Forces on an A.C.V. Executing an Unsteady Motion 



The effect of smoothing on side force (Fig. 14a) is seen to be 

 even more vivid than on resistance (Fig. 13a). Increase in sharp- 

 ness has a considerable effect on the side force for very small, or 

 for very large, yaw angles - even at this relatively high speed. At 

 the same Froude number, the effect of sharpness on unyawed wave 

 resistance (Fig. 3a) was considerably less. The linear theory pre- 

 dicts a peak dimensionless side force of 2. 63 in contrast to a dimen- 

 sionless wave resistance of 0. 73 at zero yaw angle. It seems that 

 nonlinear and viscous effects would preclude the development of such 

 large side forces in practice. 



Different Froude numbers are considered in Fig. 14b. The 

 side force (for aa = /3a = 5) is seen to be positive for super-hump 

 speeds, and therefore favorable during a coordinated turn. It reaches 

 a maximum at a yaw angle of about 30° . Thus there is an optimum 

 sideslip angle for generating the maximum side force. For sub-hump 

 speeds, there is a range of yaw angle in which the side force is nega- 

 tive. 



Unsteady yawing motion is now considered. The side force 

 for different rates of constant rotational speed after travelling at 

 zero yaw angle for a long time is presented in Fig. 15. The abscissa 

 is the yaw angle, and is proportional to the time after the initiation 

 of the manoeuver. The general effect of increasing the yaw rate is to 

 decrease the available side force. However, as typical average yaw 

 rates are in the vicinity of 5° per unit time, it is clear that the un- 

 steady influence is of secondary importance. The side force qualita- 

 tively follows the same trends at the two speeds considered, namely 

 F = 0. 6 (fig. 15a) and F = 1. (Fig. 15b). 



Finally, in Fig. 16, a manoeuver is studied, in which the 

 yaw angle is instantaneously changed from zero to 5°, 10°, 15" 

 and 20 u . The distance the ACV must travel before the steady-state 

 side force is achieved is slightly greater for larger manoeuvers. 

 Nevertheless, this effect is small. Almost the full steady-state side 

 force is generated after the vehicle has moved one craft length at 

 F = 0. 6 (Fig. 16a), and after 1.25 craft lengths at F = 1.0 (Fig. 

 16b). 



A favorable side force is developed immediately after this 

 sudden yaw manoeuver, and then increases slowly at first. It may be 

 shown that for a small jump in yaw angle, the initially generated 

 side force is just one half of the final steady- state side force. This 

 feature is evident in the curves, particularly for the smaller ma- 

 noeuvers. 



57 



