Ship stability II - GZ curves and intact stability criteria
Including requirements for specific trades
Relevant documents and M-notices: MSN 1752, MGN 675, MSC.267(85)
In the first article in this series we briefly touched on GZ curves. What is a GZ curve and what does it tell us?
A GZ curve is a graphical representation of the righting arm (GZ, measured in metres) of a ship as a function of its heel angle (in degrees). Beyond 10° of heel the metacentre moves; this is what gives us the characteristic curve shown below.
The righting arm is the horizontal distance between vertical lines running through the centre of gravity (G) and the centre of buoyancy (B) when a ship is inclined. The curve shows how the righting arm changes as the ship heels, indicating its stability at various angles. The area under the GZ curve is used to assess the overall stability of the vessel; this is the righting moment and is measured in metre radians. You might be asked to draw and label a GZ curve, so make sure you’re confident doing this.
It is possible to find the following information from a GZ curve:
Initial GM. The slope of the GZ curve at the origin is the initial stability. Normally this is straight up to around 7°.
Angle of deck edge immersion. This is where the increasing curve ‘goes straight’ before curving the other way; this is called the point of contraflexure. On the image above this is around 30°.
The maximum GZ and the angle at which it occurs. In the image above this is at 43°.
The metacentric height. Where a line at 57.296° (1 radian) intersects the curve, read the GZ at this point; this is metacentric height (GM).
The range of positive stability and the angle of vanishing stability are found by looking at where the vessels GZ curve is above 0; that is, in this example, between 0° and 73°.
Angle of vanishing stability is the angle at which the vessel ceases to have a positive righting arm; in this case, 73°.