Coupled instabilities

Coupled Instabilities

Coupled instabilities arise when multiple axes interact. The most important modes are spiral instability, Dutch roll, and pitch phugoid.

1. Spiral instability

Mechanism

• Begins with a small bank angle (random from turbulence).
• Aircraft rolls slightly → lift vector tilts → horizontal component pulls aircraft into turn.
• Yaw rate increases → outer wing flies faster → more lift there → bank amplifies.
• Without pilot correction: growing spiral dive over minutes.

Period

Long: 30-100+ s per bank doubling.

Which aircraft affected?

• Most GA aircraft are slightly spiral-unstable.
• High-wings with dihedral are particularly susceptible (e.g. C172).
• Gliders can be spiral-stable (large vertical fin).

Recovery

• Pilot notices roll and altitude dropping.
• Aileron correction: back to wings level.
• Don't pull pitch! (pull-up in bank amplifies bank — "graveyard spiral").

Risk in IMC

• In IMC without sight: pilot does not notice spiral.
• After 1-2 min unchecked: bank > 60°, speed > Vne → structural damage.
• Famous: JFK Jr. accident 1999 (Piper Saratoga, IMC, spatial disorientation).

2. Dutch roll

Mechanism

• Yaw + roll out of phase (180° offset).
• On small yaw disturbance to the left:
  1. Sideslip left → right wing advances (leading).
  2. With swept wings: right wing has more effective lift → roll left.
  3. Yaw damping acts → yaw reverses → now to the right.
  4. Sideslip right → left wing leading → roll right.
  5. Oscillation with growing amplitude possible.

Period

Short: 2-10 s.

Which aircraft affected?

• Very roll-stable + weakly yaw-stable aircraft.
• High-wing with dihedral: yes, but usually damped.
• Swept aircraft (airliners): strongly susceptible — hence yaw damper mandatory.

Recovery

• Pilot damps with rudder opposite to yaw motion.
• Aileron locked during recovery.
• Yaw damper (if available) automatic.

Symptoms

• Nose "wags" back and forth around vertical axis.
• Wings roll slightly out of phase.

3. Phugoid

Mechanism

• Pitch + altitude in oscillation.
• Pitch up → speed drops → less lift → altitude drops → speed rises → more lift → pitch up.
• In stable aircraft damped.

Period

Long: 30-90 s in GA.

Effect

• In normal flight barely noticeable — autopilot or trim maintains pitch.
• In glide without correction can grow uncontrolled.

4. Roll subsidence (aperiodic roll damping)

• Pure damping without oscillation.
• On aileron deflection: roll rate reaches steady value.
• On release: roll rate falls aperiodically to zero.
• Time constant: 0.5-2 s typical.

5. Short-period pitch

• Very short, damped pitch oscillation.
• On α disturbance.
• Period: 2-5 s.
• Strongly damped in normal aircraft.

Operational pilot recommendations

• In VFR: occasionally check bank (spiral drift), no continuous correction required.
• In IMC: constant attitude indicator scan. Recognise spiral tendency and correct.
• Airliner choice: yaw damper standard.

Academic depth

Lyapunov analysis and modal analysis are the mathematical methods to characterise these modes. Eigenvalues of the linearised system give period and damping.

Sources: Etkin & Reid Chapters 4-7 for complete treatment.

Example oscillation frequencies — GA