The spiral mode

The second of the lateral motions which we shall consider is also non­oscillatory, but this time it turns out that for most aircraft it is either very weakly damped or sometimes divergent with time. Some aircraft are so near the boundary of stability that the motion may, due to asymmetry of trim or engines, be just stable in one direction but slightly divergent in the other.

The motion is a combination of yaw and sideslip. Let us first examine the way in which the various forces and moments which influence this motion are generated.

A disturbance resulting in sideslip will lead to a sideforce caused by the relative motion of the air over the fuselage and over the fin. There will also be a yawing moment due to sideslip, which will cause an angular velocity to develop in yaw. This will be primarily due to the influence of the fin. These effects are illustrated in Fig. 12.9. In Chapter 11 it was described how, if the wing has dihedral, the wing on the side to which the aircraft is sideslipping will experience an increase in angle of attack, and the wing on the other side a corresponding decrease. This gives rise to a rolling moment away from the direction of sideslip. This, again, is a simplification. There will be other con­tributions to the rolling moment; for example due to the fin.

A rolling moment in the opposite sense is caused by the rate of yaw men­tioned above. This time it results from the fact that one wing will be moving through the air slightly faster than the other (Fig. 12.9(a)), an effect already encountered in Chapter 11. The wing which is moving at the higher speed will have the greater lift and a rolling moment will develop as shown.

The result of all this is fairly complicated as we have a mixture of side – force, and moments in both the rolling and the yawing senses. An initial side­slip will result in a yawing motion due to the force on the fin. What happens next rather depends on whether the rolling motion caused by the sideslip and dihedral is greater than that caused by the rate of yaw and the fin. Sometimes it is not, and the resultant rolling motion means that a component of weight now acts in such a way that the sideslip is increased (Fig. 12.9(b)). The aircraft slowly diverges into a spiral path. This motion is thus called ‘spiral divergence’.

Normally the motion is fairly slow, so the aircraft is able to respond rela­tively quickly to the yawing moment and the actual degree of sideslip is small. It is easily controlled and can be removed by increasing the dihedral. However, this has an adverse effect on a second, oscillatory, lateral motion.

Fig. 12.9 Forces and moments in spiral divergence

Sideslip causes sideforce on fin in turn causing yaw, and aircraft enters a curved path. Extra velocity on outer wing causes roll leading to further sideslip and divergence. Dihedral or sweep will lead to opposite rolling moment tending to stabilise motion