Using Free Surface Moments in Stability Calculations

Applies to GHS/BHS versions 6.36 and later

A partially-filled tank reduces the hydrostatic stability of the ship by virtue of the shifting of the fluid within the tank. GHS and BHS account for this "free surface" effect by actually calculating the new C.G. of the fluid with each change of trim and heel.
Another method of representing the free surface effect is to elevate the ship's center of gravity by a suitable amount. This simplifies the calculation of righting moments as a function of heel since the tank's contribution to the center of gravity is considered to be fixed. The amount by which the C.G. is elevated may be chosen such that the additional righting moment produced by a small change of heel is the same as would be produced by the shifting of the tank's contents. This elevation of the C.G., multiplied by the weight of the ship, is called the free surface moment, or FSM.
The primary disadvantage of using the FSM is that it does not accurately represent the tank's effect on stability beyond a small increment of heel, since the FSM itself can be very different at different heel angles.

Applications of the FSM
In the past, the primary advantage of using the FSM was its relative simplicity, and although the availability of high-speed computers has made that less of an issue today, there remain some applications where the FSM is still a useful shortcut.
One such application uses maximum FSM values to represent the free surface even in a case of loading where the true FSM is less than maximum. The intent is to make a few sample cases representative, in a worst-stability sense, of all the various loads which would occur during normal operation.
Another application where the FSM is necessary is in the use of precomputed maximum VCG data for a quick stability check. In order to use maximum VCG data to assess the stability of a particular load case, the effect of slack tanks is conveniently and quickly represented by the FSM. The present VCG is increased by an FSM adjustment before being compared with the maximum VCG.

GHS Facilities for using FSM
 In order to accommodate these applications, GHS associates two FSM functions with each tank. One function is used for load factors between zero and just under 95%. The other is used with loads from 95% to 100%.
Each FSM function is allowed to have one of three forms: 1) a constant value; 2) a constant value except at zero and 100% loads where the value becomes zero; and 3) a variable equal to the true FSM value at each particular load.
GHS allows the value used by the first two forms of the FSM function to be either specified directly by the user or taken from the FSM present in a particular load at a particular heel and trim. A means of finding the load which has the maximum FSM at a particular heel and trim is available.
 2 In addition, GHS provides for a minimum FSM -- a "floor" value which becomes the effective FSM when it is greater than the FSM sum from the tanks. In addition to the overall FSM floor, individual FSM floors can be designated for each of the various descriptions of tank contents.
 Assigning FSM functions to a tank is done by means of the command which has the form,

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