Because the damping of the Dutch roll depends mainly on the moment produced by the fin of the aircraft in response to the rate of yaw of the aircraft, it will be altered by changes in the fin effectiveness for a given amplitude of the motion. The fin effectiveness in response to yaw rate is reduced by increased altitude. This occurs for exactly the same reason that the effectiveness of the horizontal tail surface is reduced in response to pitch rate, as we saw earlier.
The Dutch roll therefore tends to become less stable for a particular aircraft attitude as the altitude increases. This effect can be very marked. D. P. Davies in his excellent book Handling the Big Jets (1971) states that in a landing configuration, Dutch roll can pass from a stable to an unstable
Fig. 12.13 Anhedral displayed by the Antonov AN-124, one of the largest and heaviest aircraft in the world. Aircraft with high-mounted swept wings normally require anhedral. Excessive lateral static stability can result in dynamic instability
condition between altitudes of 1000 ft to 8000 ft for a typical airliner. A similar deterioration in cruise configuration can take place between 18,000 ft and 22,000 ft.
Fortunately there is some slight compensation due to the fact that the same effect improves spiral stability with altitude. This, however, is small comfort as we are usually far more concerned with Dutch roll behaviour.
A further factor which works against us is caused by the fact that many high altitude aircraft, such as airliners, use some degree of sweepback. As we saw previously, this acts in the same way as dihedral, making the Dutch roll worse. Sometimes a degree of negative dihedral (anhedral) may be employed to counteract the effect (Fig. 12.13), but frequently it is better to avoid this and become resigned to artificially enhancing the stability characteristics, as will be described later.
Effect of structural stiffness
In the above arguments we have treated the aircraft as though it were a rigid body, but in reality there will be a considerable degree of flexibility both in the airframe and in the control systems. This will clearly influence the stability of the aircraft. In general, flexibility in, for example, the rudder will reduce the damping and make the Dutch roll less stable than before. Thus, when all factors are considered, it is difficult to design an aircraft, particularly a swept – wing aircraft which is required to cruise at high altitude, which naturally combines satisfactory spiral and Dutch roll behaviour. Nowadays the problem can be overcome electronically, as we describe in the following section.