The rate of turn required for geographically fixed turns: A formula and fast-time simulations

This paper concerns the derivation of a formula to follow geographically fi xed turns in a homogeneous current or tidal stream. Until now, various well -founded but limited approximations have been used. In principle, all these approximations are based on the formula v = omega x R. One result of this research is the development and use of a fast-time simulation program. The initial aim was to illustrate to trainees the consequences and, in particul ar, the possible dangers of these approximations. The fast-time simulation program can be used in support of real-time simulation. Comparisons with re al-time simulations carried out by the Dutch Pilots' Corporation (STODEL) i ndicate that the fast-time simulations generate turning-circle diameters th at differ by a maximum 4 percent. The relationship with path-prediction is also dealt with. The possibility of applying the developed formulae in prac tice and for passage planning is currently under investigation. The fast-ti me simulation program has not been developed for one specific ship: apart f rom the use of an assumed position of the pivoting point at 1/3 of the ship 's length from the bow, it does not take hydrodynamic effects into account.