Considering the possibilities of solving the non-linear equations of motion numerically on a digital computer, the author contrived a method for numerical calculation of the steered motion of ships in uniform wind and flow.
The aerodynamic forces and moments and the longitudinal hydrodynamic force were taken in as the intermittent functions of relative wind direction and the Froude number respectively, and were interpolated at need. The so-called rotary derivatives were decided by a least-squares method, up to the third order of transverse velocity, turning rate and rudder angle, from the tested points at various values of the parameters.The equations of motion were described on the absolute motion of ship, and the external and intertia forces and moments caused by the relative motions were calculated at every small time intervals and integrated.
As an example, calculations were carried out on a mammoth tanker regarding the required lowest speed and the course stability in a straight course and the turning behaviours in wind and flow. Results of the calculation on the turning characteristics in calm sea were compared with the tested results on a free-running model and on the actual ship.
The following conclusions were obtained concerning the method of the calculation and the calculated results on the steered motions of a ship in wind and flow.
(1) The non-linear equations of the un-steady motion of a ship can be calculated numerically on a digital computer.
(2) The required minimum speed and the course stability on a straight course within the limits of definite rudder and drift angles can be calculated.
(3) In some cases the course stability index has a periodic solution.
(4) At the above-mentioned minimum speed, the ship tends to be course-unstable mainly in case of heading flow and of following wind, though the stability is improved by the higher ship speed.
(5) The effect of wind and flow change remarkably according to the loading condition of ship.
(6) The average direction of the macroscopic “drift” of the steadily turning ship does not necessarily coincide with that of the uniform wind or flow, and the average speed of the “drift” is smaller than that of wind or flow.