Expression of the interactions and the coupling terms are various among research institutes. Especially on inflow velocity to the propeller, inflow velocity and attack angle to the rudder, various estimation formulas are proposed.

　

 In this section, under constant hydrodynamic conditions prediction of interactions are discussed as follows:

　

　

　

4.1 Expression of wake fraction 1-wP

　

 In this section, the relation between the estimated maneuvering motion and the expression on wake fraction at propeller position is discussed. In all of following discussion, mathematical model of hydrodynamic force acting on hull are same and hydrodynamic derivatives are gotten from captive test using 2.5m model. Hydrodynamic derivatives gotten by experiments at model point condition are applied. Following expression are compared,

　

1)

1 - wP = 1 - wPO(JP) + kw1(β - l'Pr') + kw2(β - l'Pr')²　(8a)

　

1 - wPo(JP) - awo + aw1JP + aw2J²P　(9)

 The effects of propeller loads and the effect of maneuvering motion such as turning and swaying motion are contained in the expression of wake fraction at propeller position.

　

2)

1 - wP = 1 - wPO + kw1(β - l'Pr') + kw2(β - l'Pr')²　(8c)

　

 The effect of maneuvering motion such as turning and swaying motion are contained in the expression of wake fraction at propeller position. Propeller load is treated as constant.

3)

1 - wP = 1 - wPO(JP)　(9)

 The effects of propeller loads are contained in the expression of wake fraction at propeller position. It is assumed that maneuvering motion make no effect on wake fraction.

　

 The predicted maneuvering motions using expressions mentioned above are compared in this section.

 Fig. 6 show the simulation results of turning motion applied rudder angle 30 degree. The solid lines indicate the measured results in free running model test using 2.5m model. Dotted line indicate the estimated one by using (8a), (9), chain line indicate the estimated one by using (8c), broken line indicate the estimated one by using (9). The solid line in time history indicate inflow velocity in to propeller: uP that is estimated by using propeller open chart and propeller thrust measured in free running model test. Rate of turn and thrust are made non-dimension by initial speed: Uo. Wake fraction 1-wp is important factor to estimate the thrust and rudder force. The difference of predicting method of 1-wp gives the affect on the turning trajectories. Especially, turning trajectories using (8a) and (9), (8c) shows difference from trajectory using (9). With regarding to time histories, rate of turn show similar tendency by applying any prediction method. uP estimated by propeller thrust in free running model test increased right after steered rudder, then reduced corresponding to ship's speed down and shows constant value. uP estimated by (8a) and (9), (8c) show similar tendency to measured one. Estimation of uP without taking turning motion into account shows big difference from others. Estimation of uP applying only effect of propeller loading shows small uP. Especially, the difference appears at the first phase of turning. The difference between measured uP and estimated uP become small in steady turning motion.

 The estimations of propeller trust show similar tendency. Estimated thrusts considering the effect of turning motion reappear the change of thrust right after steered rudder. The measured thrust once reduced and then increase to constant value. The estimated thrust considering only propeller loading dose not show the drop right after steering rudder. However, the estimated thrust in steady turning situation shows good agreement with measured one.