The Dutch roll

The two ‘lateral’ motions which we have so far discussed have not been oscillatory in nature. The first was a heavily damped motion which takes place almost entirely in roll and the second, the spiral mode, primarily involves motions in yaw and sideslip. A third motion also occurs which takes the form of an oscillation.

This motion mainly consists of a combination of roll and yaw and the result is rather similar to a boat crossing a choppy sea obliquely to the waves. It has acquired the somewhat libellous name of ‘Dutch roll’ because of the supposed resemblance to the motion of a drunken Dutch sailor. The authors dissociate themselves entirely from any suggestion that Dutch sailors are more prone to intoxication than those of other nations, or that, when intoxicated, their gait is peculiarly eccentric!

Because the motion involved in Dutch roll is particularly unpleasant to the occupants of the aircraft, steps are usually taken to ‘design it out’ as far as possible, even though this usually means that some degree of spiral instability results.

The way in which the motion develops is as follows. If the aircraft is dis­turbed in the yawing sense then the fin will provide the restoring moment, known as ‘weathercock stability’, which will bring the aircraft back to its original heading. There will be an overshoot, however, and the aircraft will oscillate about its equilibrium position (Fig. 12.10). At the point of overshoot there will be an additional force on the fin due to the angular velocity in yaw (Fig. 12.10) and this will tend to oppose the motion and damp out the oscillations.

The motion is much more complicated than this, though, because during the period when the aircraft is yawed a rolling moment will be caused by the dihedral and sweep effects, as we have seen previously. This rolling moment will be maximum at the maximum angle of yaw (Fig. 12.11). There will also be a rolling moment due to the rate of yaw because one wing is travelling through the air at a higher speed than the other. Unlike the spiral mode, this tends to reinforce the rolling moment due to dihedral and sweep. However it will have its maximum value when the yawing velocity, rather than angle, is at its greatest. The motion is therefore a complicated mixture of rolling and yawing. No wonder it is so unpleasant!

The rolling motion will also react back on the motion in yaw. When the air­craft is rolled there will be a weight component inducing sideslip. This sideslip velocity will reduce the damping moment provided by the fin as the aircraft passes through the equilibrium position (Fig. 12.12). Thus the effect of dihed­ral or sweep, both of which encourage roll, is to reduce the damping of the motion. They also cause a slight reduction in the frequency of the oscillation.

Typically the motion has a period of a few seconds. For straight-wing air­craft the damping is usually quite good, but for swept-wing aircraft it can cause more of a problem, because the sweep accentuates the rolling and sideslip.

Air stream

Yawing displacement causes fin force tending to restore aircraft to its original attitude

LL >

As aircraft passes through its original position

yawing velocity is maximum. Resulting fin force opposes the motion, tending to damp oscillation

Fig. 12.10 Effect of fin in Dutch roll

Unfortunately, when we considered the spiral instability we found that increas­ing dihedral had the effect of improving the stability. Thus, if we decrease dihed­ral to improve damping in Dutch roll we make the spiral divergence worse. Usually a small degree of spiral instability is tolerated in order to alleviate the less pleasant Dutch roll.