √(360 000/73.5) = √4898 = 70.0 m/s.
2. With devices: V_s = √(360 000/(1.225 × 40 × 2.4)) = √(360 000/117.6) = √3061 = 55.3 m/s.
3. Check: √(1.5/2.4) = 0.791, and 70.0 × 0.791 = 55.3 m/s ✓.
4. Landing distance ratio ∝ V_s² ∝ 1/C_L,max = 1.5/2.4 = 0.625.

Answer: V_s = 70.0 m/s clean, 55.3 m/s with high-lift devices; landing distance falls to about 62 % of the clean value.

Example 2 (GATE level). A thin airfoil has a plain flap of 25 % chord deflected 10°. Using thin airfoil theory, find Δc_l and the change in zero-lift angle, and comment on real flaps.

1. cos θ_h = 2E − 1 = 2 × 0.25 − 1 = −0.5 ⇒ θ_h = 120° = 2.094 rad.
2. π − θ_h + sin θ_h = 1.047 + 0.866 = 1.913; dc_l/dδ = 2 × 1.913 = 3.83 per rad.
3. δ = 10° = 0.1745 rad; Δc_l = 3.83 × 0.1745 = 0.668.
4. Δα_L=0 = −Δc_l/(2π) = −0.668/6.283 = −0.106 rad = −6.1°.
5. Flap effectiveness τ = (dc_l/dδ)/(2π) = 0.61: each degree of flap is worth about 0.61° of angle of attack. A real plain flap would achieve perhaps 70 % of this, Δc_l ≈ 0.47.

Answer: Δc_l ≈ 0.67 (theory), α_L=0 shifts by −6.1°, flap effectiveness ≈ 0.61.

Common mistakes

• Saying slats mainly increase camber. Their chief effect is delaying leading-edge separation and raising the stall angle.
• Saying flaps increase the stalling angle. Trailing-edge flaps usually reduce it slightly while raising C_L,max.
• Basing C_L on the extended (Fowler) area in one place and the clean area in another.
• Forgetting the nose-down pitching moment of trailing-edge flaps and the trim drag it brings.
• Using stall speed ∝ 1/C_L,max instead of 1/√C_L,max.
• Expecting real flaps to match the thin-airfoil Δc_l.

For GATE AE

Expect: stall speed with and without high-lift devices; ratio of speeds or distances from C_L,max values; thin-airfoil flap effectiveness for a given flap-chord ratio; and MCQs comparing plain, split, slotted and Fowler flaps, slats and Krueger flaps — especially which device raises the stall angle and which adds area. Sketch the c_l–α curves for each device; most MCQs are answered from that sketch.

Quick check

1. Which flap type increases both camber and wing area?
2. C_L,max rises from 1.6 to 2.5: by what factor does the stall speed change?
3. Does a slat mainly shift or extend the lift curve?
4. Why are flaps retracted in cruise?

Answers: 1. The Fowler flap. 2. √(1.6/2.5) = 0.80. 3. It extends it to a higher stall angle. 4. They add large drag and a nose-down moment with no benefit at cruise C_L, and their placard speeds are below cruise speed.