Aircraft dynamic modes
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Source: Flight dynamics
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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.
If the wind is not coming from the front, the aeroplane adjusts its direction by means of the horizontal stabilizer and the vertical fin, which are far behind the center of mass like in a shuttlecock. Such an aeroplane would dive, therefore the elevator is slightly pulled so that the aeroplane flies the so called phugoid, which is damped by drag into a glide. Any rotation is damped, but the yaw-rotation leads to different lift on the wings and induces roll. For simplicity in this article lets assume that this effect is slightly overcompensated by twisting the wings so the outer part has negative lift, or by bending the wing on a circle around the center of rotation that is using a swept wing, or by using a slight positive dihedral on the wing and strong negative dihedral on the horizontal stabilizer, or a vertical fin below the fuselage, or any combination of these. Such an aeroplane tends to fly spirals, therefor the dihedral is made more positive, the vertical fin area is reduced, and the center of mass is lowered until a stable region is reached between spiraling and the dutch roll.
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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 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. 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] Detection
While descending turns are commonly performed by pilots as a standard flight manoeuvre, the spiral dive is differentiated from a descending turn owing to its feature of accelerating speed. It is therefore an unstable flight condition and pilots are trained to recognise its onset, and to implement recovery procedures safely and immediately. Without intervention by the pilot, acceleration of the aircraft will lead to structural failure of the airframe, either as a result of excess aerodynamic loading or flight into terrain. Spiral dive training therefore revolves around pilot recognition and recovery.
[edit] Recovery
Spiral dive accidents are typically associated with visual flight (non-instrument flight) in conditions of poor visibility, where the pilot's reference to the visual natural horizon is effectively reduced, or prevented entirely, by such factors as cloud or darkness. The inherent danger of the spiral dive is that the condition, especially at onset, cannot be easily detected by the sensory mechanisms of the human body. The physical forces exerted on an aeroplane during a spiral dive are effectively balanced and the pilot cannot detect the banked attitude of the spiral descent. If the pilot detects acceleration, but fails to detect the banked attitude associated with the spiral descent, a mistaken attempt may be to recovery with mere backpressure (pitch-up inputs) on the control wheel. However, with the lift vector of the aircraft now directed to the centre of the spiral turn, this erred nose-up input simply tightens the spiral condition and increases the rate of acceleration and increases dangerous airframe loading. To successfully recover from a spiral dive, the lift vector must first be redirected upward (relative to the natural horizon) before backpressure is applied to the control column. Since the acceleration can be very rapid, recovery is dependent on the pilot's ability to quickly close the throttle (which is contributing to the acceleration), position the lift vector upward, relative to the earth's surface before the dive recovery is implemented; any factor that would impede the pilot's external reference to the earth's surface could delay or prevent recovery. The quick and efficient completion of these tasks is crucial as the aircraft can accelerate through maximum speed limits within only a few seconds, where the structural integrity of the airframe will be compromised.
For the purpose of flight training, instructors typically establish the aircraft in a descending turn with initially slow but steadily accelerating airspeed – the initial slow speed facilitates the potentially slow and sometimes erred response of student pilots. The cockpit controls are released by the instructor and the student is instructed to recover. It is not uncommon for a spiral dive to result from an unsuccessful attempt to enter a spin, but the extreme nose-down attitude of the aircraft during the spin-spiral transition makes this method of entry ineffective for training purposes as there is little room to permit student error or delay.
All spiral dive recoveries entail the same recovery sequence: first, the throttle must immediately closed; second, the aircraft is rolled level with co-ordinated use of ailerons and rudder; and third, backpressure is exerted smoothly on the control wheel to recover from the dive.
[edit] Dutch roll
The second lateral motion is an oscillatory combined roll and yaw motion called Dutch roll, perhaps because of its similarity to an ice-skating motion of the same name made by Dutch skaters; the origin of the name is unclear. 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.
