Aircraft dynamic modes
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The dynamic stability of a vehicle denotes the complete study of the motion occurring after the vehicle has been disturbed. If the aircraft returns to equilibrium without overshoot, the motion is a simple subsidence. If the disturbing moment produced by the deviation tends to overshoot, the motion is called divergence.
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[edit] Long and short period oscillations
Oscillating motions can be described by two parameters, the period of time required for one complete oscillation, and the time required to damp to half-amplitude, or the time to double the amplitude for a dynamically unstable motion. The longitudinal motion consists of two distinct oscillations, a long-period oscillation called a phugoid mode and a short-period oscillation referred to as the short-period mode.
The phugoid or long-period mode is the one in which there is a large-amplitude variation of air-speed, pitch and flight path angle, and altitude, but almost no angle-of-attack variation. The phugoid oscillation is really a slow interchange of kinetic energy (velocity) and potential energy (height) about some equilibrium energy level as the aircraft attempts to re-establish the equilibrium level-flight condition from which it had been disturbed. The motion is so slow that the effects of inertia forces and damping forces are very low. Although the damping is very weak, the period is so long that the pilot usually corrects for this motion without being aware that the oscillation even exists. Typically the period is 20-60 seconds.
The short-period mode is a very fast, usually heavily damped, oscillation with a period of a few seconds. The motion is a rapid pitching of the aircraft about the center of gravity. The period is so short that the speed does not have time to change, so the oscillation is essentially an angle-of-attack variation. The time to damp the amplitude to one-half of its value is usually on the order of 1 second.
[edit] Spiral dive
There are two types of possible lateral dynamic motion. The first is called the spiral mode. If a spirally unstable aircraft, through the action of a gust or other disturbance, gets a small initial roll angle to the right, for example, a gentle sideslip to the right is produced. The sideslip causes a yawing moment to the right. If the dihedral stability is low, and yaw damping is small, the directional stability keeps turning the aircraft while the continuing bank angle maintains the sideslip and the yaw angle. As this spiral gets continuously steeper and tighter until finally, if the motion is not checked a steep, high-speed, spiral dive results. The motion develops so gradually, however that it is usually corrected unconsciously by the pilot, who may not be aware that spiral instability exists.
To be spirally stable, an aircraft must have some combination of a sufficiently large Dihedral (which increases roll stability) and a sufficiently long vertical tail arm (which increases yaw damping). Increasing the vertical tail area then magnifies the degree of stability or instability.
The spiral dive should not be confused with a Spin (flight).
[edit] Dutch roll
The second lateral motion is an oscillatory combined roll and yaw motion called Dutch roll because of its similarity to an ice-skating figure of the same name made by Dutch skaters. The Dutch roll may be described as a yaw and roll to the right, followed by a recovery towards the equilibrium condition, then an overshooting of this condition and a yaw and roll to the left, then back past the equilibrium attitude, and so on. The period is usually on the order of 3-15 seconds. But it can vary from a few seconds for light aircraft to a minute or more for airliners. Damping is increased by large directional stability and small dihedral and decreased by small directional stability and large dihedral. Although usually stable in a normal aircraft, the motion may be so slightly damped that the effect is very unpleasant and undesirable. In swept-back wing aircraft, the Dutch roll is solved by installing a yaw damper, in effect a special-purpose automatic pilot that damps out any yawing oscillation by applying rudder corrections. Some swept-wing aircraft have an unstable Dutch roll. If the Dutch roll is very lightly damped or unstable, the yaw damper becomes a safety requirement, rather than a pilot and passenger convenience. Dual yaw dampers are required and a failed yaw damper is cause for limiting flight to low altitudes, and possibly lower mach numbers, where the Dutch roll stability is improved.
