Dynamic modes and damping

Two different pitch time scales

A statically stable aircraft may oscillate after a disturbance. The amplitude trend determines dynamic stability.

Short-period motion

The short-period mode is a relatively rapid coupled α and pitch-rate motion. Damping normally suppresses the oscillation. Its exact period and damping depend on the aircraft, speed and control system.

A pilot who responds late to a rapid motion can add energy instead of removing it, contributing to pilot-induced oscillation. Control sensitivity, delay, gain and task demands matter together.

Phugoid energy exchange

The phugoid is a slower exchange between speed and height, often with relatively small α change in an idealised lightly damped case. Speed increases as height is lost and the reverse occurs during the climb portion.

The modes are idealised descriptions around a flight condition. Large disturbances, control laws and saturation can invalidate the small-disturbance picture.

Judge a response from successive peaks

Suppose recorded pitch-disturbance peaks are 5°, 3° and 1.8°. Each peak is 60% of the preceding peak, so the response is decaying. If the peaks were 5°, 5° and 5°, the motion would be undamped in that observation. Peaks of 5°, 6° and 7.2° would instead show a growing response, even if the first moment opposed the original α disturbance.

Do not classify damping from a single displacement that happens to be near zero. An oscillation crosses zero repeatedly while its envelope may still grow. Compare like-signed peaks or the overall envelope across time, and identify whether the observed motion is dominated by the rapid α/pitch-rate mode or slower speed–height exchange.

Play the laboratory with positive, zero and negative damping ratios. Keep the initial amplitude and natural frequency fixed. Explain which parameter changes the decay rate and which changes the oscillation time scale. The displayed frequency is supplied; assigning the curve to a real aircraft would require identified aerodynamic, inertial and control-system data.

Dutch roll and spiral are different motions

The same aircraft can have a well-damped rapid mode and a weakly divergent slow mode.

Dutch roll

Dutch roll couples yaw and roll in an oscillation. Directional restoring tendency, dihedral effect, damping and inertia determine the response. Swept-wing aircraft often use a yaw damper to improve damping.

A yaw damper adds appropriately phased control action. It is not a replacement for a pilot’s understanding of degraded systems or the approved limitations after its failure.

Spiral and roll subsidence

Roll subsidence is the usually rapid decay of roll rate after a disturbance when roll damping dominates. Spiral motion is slower and can develop into increasing bank and descending flight if the mode is unstable and uncorrected.

The laboratory varies damping of a normalised second-order response. It teaches decay, neutral oscillation and growth; it does not calculate a real aircraft’s modal frequency or handling quality.

Separate damping from a restoring spring

A yawing disturbance can create a restoring fin moment that brings the nose back toward the relative flow. If there is insufficient damping, the aircraft can overshoot and repeat the yaw–roll motion. A correctly phased yaw damper removes oscillation energy; merely increasing the restoring tendency is not the same operation.

In the laboratory, ζ = 0.25 gives a decaying envelope, while ζ = 0 gives constant amplitude under the ideal equation. Negative ζ makes the envelope grow. Increasing the natural frequency changes how quickly the oscillation cycles and also the decay rate per second for a fixed positive damping ratio. These effects should be described with time and amplitude rather than a vague claim of “more stability”.

When a yaw damper becomes unavailable, consult the approved system and operating limitations. The synthetic oscillator cannot establish a safe altitude, speed or turbulence limit for the degraded aircraft. Its purpose is to make the lost damping mechanism visible so the operational restriction has an understandable cause.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.