More on Stability with Water Ballast

John Gilbert asked a question in response to my recent post, Stability with Water Ballast.

I do not get why the red and blue curves do not meet up at 180 degrees. Inverted the boat has no windward side as you point out, so you have water ballast on one side and none on the other side. As you have drawn the curves you have powerful stability in the  inverted position with the water on one side (red), but actually a righting moment if you have water on the other side(blue). What is the difference?

To help with understanding this I thought it better to write a new post that expands on the dynamics of stability than to try to answer it in the comments section after that post.

This will be more easily understood by seeing a diagram showing the stability graph expanded through a full 360 degrees rather than all conditions overlaid on top of each other in a 0-180 degree range. This is exactly the same stability info for the Didi 950 as shown in the graph of my earlier post but shown in a different manner.

Diagram of Stability through 360 Degrees

I will start with the green curve. This shows the stability without water ballast. The centre of gravity (CG) is on centreline. The stability curve intersects with the horizontal grid line at 0 degrees heel and increases identically both to left and right of the 0 degree line, so the boat will float without any heel to either side when right way up. The boat will stay that way in the absence of any wind, wave action or crew movement on the boat.

Follow the green curve until it comes down past 130 degrees to again intersect with the horizontal line at the Angle of Vanishing Stability (AVS). Then it enters a range of negative stability where it will proceed toward upside-down. At 170 degrees it crosses to above the horizontal line again. This indicates that the superstructure volume is trying to turn it back upright and doesn't want the boat to lie totally inverted. It will easily flop back and forth between the 170 and 190 degree points. The boat can return to upright along either green curve.

This all depends on a totally waterproof superstructure, of course. In practice water is likely to enter the boat at a rate that depends on what is open at the time, which will affect the inverted stability. 

Moving on to the stability with water ballast, in my earlier post I said that the boat will capsize along the red curve and recover along the blue curve. I explained the relationship between the two curves but that relationship is not easy to visualise if only seen across the 180 degree range.

In the diagram above you can see that the red and blue curves only meet in two places and both are on the horizontal line. These are the two points at which the boat will rest when there are no outside influences from wind, waves or crew movement.

The boat cannot rest totally upright nor totally upside-down because the weight of the water to one side is heeling it toward that side. It will rest at approximately -5 degrees heel instead of upright and at 200 degrees instead of upside-down when inverted.

Bearing in mind that the areas of the curves below the horizontal line indicate how much energy it needs for the boat to get past the AVS points so that it can right itself when in that 200 degree situation, it is now easy to see that it will take a large amount of wave energy to get past the AVS of the red curve but a very small amount of wave action to get past the AVS of the blue curve.

This graphic shows that if a water ballasted boat capsizes it will do so along the red curve but it is very unlikely to return along that same path, nor is it likely to stay capsized for long. Once past the AVS of the red curve the negative stability will push it to 20 degrees past upside-down. After that the blue curve will take over and almost guarantee that the boat returns to right-way-up pronto.