3.3 Acceleration Derivatives

　

 As with the velocity derivatives a multiple regression analysis was performed for the uncoupled acceleration terms, Eq.(7). Again, the decision to retain any given variable was based on the attained t-statistic and all remaining attained values are above 5% significance.

　

　

 Insufficient data was available for the estimation of the coupled acceleration derivative. For completeness, and to proceed with the post analysis, suitable equations have been taken from the existing literature [11]; Eq.(8) and (9).

　

　

 Next, a scheme is proposed for calculating the pod contribution of the manoeuvring derivatives both stabilising and control. Methods are described for estimating the strut lift, pod body interaction and propeller race effects. Finally methodology and equations for the prediction of the velocity and acceleration stabilising derivatives and the linear control derivatives are presented for both rotating pod and flap combinations.

　

4.1 Initial Assumptions

　

 We begin by assuming conventional lift theory as shown in Eq.(10).

　

　

 However, there are two flow vectors which effect the lift, one caused by the ship advance velocity and the other caused by the accelerated propeller race. Then, these two flow velocities are combined in Eq.(11). Where δ is the helm angle with associated coefficient and α is the propeller race flow angle with respect to the pod with associated coefficient. However, as the lift curve slope is a function of form then the two slopes should be equivalent; Eq.(12). Further, the propeller race is assumed parallel to the pod body thus, assuming negligible downwash angle, gives the result shown in Eq.(13).