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Control and Stability 10

Stability and Control

Longitudinal Dynamic Stability

The considerations of longitudinal dynamic stability are concerned with the time history response of the aeroplane to disturbances, i.e. the variation of displacement amplitude with time following a disturbance.

From previous definition:

•dynamic stability will exist when the amplitude of motion decreases with time, and

•dynamic instability will exist if the amplitude increases with time.

An aeroplane must demonstrate positive dynamic stability for the major longitudinal motions. In addition, the aeroplane must demonstrate a certain degree of longitudinal stability by reducing the amplitude of motion at a certain rate. The required degree of dynamic stability is usually specified by the time necessary for the amplitude to reduce to one-half the original value: the time to damp to half-amplitude.

The aeroplane in free flight has six degrees of freedom: rotation in roll, pitch, and yaw and translation in the horizontal, vertical and lateral directions. In the case of longitudinal dynamic stability, the degrees of freedom can be limited to pitch rotation, plus vertical and horizontal translation.

Since the aeroplane is usually symmetrical from left to right, there will be no need to consider coupling between longitudinal and lateral / directional motions.

Thus, the principal variables in the longitudinal motion of an aeroplane will be:

•The pitch attitude of the aeroplane.

•The angle of attack (which will differ from the pitch attitude by the inclination of the flight path).

•True airspeed (TAS)

The longitudinal dynamic stability of an aeroplane generally consists of two basic modes of oscillation:-

•long period oscillation (phugoid)

•short period motion

While the longitudinal motion of the aeroplane may consist of a combination of these modes, the characteristics of each mode are sufficiently distinct that each oscillatory tendency may be studied separately.

Stability and Control

Long Period Oscillation (Phugoid)

The first mode of dynamic longitudinal stability consists of a long period oscillation referred to as the phugoid.

The phugoid or long period oscillation involves noticeable variations in:

•pitch attitude,

•altitude and

•airspeed, but

•nearly constant angle of attack (not much change in load factor).

The phugoid is a gradual interchange of potential and kinetic energy about some equilibrium airspeed and altitude. Figure 10.52 illustrates the characteristic motion of the phugoid.

Figure 10.52 Long period oscillation (phugoid)

The period of oscillation in the phugoid is between 1 and 2 minutes. Since the pitch rate is quite low and only negligible changes in angle of attack take place, damping of the phugoid is weak. However, such weak damping does not necessarily have any great consequence. Since the period of oscillation is so great, long period oscillation is easily controlled by the pilot. Due to the nature of the phugoid, it is not necessary to make any specific aerodynamic provisions to counteract it.

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Stability and Control 10

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Control and Stability 10

Stability and Control

Short Period Oscillation

The second mode of dynamic longitudinal stability is the short period oscillation.

Short period oscillation involves significant changes in angle of attack (load factor), with approximately constant speed, height and pitch attitude; it consists of rapid pitch oscillations during which the aeroplane is constantly being restored towards equilibrium by its static stability and the amplitude of the short period oscillations being decreased by pitch damping.

Figure 10.53 Short period oscillation

Short period oscillation at high dynamic pressures with large changes in angle of attack could produce severe ‘g’ loads (large changes in load factor).

Shown in Figure 10.53, the second mode has relatively short periods that correspond closely with the normal pilot response lag time, e.g. 1 or 2 seconds or less. There is the possibility that an attempt by the pilot to forcibly damp an oscillation may actually reinforce the oscillation (PIO) and produce instability.

Short period oscillation is not easily controlled by the pilot.

If short period oscillation occurs, release the controls; the aeroplane is designed to demonstrate the necessary damping. Even an attempt by the pilot to hold the controls stationary when the aeroplane is oscillating may result in a small unstable input into the control system which can reinforce the oscillation to produce failing flight loads.

Modern, large high speed jet transport aircraft are fitted with pitch dampers, which automatically compensate for any dynamic longitudinal instability.