General HydroStatics
Ship Stability Software
Command of the Week
(New or interesting aspects of GHS that you may not know about)


Free-surface moments. Who needs them?

The FSMMT command provides six forms of free surface moments applying to tanks. And if that isn't wild enough, up to three forms can be attached to the same tank simultaneously!—for different loads, of course.

None of this has been dreamed up by the GHS developers. These sundry treatments of free surface exist because of the demand for them.

If you allow GHS do things naturally, it recalculates the CG of every tank load whenever the heel or trim angle changes. It doesn't need free-surface moments at all. Run a righting-arm curve and you get the true stability picture. Not so with free-surface moments.

A free-surface moment will predict what happens to the CG of a tank load when the heel angle increases up to a moderate inclination: raise the CG according to the free-surface moment, and you get an approximation to the effect of the CG shift in the tank. But beyond a few degrees of heel, the free-surface method often gives increasingly false contributions to the righting arm. In some cases the errors are significant.

So why use free-surface moments? In short, because some stability criteria require that a free-surface method be applied.

Commonly the maximum free surface moment that the tank would see at any load is used for all loads. The justification for this is that free surface can increase abruptly as a tank's volume changes and thereby reduce initial stability significantly. So one sample tank loading does not necessarily represent the stability of similar loadings. By assuming the maximum free-surface moment at all times there are no surprises—for the most part. There are cases where the FSM methods overestimate stability.

A combination of the FSM method and the true-CG-shift method could cover those cases by increasing the CG by an amount representing the difference between the formal FSM and the true FSM, then running the righting-arm curve with CG shifts. GHS can do that too.

The load case shown below is interesting because it overestimates stability using the FSM method, even with maximum FSM.

Here is the righting-arm curve with true CG shifts:

With no CG shifting but rather raising the CG according to the FSM:

With no CG shifting but rather raising the CG according to the maximum FSM:

With true CG shifting and raising the CG by the difference between the CG elevations above. (Note that only the "fixed" CG is shown with the CG-shift methods since the total CG varies.):

Try it yourself:

 WEIGHT 147, 3.2F, 0, 10.0
 LOAD 0.5
  RA %1
 .RA "/FSM"
 LOAD 0.5
 .RA "/FSM"

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