Representation of a Fixed Propeller and Rudder

A fixed longitudinal propeller and rudder are represented as a steerable thruster which has two barred zones and available thrust magnitude which depends on the thrust direction. The characteristics of a propeller-rudder unit are determined for the maximum available ahead and astern thrust of the propeller for a range of angles up to the maximum allowable rudder angles. The total longitudinal and transverse forces due to the propeller-rudder unit for a rudder angle are given for ahead and astern thrust as:

• Ahead Thrust

• Astern Thrust

The coefficients , and are interaction coefficients, which depend on the rudder type and whether the thrust is ahead or astern.

The force produced by a propeller thrust T is assumed to be linearly proportional to that obtained with the maximum ahead or astern thrust and is given by:

The equivalent steerable thruster is represented by the resultant force and barred zone given by:

• Ahead Thrust

• Astern Thrust

The moment generated by the unit is given by

where is an effective lever arm of the rudder which is located at a distance from midships. is independent of the rudder angle.

The lever arm and rudder forces and depend on the rudder characteristics and the relative speed of flow into the rudder. This depends on the propeller characteristics and the vessel speed. Hence the longitudinal and transverse forces are given by

where is the relative direction of the flow into the rudder. The lift and drag forces L, D are obtained from the non-dimensional lift and drag coefficients and which depend on rudder angle and are defined by

where is the rudder area and is the relative speed of the flow into the rudder. Default lift and drag coefficients are given in Default Rudder Data for a normal rudder at two aspect ratios. The lift and drag forces are reduced to 85% of the ahead values when the propeller is thrusting astern.

The relative flow into the rudder and angle are determined in the program using methods based on References 50.

The rudder-propeller characteristics are not symmetrical for port and starboard rudder angles when a vessel side velocity is included. The program uses the equivalent steerable thruster characteristics in the thruster allocation logic, which is described in the next section. The propeller thrust and rudder angle is then determined by interpolation for the characteristic of the unit.

Where two rudders are present and the rudders can be operated independently, the rudder-propeller units can be represented as two independent equivalent steerable thrusters. Where the rudder angles are coincident, the units are initially treated as independent units and the rudder angles are then fixed at the calculated port and starboard rudder angle in turn. The holding capability is then re-evaluated and the optimum condition chosen. If holding is not possible with either of these conditions, the rudders are fixed with zero rudder angles.