The phenomenon of the slowly varying drifting force on a mowed object in a random sea is explained and illustrated from the results of several model tests with a rectangular barge. These tests, conducted at the Netherlands Ship Model Basin, were an extension of an object executed program. Using the results of measured or calculated drifting forces on an object moored in regular waves, a prediction can be Made of the drifting forces induced by wave trains consisting of regular wave groups.

Also, for an irregular wave train the drifting force on the barge can be computed as a function of time, which makes it possible to calculate the surge motion of the barge. The results of tests and calculations show a reasonable agreement.


In the last few years the problems concerning the mooring of objects in random seas have gained much attention as a result of the necessity to load and discharge big tankers in open sea, or because the sea bottom has to be explored and exploited by vessels operating from the water surface.

Generally a floating object moored in waves will be subjected to forces causing horizontal and vertical motions and to moments causing angular motions about the horizontal and vertical axes. Here we will deal with the horizontal surge motion of a rectangular barge moored by means of linear springs in head waves. The surge motion can be split up into a mean excursion, a slowly varying motion, and a higher frequency oscillation around the slowly varying position. The period of the higher frequency oscillation is equal to that of the wave motion; and since a considerable amount of literature is available concerning this part of the motion, it will not be treated in this paper.

From the results of model tests in regular waves the mean drifting force on the barge could be determined as a function of the wave frequency. Using these data, the long-periodical surge motion of the barge was calculated for different stiffnesses of the mooring system for the condition in which the barge was moored in a wave train consisting of regular wave groups.

The results of these calculations are compared with model test results. From these and earlier executed tests it is clear that resonance phenomena may occur when the period with which the wave groups encounter the barge equals the natural period of the surge motion of the moored barge. period of the surge motion of the moored barge. It also appears to be possible to calculate the drifting force induced by regular wave groups when such a wave train is taken to consist of two regular waves with a small difference in frequency. The regular wave groups, used for a clear demonstration of certain long-periodical phenomena, have mainly educational value. Regular wave groups will seldom occur. Generally the wave height changes irregularly.

To estimate the drifting forces exerted on an object in a particular irregular wave train as a function of time, a method exists which produces reasonable results. This method, based on the principle of known drifting force in regular waves, principle of known drifting force in regular waves, will be dealt with. Starting from the obtained drifting force, the surge motion of the object moored in this particular wave train can be calculated. This is illustrated by comparison of some calculated surge motion records with those of measured ones.


The hydrodynamic forces on an object floating in regular waves may be resolved in an oscillatory part and in a constant part, of which the latter is part and in a constant part, of which the latter is known as the steady drifting force. Maruo shows that, for the two-dimensional case of an infinitely long cylinder floating in regular waves with its axis perpendicular to the wave direction, the steady drifting force Fd per unit length satisfies:

Fd = 1/2 pga .


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