Aircraft dynamic modes

The dynamic stability of an aircraft refers to how the aircraft behaves after it has been disturbed following steady non-oscillating flight.^[1]

Longitudinal modes

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.

Phugoid (longer period) oscillations

Main article: Phugoid

The longer period mode, called the "phugoid 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 pilot generally can control this oscillation himself.

Short period oscillations

With no special name, the shorter period mode is called simply the "short-period mode". The short-period mode is a usually heavily damped oscillation with a period of only 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. Ability to quickly self damp when the stick is briefly displaced is one of the many criteria for general aircraft certification.

Lateral-directional modes

"Lateral-directional" modes involve rolling motions and yawing motions. Motions in one of these axes almost always couples into the other so the modes are generally discussed as the "Lateral-Directional modes".^[2]

There are three types of possible lateral-directional dynamic motion: roll subsidence mode, spiral mode, and Dutch roll mode.

Roll subsidence mode

Roll subsidence mode is simply the damping of rolling motion. There is no direct aerodynamic moment created tending to directly restore wings-level, i.e. there is no returning "spring force/moment" proportional to roll angle. However, there is a damping moment (proportional to roll rate) created by the slewing-about of long wings. This prevents large roll rates from building up when roll-control inputs are made or it damps the roll rate (not the angle) to zero when there are no roll-control inputs.

Roll mode can be improved by dihedral effects coming from design characteristics, such as high wings, dihedral angles or sweep angles.

Dutch roll mode

Main article: 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.

Spiraling

Spiraling is inherent. All aircraft trimmed for straight-and-level flight, if flown stick-fixed, will spiral. Some types will spiral-dive. The difference is determined by the design of the aircraft. If a spiral dive is entered unintentionally, the result can be fatal as explained below.

A spiral dive is not a spin; it starts, not with a stall or from torque but with a random, increasing roll and airspeed. Without prompt intervention by the pilot, this can lead to structural failure of the airframe, either as a result of excess aerodynamic loading or flight into terrain. The aircraft initially gives little indication that anything has changed. The pilot’s “down” sensation continues to be with respect to the bottom of the airplane, although the aircraft actually has increasingly rolled off the true vertical. Under VFR conditions, the pilot corrects for this deviation from level automatically using the true horizon, while it is very small; but in IMC or dark conditions it can go unnoticed: the roll will increase and the lift, no longer vertical, is insufficient to support the airplane. The nose drops and speed increases: the spiral dive has begun.

This sequence is more likely with some configurations, such as low wing. With other configurations, such as high wing and relatively low power, the spiral does not become a dive.

The forces involved

Say the roll is to the right. A sideslip develops, resulting in a slip-flow which is right-to-left. Now examine the resulting forces one at a time, calling any rightward influence yaw-in, leftward yaw-out, or roll-in or -out, whichever applies. The slip-flow will:

push the fin, rudder, and other side areas aft of c.g. to the left, causing a right yaw-in,
push side areas ahead of the c.g. to the left, causing a left yaw-out,
push the prop-normal effect to the left, causing a yaw-out,(1)
push the right wingtip up, the left down, a left roll-out owing to the dihedral angle,
cause the left wing to go faster, the right wing slower, a roll-in,
cause the left wing to fly at a lower angle of attack with less drag than the right, a yaw-in(2) and simultaneous roll-in,
push the side areas of the aircraft above the c.g. to the left, a roll-out,
push the side areas of the aircraft below the c.g. to the left, a roll-in,

Also, an aerodynamic force is imposed by the relative vertical positions of the fuselage and the wings, creating a roll-in leverage if the fuselage is above the wings, as in a low wing configuration; or roll-out if below, as in a high-wing configuration.

Thus, a spiral dive results from the netting-out of many forces depending partly on the design of the aircraft, partly on its attitude, and partly on its throttle setting (a susceptible design will spiral dive under power but may not in the glide).

Examples

Flown stick-fixed under climb rpm a low-wing Cherokee will be in a spiral dive in less than a minute, but a high-wing Cessna 150 will climb while spiraling, like a big free-flight model airplane, all of which have high wings, some very high on pylons. Success in contests depends upon their models’ ability to climb fast in a tight spiral, under very high power, without pilot input and without spiral diving.

Excess energy in and recovery from a spiral dive

A diving aircraft has more kinetic energy (which varies as the square of speed) than when straight-and-level. To get back to straight-and-level, the recovery must get rid of this excess energy safely. The sequence is: Power all off; level the wings to the horizon or, if horizon has been lost, to the instruments; kill the zoom resulting from the excess speed (which will result in the same high forces as those encountered at the bottom of a loop), using steady and gentle forward stick; maintain a nose-up attitude (to bleed off the excess kinetic energy) until a desired speed is reached; level off and restore power.

Notes:

1. Re prop normal: A prop rotating under power is an invisible fin at the nose which is, in effect, a surface at right angles to any airflow arriving from any angle. It is called “normal” because it is at right angles (normal) to the longitudinal axis of the aircraft and also to any side flow. Its effect depends on throttle setting (high at high rpm, low at low) and the attitude of the aircraft.

2. Re angle of attack: A climbing aircraft encounters a slow downward airflow and a fast forward airflow. The vector sum of these, plus the angle of incidence rigged into the aircraft, makes up the angle of attack of the wings. Also, because the aircraft is yawing, the left wing is flying faster than the right even though both are connected to the same aircraft. The resulting left wing vector flattens and lengthens, while the right vector does the reverse. Thus the left wing is flying faster at a lower angle of attack than the right wing, a roll-in couple. This effect reverses when the aircraft is descending, preventing rather than promoting a spiral dive.

References

↑ Etkin, Bernard; Dynamics of Flight; 1982; ISBN 0-471-08936-2
↑ "Lateral" is used although the rolling motions are about the longitudinal axis

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