This paper concerns the derivation of a formula to follow geographically fixed 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 = ω × 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 particular, the possible dangers of these approximations. The fast-time simulation program can be used in support of real-time simulation. Comparisons with real-time simulations carried out by the Dutch Pilots' Corporation (STODEL) indicate that the fast-time simulations generate turning-circle diameters that differ by a maximum 4 percent. The relationship with path-prediction is also dealt with. The possibility of applying the developed formulae in practice and for passage planning is currently under investigation. The fast-time simulation program has not been developed for one specific ship: apart from 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.