MAXVCG with off-center TCG.
Question: The vessel which I am working on required the center of gravity to be to port of the centerline for equilibrium. When I ran the MAXVCG command, the TCG was set to zero. This resulted in an additional moment of W * tcg to starboard.
In order to simulate the off-center CG, an additional moment must be applied to port equal to the moment created by the shift in TCG.
As I understand, the RAH command assumes the vessel is in equilibrium condition and then calculates the righting arms. There is no shift in the TCG. Is this correct? Also, how does the SOLVE MAXVCG command interpret this situation?
You are correct about the MAXVCG process using TCG=0. Since the effect of a TCG on the righting arms is the addition of -TCG*COS(heel), you can get the same result by the addition of a cosine heeling moment of TCG*DISPL.      Using the RA command, you have the choice of doing it in the same way (TCG=0 and a compensating heeling moment) or using the TCG<>0 without the compensating heeling moment.      The SOLVE MAXVCG command does not set the TCG to zero. This command is like the RA command in that it deals with a specific condition. The MAXVCG command, on the other hand, is designed to produce a Maximum VCG which applies to ANY condition which has the given displacement and LCG (or initial trim) and TCG=0, under the same heeling moments, damage, wave, etc.     

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