Equilibrium analysis lets you determine the draft, heel and trim of the hull as a result of the loads applied in the table in the Loadcase window. The analysis can be carried out in flat water or in a waveform.

Select Equilibrium  from the Analysis Type option in the Analysis menu.

§   Displacement and Centre of Gravity using the Loadcase window

Also see:

Setting the Frame of Reference on page 20

The following environments can be applied to the Equilibrium analysis:

§   Fluid simulation of tank fluid centre of gravity

§   Density

§   Wave Form (if any)

§   Hog and Sag (if any)

§   Damage (or Intact) from the Analysis toolbar

§   Grounding (if any)

§   Criteria

Equilibrium Results are:

§   Hydrostatic data

§   Freeboard of key points, deck edge and margin line

§   Criteria evaluation

§   Time stepping animation

§   Curve of areas

Hydrostatic data

Height/freeboard above free surface

The freeboard of each Key Point is also calculated. The freeboard is for the vessel condition currently displayed in the Design view and is recalculated after each Equilibrium and Specified Conditions analysis. The freeboard calculated is the vertical distance of the Key Point above the local free surface; hence the local free surface height if a waveform is selected will be taken into account.

Freeboard of key points.

Negative freeboards, i.e. where the Key Points are immersed are displayed in red. The longitudinal positions at which the minimum freeboard for the margin line and deck edge occurred are also specified.

Stability Criteria Evaluation

The criteria results are displayed in the Criteria tab in the results window.

Equilibrium Animation in Waves

If performed in conjunction with analysis in waves, the Equilibrium analysis will automatically phase-step the waveform through a complete wavelength. This gives ten columns of results, one for each position of the wave crest. If necessary the results of this phase stepping can be animated giving a simple, quasi-static simulation of the hull motion in waves (Display | Animate).

Note:

This simulation only includes static behaviour at each wave phase, and does not cover dynamic or inertial forces. This can be done using Seakeeper.

The definition of equilibrium is “Position or state where object will remain if undisturbed”. You can distinguish equilibrium into two types:

§   Stable, when disturbed the object will return to its equilibrium position

§   Unstable, when disturbed the object will not return to its equilibrium position

With ships, an unstable equilibrium can exist when the KG > KM, i.e. the centre of gravity is above the metacentre (negative GMt). In real world a ship in unstable equilibrium will roll from the upright unstable equilibrium position to a position of stable equilibrium and assume an “angle of loll”. Since Hydromax starts the equilibrium analysis in upright position, it has no way of determining whether the equilibrium is stable or unstable. This means that unstable equilibrium may be found instead of the stable equilibrium. Therefore it is recommend to check the value of GMt yourself after doing an equilibrium analysis or perform a Large Angle Stability analysis and look at the slope of the GZ curve through the equilibrium heel angle.

The graph above shows the results of a Large Angle Stability analysis for a vessel with negative initial GMt. In practice this vessel would have a loll angle of approximately 25 degrees. If an equilibrium analysis is performed for this vessel with the transverse arm set to zero, Hydromax will find the unstable equilibrium position with zero degrees of heel.

In practice, it is desirable to find the stable equilibrium position. To do this, first ensure that the tolerances (Edit | Preferences) are set as sensitive as possible. This will ensure that the smallest possible heeling moment is required to find stable equilibrium position. Then create a very small heeling moment by offsetting one of the weight items in the loadcase window TCG by just a fraction. The equilibrium analysis will now find the stable equilibrium position.

Note:

It is good practice to always perform a Large Angle Stability analysis as well as the equilibrium analysis to check if the vessel is in stable or unstable equilibrium. This is most likely to occur if the VCG is too high and the vessel has negative GM when upright. The problem can be overcome by offsetting the weight of the vessel transversely by a small amount.