Good day, how does a GZ curve look for a vessel with a GM of 0?

The Rawson and Tupper equation for a wall-sided ship (valid from 0 degrees to the angle of deck edge immersion) states that GZ = GM*sin(a) + (BM/2)*tan^2(a)*sin(a), where a is the heel angle. If GM = 0, the GZ curve would follow the form of the second term of the Rawson and Tupper equation up to the angle of deck edge immersion. For a more traditional hull form, the (BM/2)*tan^2(a) would need to be replaced by Niedermairâ€™s hull form factor.

GM is the initial slope of the GZ curve so it would looks almost like this:

Loadcase 2 above has a slightly negative GM.

Slope = 0 the GZ curve would initially follow the X-axis.

Okay thank you for your response. With reference to the diagram provided, could it concluded that with load case 1, the KG is relatively low so the rolling period is short while with load case 2 the KG is relatively high so the rolling period is long.?

Thank you for your response.

The relationship is between GM and rolling period.

This is from La Dage and Gemert:

Here is the text:

Effect of GM on rolling. The first point to be made quite clear is that GM is by no means the only factor involved in the manner in which a ship rolls, although it is an important one. We know that with increased metacentric height a vessel will roll more quickly; that is, her period of roll in seconds will be short. The effect of GM on amplitude is less well known. It should be clearly recognized by shipâ€™s officers that a stiff ship in heavy weather not only has a short period of roll but also a large amplitude. Conversely, a tender ship is apt to have a long period of roll with small amplitudes.

To understand the reason why a large GM produces large amplitudes, we can compare a stiff ship with a raft. The raft as a type of vessel represents the acme of stiffness. And how does a raft behave in waves? Does it not assume exactly slope of the seas, thus inclining to large amplitudes? The stiff ship attempts to do the same. She is quick and alive, responding immediately as a wave rolls up her side and under her bottom. The stiff ships bobs about like a cork. The tender ship, on the contrary is sluggish. She lags behind the motion of the waves and thus tends to roll to lesser amplitudes.

Thanks for the clarification.

Ship stability is complex subject and for practical uses itâ€™s not necessary to get too deep into the weeds. I stick to whatâ€™s in La Dage.

In general GM is used for what is called initial stability and righting arm (GZ) is used for stability at large angles of inclination.