Limiting KG analysis allows you to analyse the hull at a range of displacements to determine the highest value of KG that satisfies the selected stability criteria. GZ curves are calculated for various KG values. After each cycle, the selected criteria are evaluated to determine whether the CG may be raised or must be lowered.

When comparing the results of a limiting KG analysis to that of a Large Angle Stability analysis, it is essential that the same heel angle intervals are used and that the free-to-trim options and CG are the same. Some criteria, notably angle of maximum GZ, are extremely sensitive to the heel angle intervals that have been chosen.

Select Limiting KG from the Analysis Type option in the Analysis menu or toolbar.

The initial conditions required for Limiting KG analysis are:

§   Displacement from the Analysis menu, select range for analysis

§   Heel from the Analysis menu, select range for calculation of GZ curves

§   Trim (fixed or free) from the Analysis menu

The range of displacements to be used is set in the same way as they are set in the KN analysis.

The heel angles used may differ from those used in the Large Angle Stability and KN analyses. To set the range of angles, select Heel from the Analysis menu. See Large Angle Stability on page 67 for further details.

For information on Trim settings for Limiting KG Analysis, see: Trim for KN, Limiting KG and Floodable Length analyses on page 96.

Note:

Since Limiting KG can be quite a time consuming analysis, you may wish to use a smaller number of heel angles than for the Large Angle Stability calculations. (However this will cause some loss of accuracy.)

Limiting KG calculations will be significantly faster if the trim is fixed.

§   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

§   Criteria

Limiting KG analysis results are

§   Limiting KG values, for each displacement and the limiting criterion.

§   Limiting KG vs displacement graph

The Limiting KG value is measured from the baseline, which is not necessarily the same as the zero point.

The Limiting KG analysis also checks that any selected equilibrium based criteria are passed at each VCG that it tries. However, you must still have at least one Large Angle Stability criterion selected.

Criteria are only evaluated on the positive side of the GZ curve, so if there is any form of asymmetry, it may be necessary to run the analysis heeling the vessel to both starboard and port (this can be done automatically in the Batch Analysis).

After a Limiting KG analysis has completed, the results in the Criteria results table display “Not Analysed”, this is because they do not necessarily refer to the final KG and would be misleading. If you require the limiting KG for each criterion individually or wish to perform a Large Angle Stability and Equilibrium analysis at each of the displacements and the corresponding limiting KG, this can be done in the Batch Analysis.

Some criteria may depend on the vessel displacement and or vessel’s VCG. Where these values are explicit in the criterion’s definition in Hydromax, the correct values of displacement and VCG will be used in the evaluation of these criteria. However, problems can arise if the criterion is only available in its generic form – most commonly heeling arm criteria where the heeling arm is specified simply as a lever and not as a moment. In this case, since the heeling arm is not related to the vessel displacement in its definition within Hydromax, the heeling arm will remain constant for all displacements (where it is perhaps desired that the heeling arm should vary with displacement. For example in the case where the heeling moment, rather than the heeling arm is constant).

Important:

For important information on varying displacement while evaluating criteria see Important note: heeling arm criteria dependent on displacement on page 183.

Convergence Error on page 98 in the Analysis Settings section.

Hydromax will iterate to a KG value that just passes all criteria you have specified in the criteria dialog. Hydromax will start with a set start KG value (e.g. 1 meter), run a large angle stability analysis and check the selected criteria. If any of the criteria fail, Hydromax will lower the KG and try again. If the criteria pass, Hydromax will raise the KG value and try to make the criteria fail. Hydromax will continue doing this until the limiting KG value has been iterated to within 0.1mm. If this tolerance is not achieved in a certain number of iterations, Hydromax will move on to the next displacement.

When performing a Limiting KG analysis, Hydromax will evaluate any equilibrium-based criteria that are selected for testing and act accordingly. However, at least one GZ-based criterion must also be selected. This is because to perform a sensible search, Hydromax must have at least one criterion that will improve by reducing the VCG; Hydromax assumes that raising the VCG will make criteria more likely to fail and that reducing the VCG will make the criteria more likely to pass. This is not necessarily the case for equilibrium-based criteria such as freeboard requirements or for GZ-based criteria such as Angle of maximum GZ; if only these types of criteria are selected, Hydromax may have difficulty in finding a true limiting KG and specify convergence errors.