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The phugoid
So far we have looked at the short period pitching motion of an aircraft. This, however, is not the only type of longitudinal motion we shall encounter. There are, in fact, two types of oscillation which can take place. Fortunately the second motion is of a much lower frequency than the SPPO and, although the two motions will in reality take place simultaneously, we can consider them separately for a conventional aircraft without too much error.
When the aircraft’s flight path is disturbed so that its downward slope is increased, a weight component will act in the direction of flight (Fig. 12.6). This will cause the speed to increase. The fact that the aircraft is statically stable and the motion relatively slow means that it keeps in trim and the angle of attack remains nearly constant. Thus the increase of speed leads to an increase in the lift. The downward slope of the flight path is therefore reduced, as shown in Fig. 12.6.
Eventually the increase in lift causes the aircraft to rise again and another oscillating motion takes place. In this case both the aircraft speed and height change; the maximum speed corresponding to the minimum height, and vice versa. Another way of viewing this motion is to consider it as an oscillatory interchange between the kinetic and potential energies of the aircraft.
Once more, if this were all that happened the motion would persist at constant amplitude in an undamped state. However, as the speed increases the drag of the aircraft also increases. Conversely, when the speed is lowest at the highest point of the flight path (Fig. 12.7) the drag will be reduced. The drag variation thus works to oppose the speed variation and serves to damp out the
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Fig. 12.6 Phugoid Weight component causes increase in speed. This increases lift and this levels out flightpath |
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Fig. 12.7 Damping of Phugoid Increasing drag restricts speed increase in lower part of trajectory, damping the motion slightly |
oscillations. The overall effect is also to damp out the variation in height which accompanies the speed change.
For most aircraft, this drag change has a very weak effect. The motion will be effectively undamped and the oscillations will persist at an almost constant amplitude. The motion has a low frequency, typically taking about a minute to complete a cycle. Because of the very long period of the oscillation, this motion usually presents no problems either to a pilot or an automatic pilot since there is ample opportunity to damp the motion by use of the controls.
This motion is called a ‘phugoid’; a term invented by F. W. Lanchester, one of the great pioneers of flying. He was, unfortunately, given to inventing impressive sounding names for such phenomena!
Although the phugoid is relatively easy to control it can cause complications if allowed to develop too far. A height change between the top and bottom of 300 m or so is quite possible, and it does not need much imagination to see the difficulties that this could cause on landing!
A further interesting thing to note is that the motion we have described depends on the aircraft remaining in longitudinal trim. Thus a rearward movement in the centre of gravity can not only disturb the static stability, but can also have gravely detrimental effects on the phugoid behaviour.
Lateral stability
The asymmetrical lateral motion is made up of three basic motions which can be combined together. These are sideslip, roll and yaw (Chapter 11). As in the case of the symmetrical longitudinal motions studied above, a complicated series of movements takes place simultaneously. These movements are, for most conventional aircraft, sufficiently separated in characteristic frequency and damping for us to consider them in isolation, as we did for the phugoid and SPPO. In doing this, however, we must remember that they will in reality take place simultaneously.
