Glossary term

Spiral Mode

Slow lateral-directional aircraft mode involving bank angle, yaw and sideslip, assessed for spiral convergence, divergence and pilot or autopilot workload.

Branch: Aerospace Engineering
Glossary type: phenomenon
Content: Glossary term
Updated: Jun 24, 2026
Revision: v1.0.0 · reviewed

Definition

phenomenon

Spiral mode is a slow lateral-directional aircraft mode in which bank angle, yaw and sideslip can converge slowly or diverge into a tightening turn if not corrected.

Spiral mode is usually represented by a slow real eigenvalue of the lateral-directional state-space model. A stable spiral mode gradually reduces bank disturbance, while an unstable spiral mode can let bank angle, turn rate and load factor grow over tens of seconds. It depends on the balance of dihedral effect, directional stability, roll damping, yaw damping, control effectiveness, mass properties, configuration, Mach number and flight-control laws.

Spiral mode is a slow lateral-directional aircraft mode involving bank angle, yaw and sideslip. A small bank disturbance may decay gradually if the mode is stable, or it may grow slowly into a tightening turn if the mode is unstable and no pilot, autopilot or stability-augmentation correction is applied.

In a linearized lateral-directional model, spiral mode is often associated with a slow real eigenvalue rather than an oscillatory pair. With the convention:

x(t)=x_0e^{\lambda_{sp}t}

a negative $\lambda_{sp}$ indicates decay, while a positive $\lambda_{sp}$ indicates divergence. The sign convention must match the state-space model, because a copied eigenvalue without model definition is not evidence.

Engineering Role

Spiral mode matters because it affects pilot workload, autopilot bank-hold authority, heading capture, envelope protection, upset recovery, instrument-flight monitoring and long-duration flight-test interpretation. It is usually slower than Dutch roll, so it can look harmless in short traces while still producing unacceptable bank-angle growth over a longer interval.

The mode is governed by the balance of lateral stability and directional stability. Dihedral effect, sweep, vertical-tail volume, roll damping, yaw damping, aileron effectiveness, rudder effectiveness, mass moments of inertia, configuration, Mach number and control-law scheduling all influence the result. A single derivative rarely explains the mode by itself.

Worked Example: Time to Double Bank Angle

A lateral-directional model predicts an unstable spiral eigenvalue:

Parameter	Value
Spiral eigenvalue, $\lambda_{sp}$	$+0.018\ \text{s}^{-1}$
Initial bank disturbance, $\phi_0$	$5.0^\circ$
Review time window	$60\ \text{s}$
Screening target	no bank-angle doubling before $30\ \text{s}$

For a positive real eigenvalue, the time to double the disturbance is:

\displaystyle t_2=\frac{\ln 2}{\lambda_{sp}}

Substitute the eigenvalue:

\displaystyle t_2=\frac{0.693}{0.018}=38.5\ \text{s}

The simplified target is satisfied because:

38.5\ \text{s}>30\ \text{s}

The bank angle after $60\ \text{s}$ is:

\phi(60)=\phi_0e^{\lambda_{sp}60}

\phi(60)=5.0e^{0.018(60)}=14.7^\circ

Now consider a control-law change that moves the spiral eigenvalue to:

\lambda_{sp}=-0.030\ \text{s}^{-1}

The decay time constant is:

\displaystyle \tau=\frac{1}{|\lambda_{sp}|}=\frac{1}{0.030}=33.3\ \text{s}

The same $5.0^\circ$ disturbance after $60\ \text{s}$ becomes:

\phi(60)=5.0e^{-0.030(60)}=0.83^\circ

Engineering comment: the first case passes the simple time-to-double screen but is still divergent. A release decision should not stop there. The review should also check bank-angle limits, load factor, turn rate, heading error, pilot workload, autopilot authority, aileron and rudder rate limits, sensor validity, degraded modes, turbulence sensitivity and uncertainty in the aerodynamic derivatives.

Distinction from Dutch Roll and Roll Subsidence

Spiral mode is different from Dutch roll. Dutch roll is an oscillatory yaw-roll-sideslip mode and is usually described by natural frequency and damping ratio. Spiral mode is usually nonoscillatory and slow, so eigenvalue sign, time constant and time to double are more useful first checks.

Spiral mode is also different from roll subsidence. Roll subsidence is usually a fast, heavily damped roll-rate decay dominated by roll damping. Spiral divergence concerns the slower bank-yaw-sideslip balance that can make the aircraft settle into an increasing turn.

The modes are separated for analysis, but real aircraft can couple them through mass properties, flexible modes, actuator limits, yaw dampers, aileron-rudder interconnects, envelope protection and pilot input. A clean modal label should not hide poor time-domain behavior.

What Changes Spiral-Mode Behavior

Spiral-mode stability and time scale depend on:

dihedral effect, wing sweep and lateral stability;
vertical-tail sizing, directional stability and rudder effectiveness;
roll damping, yaw damping and roll-yaw coupling;
aileron effectiveness, adverse yaw and coordinated-turn logic;
mass moments of inertia and fuel or payload distribution;
Mach number, dynamic pressure, altitude, flap setting and landing gear state;
autopilot bank hold, turn coordination, yaw damping and envelope protection;
sensor filtering, gyro bias, estimator drift and latency;
stores, icing, damage, asymmetric thrust and aeroelastic deformation.

Because the mode is slow, test duration matters. A short lateral-directional excitation may show acceptable damping of the oscillatory mode while missing a slow spiral divergence that becomes visible only after tens of seconds.

Validation and Common Mistakes

Spiral mode can be identified from state-space eigenvalues, flight-test bank releases, heading-hold or bank-hold telemetry, system-identification models, simulation sweeps or pilot-in-the-loop assessment. A defensible record states the flight condition, configuration, mass properties, center-of-gravity position, control-law mode, sensor filtering, actuator limits, atmospheric condition, sign convention and uncertainty.

Common mistakes include:

calling the aircraft stable because Dutch-roll damping is acceptable;
treating a positive spiral eigenvalue as harmless without checking time to double;
using a test window too short to reveal a slow divergence;
ignoring bank-angle growth, load factor and airspeed change during the spiral;
comparing eigenvalues from models that use different lateral-directional states or signs;
assuming autopilot correction is available in degraded modes;
checking lateral-directional modes without control-surface limits and sensor validity.

REF

Disciplines