Control surface effectiveness and reversal

Why it matters

An aileron is supposed to roll the aircraft by changing the lift on the wing. On a flexible wing the aileron also twists the wing, and that twist works against it. As speed rises the aileron loses effectiveness, and at the reversal speed it produces no net rolling moment at all; above it the aircraft rolls the wrong way. Aileron reversal limited the speed of several early jet fighters and still drives the torsional stiffness of thin, high-aspect-ratio wings and the choice of spoilers or inboard ailerons on transports.

Key ideas

Mechanism. Deflecting a trailing-edge aileron downward by δ increases the section lift (C_Lδ·δ) but also produces a nose-down pitching moment (C_Mδ·δ with C_Mδ negative), because the extra lift acts far aft. This nose-down moment twists the wing nose-down about the elastic axis, reducing angle of attack and hence lift. The control-induced lift grows with q; so does the twist that cancels it. At the reversal dynamic pressure q_R the two cancel exactly.

Typical-section model. Airfoil of area S and chord c on a torsion spring K_θ at the elastic axis (EA); aerodynamic centre (AC) a distance e ahead of the EA; lift-curve slope a = C_Lα; control derivatives C_Lδ (> 0) and C_Mδ (< 0, about the AC). Moment equilibrium about the EA gives the elastic twist for an aileron deflection δ:

θ = q·S·(e·C_Lδ + c·C_Mδ)·δ/(K_θ − q·S·e·a)

and the total lift change ΔL = q·S·(a·θ + C_Lδ·δ). Dividing by the rigid value q·S·C_Lδ·δ gives the effectiveness

η = (1 − q/q_R)/(1 − q/q_D), with q_R = −K_θ·C_Lδ/(S·c·a·C_Mδ) and q_D = K_θ/(S·e·a)

Reading the result.

• η = 1 at q = 0 (rigid behaviour) and η = 0 at q = q_R (reversal). Above q_R, η < 0: control action reversed.
• q_R does not depend on e: the effect of the AC offset cancels between lift and twist. Reversal is governed by torsional stiffness and the control derivatives.
• If q_R < q_D (the usual case for a well-designed wing) effectiveness falls steadily to zero. The q_D term amplifies all lift, so near divergence the behaviour changes.
• Reversal is not a structural failure or instability; the wing remains in stable equilibrium. It is a loss of control, and design requirements call for adequate roll power (often 50 % or more effectiveness) throughout the envelope, with q_R well above the dive speed.

3-D effects and remedies.

• On a real wing the twist builds up from root to tip, so outboard ailerons lose effectiveness first. Many transports lock out outboard ailerons at high speed and use inboard ailerons or spoilers, which produce little twisting moment.
• Increase wing torsional stiffness (GJ) near the aileron, use a stiffer, shorter-span aileron, or use differential tailplanes (tailerons) or active controls.
• Sweepback adds bending–torsion coupling that further reduces aileron effectiveness, because the bending caused by the aileron lift washes out the outer wing.
• Elevators and rudders on flexible fuselages and tails lose effectiveness by the same mechanism.

Links. Like divergence, reversal is static (A–E edge of Collar's triangle) and uses the same aerodynamic stiffness q·S·e·a. It is a fixed-q phenomenon, so the reversal true airspeed rises with altitude.

Formulas

η = (1 − q/q_R)/(1 − q/q_D) — aileron effectiveness, ratio of flexible to rigid lift change (dimensionless).

q_R = −K_θ·C_Lδ/(S·c·a·C_Mδ) — reversal dynamic pressure (Pa); K_θ (N·m/rad), S (m²), c chord (m), a = C_Lα (1/rad), C_Lδ (1/rad), C_Mδ (1/rad, negative, about the AC).

q_D = K_θ/(S·e·a) — divergence dynamic pressure (Pa); e distance of AC ahead of EA (m).

θ = q·S·(e·C_Lδ + c·C_Mδ)·δ/(K_θ − q·S·e·a) — elastic twist (rad) due to aileron deflection δ (rad).

V_R = √(2·q_R/ρ) — reversal speed (m/s).

Worked examples

Example 1 (standard). A typical section (1 m span) has S = 1.5 m², c = 1.5 m, e = 0.225 m, a = 2π per rad, C_Lδ = 1.8 per rad, C_Mδ = −0.30 per rad and K_θ = 5.0 × 10⁴ N·m/rad. Find the reversal speed at sea level and the aileron effectiveness at 150 m/s.

1. q_R = −K_θ·C_Lδ/(S·c·a·C_Mδ) = 5.0 × 10⁴ × 1.8/(1.5 × 1.5 × 6.283 × 0.30) = 90 000/4.241 = 21 220 Pa.
2. V_R = √(2·q_R/ρ) = √(2 × 21 220/1.225) = 186.1 m/s.
3. q_D = K_θ/(S·e·a) = 5.0 × 10⁴/2.1206 = 23 580 Pa (from the divergence topic).
4. At 150 m/s, q = 13 781 Pa: η = (1 − 13 781/21 220)/(1 − 13 781/23 580) = 0.3506/0.4155 = 0.844.

Answer: V_R ≈ 186 m/s; at 150 m/s the aileron gives about 84 % of its rigid-wing lift.

Example 2 (GATE level). For the same section geometry and aerodynamics, what torsional stiffness gives a reversal speed of 250 m/s at sea level? With that stiffness, what is the effectiveness at 200 m/s?

1. Required q_R = 0.5 × 1.225 × 250² = 38 281 Pa.
2. From q_R = −K_θ·C_Lδ/(S·c·a·C_Mδ): K_θ = q_R·S·c·a·|C_Mδ|/C_Lδ = 38 281 × 4.241/1.8 = 9.02 × 10⁴ N·m/rad.
3. New q_D = 9.02 × 10⁴/2.1206 = 42 530 Pa.
4. At 200 m/s, q = 24 500 Pa: η = (1 − 24 500/38 281)/(1 − 24 500/42 530) = 0.3600/0.4239 = 0.849.

Answer: K_θ ≈ 9.0 × 10⁴ N·m/rad (1.8 times the original); effectiveness at 200 m/s ≈ 0.85.

Common mistakes

• Confusing reversal with divergence: reversal is loss of control power with the wing still stable; divergence is structural instability.
• Expecting the AC–EA offset e to change q_R; it cancels out (it affects q_D and so η, but not where η = 0).
• Sign errors in C_Mδ: a trailing-edge-down aileron gives a nose-down (negative) moment.
• Using effectiveness to mean C_Lδ; effectiveness is the ratio of flexible to rigid control power.
• Forgetting that outboard ailerons on swept, flexible wings lose effectiveness fastest.

For GATE AE

Expect the reversal dynamic pressure or speed of a typical section from given stiffness and control derivatives, the effectiveness ratio at a given speed, the stiffness needed for a required reversal speed, and conceptual questions comparing reversal with divergence, the effect of altitude, and remedies (spoilers, inboard ailerons, stiffness). Practise the sign of C_Mδ.

Quick check

1. What is the aileron effectiveness at the reversal speed?
2. Does the AC–EA offset e appear in q_R?
3. If K_θ is doubled, by what factor does V_R change?
4. Above V_R, a right-roll command produces what?
5. Why are spoilers attractive for roll control at high speed?

Answers: 1. zero; 2. no; 3. √2; 4. a roll to the left; 5. they create little twisting moment on the wing, so they keep their effectiveness.