The computation of low frequency mooring forces on a tanker exposed to survival conditions requires knowledge of the hydrodynamic excitation and reaction forces. The low frequency excitation is caused by wave drift forces. The reaction forces on the tanker are a combination of added mass forces, wave drift damping forces, viscous forces and damping forces due to interaction with the mooring chains.
Withers  showed that for a chain turret moored tanker the interaction forces between the mooring system and the tanker contribute significantly to the low frequency motions of the tanker. In  Huijsmans presented an approximate method to include the interaction forces due to high and low frequency motions of the chain-turret moored tanker.
In this paper a direct simulation method for a chain-turret moored tanker will be applied for the correct instantaneous low and high frequency motions ofthe tanker, including the dynamic behaviour of the mooring chains. The latter will be modeled by a lumped mass method.
Comparison will be made of the direct Simulation method and an approximate method using the average chain damping. An evaluation of the chain damping contribution will be made using model test results and computations.
A moored tanker exposed to irregular head seas performs small amplitude wave frequency pitch, heave and surge motions and relatively large amplitude low frequency surge motions around a mean surge displacement. The mean surge displacement and the low frequency surge motions are due to the second order wave drift forces. Since the total damping of the low frequency motions is small, and in irregular head seas the frequency of the slowly varying forces corresponds to the natural surge frequency of the system, resonance occurs. Large low frequency surge motions and consequently large mooring forces may be the result.
For the design of the mooring system, the large amplitude motions and the corresponding forces are required and it is therefore of eminent importance to have knowledge about the low frequency excitation and reaction forces. The excitation and reaction forces as acting on a chain turret moored tanker are given below:
current velocity dependent wave drift forces/wave drift damping;
relative viscous/current force;
relative wind force;
inertia force due to virtual mass of thetanker;
reaction force caused by the mooringsystem.
All but the last item in the above list have been extensively discussed byWithers . The contribution of the mooring system to the low frequency surge motions has been a subject of considerable attention in the past years.
In a static sense the reaction force on the tanker moored by a chain-turretsystem represents the load displacement curve, being the restoring force. In reality, due to the low and high frequency motions of the turret, the chains are movingthrough the fluid.