Thursday, February 27, 2014

Stability with Water Ballast

A potential builder of the Didi 950 asked me a question about stability with water ballast. He could not find an explanation on the Internet describing the effects of water ballast on a boat when capsized, so here it is.

After looking at the stability curve, he was concerned that the stability curve with water ballast to windward, the normal position for sailing in strong winds, has a very large area of negative stability. He wanted to know how that affects the time that the boat will take to right itself if capsized. This is a natural question following the amount of discussion that has been happening after our recent capsize in the Didi 38 "Black Cat" and the very rapid manner in which she returned to upright.

Shown below is the stability graph of the Didi 950 in fully loaded condition; click on the diagram to enlarge it. This is the condition of lowest stability due to the inclusion of crew, stores, liquids and many other weights that are above the centre of gravity (CG) of the boat. There are three curves shown. When looking at the graph, consider that the area enclosed by each curve above the horizontal 0 line is a measure of the energy that is required to take the boat from upright to the point of vanishing stability (AVS) where the curve crosses the 0 line. Until the AVS is reached, the boat will return to upright if no additional heeling force is applied to it.  Beyond the AVS the boat will continue to full capsize unless there is another force being applied that will return it to the positive side of the AVS.

The green curve is with ballast tanks empty, so akin to sailing a boat that has no water ballast. This curve is very similar in form to that of "Black Cat", with the area enclosed by the curve above the 0 line many times greater than the area enclosed by the curve below the 0 line. She would right herself very quickly with no water ballast. The red curve is with the windward ballast tanks filled, good for powering to windward or power-reaching in strong conditions. The blue curve is with the leeward ballast tanks filled. One would not sail her like this but it is a situation that could result from an accidental gybe in strong winds.
Didi 950 Stability Graph. Click to enlarge.
With no wind or waves and the ballast tanks on one side filled, the boat will not rest upright. It will heel over until it stabilises at a heel angle that places the CG vertically in line with the centre of buoyancy (CB). That will be the nearest crossing of the curve with the 0 line, which is at 5 degrees in this case, seen on the blue curve. Add some wind to bring the boat to 0 degrees heel and the righting moment that is working is the point where the red curve hits the left edge of the graph. Without water ballast the boat must heel to 6 degrees to reach the same righting moment. That is where the power benefit is coming from with water ballast, the boat will sail more upright than with empty tanks, in the same wind strength.

Note that all three curves are closely bunched when the boat is heeled 90 degrees. This is a knock-down situation, probably from losing control when driving hard downwind under spinnaker. The mast is horizontal but not in the water. This bunching of the curves at 90 degrees is because of the position of the ballast tanks in this design, low in the boat fairly close to the vertical CG. There would be a bigger spread if the tanks were located high up under the deck.

The red curve shows the benefit of increased righting moment when the windward tank is filled. There is considerably greater gain in stability shown by the red curve than lost stability, shown by the blue curve, when ballast is on the wrong side.

All three curves show that the wind alone can't capsize the boat. When the mast hits the water there is still considerable righting moment available for all three situations. If the boat is in large waves and hit by a big one while knocked flat, the added energy from the wave can capsize the boat in all three situations. 

It seems counter-intuitive but the condition most likely to invert the boat under wave action after a knock-down is with the water ballast to windward (red), i.e. the condition in which the boat will be sailed in strong winds. This is because after the water ballast passes beyond the point where it is vertically above the overall CG of the boat that extra weight is on the wrong side of the CG and is helping to capsize the boat rather than to bring it back to upright. It pulls the red curve below the green curve and reduces the AVS from 133 degrees to 122 degrees. 

Overall it takes more energy to capsize the boat from upright with water ballast than without, evaluated by comparing the area enclosed by the red curve with the area enclosed by the green curve. When the area enclosed by the blue curve is compared with the green curve, there is very little difference. It will take a similar amount of energy to capsize the boat without water ballast and with water ballast on the wrong side, when going from upright. Ironically, the wrong side has the greatest amount of reserve stability after a knock-down and has the greatest angle of AVS, so it is the condition least likely to capsize after a knock-down.

Back to our capsizing boat. Once past 122 degrees it is into a big range of negative stability that shows as the area enclosed by the red curve below the 0 line, taking it all the way to 180 degrees, i.e. totally upside-down. But see that the curve does not return to 0 at 180 degrees, which means that it is unstable at that angle. Same as happens when the boat is upright, the water ballast off to one side prevents the boat from resting at the 180 degree position. It has to rotate to where the CG is vertically aligned with the inverted CB. That is at the point where the curve crosses the 0 line. If the red curve is extended to the zero line it will be to the same angle that the blue curve crosses,  i.e. 160 degrees.
There is no windward or leeward when the boat is upside-down, the sails are under water. The boat is stable in the 160 degree position, so leaning 20 degrees to one side of upside-down. It needs to get past the nearest zero crossing to come back to upright. The boat doesn't care which way it goes. It needs a lot of energy to go back the way that it came along the red curve but very little energy to get to the 140 degree AVS crossing of the blue curve. With the motion from just a small wave it will continue past that 140 degree point. Once that point is passed, the righting moment of the blue curve takes control and will return her to upright. If the rig is still standing then the sails will fill and she will be back into the stability situation shown by the red curve. She has capsized along the red curve and righted herself along the blue curve.
In essence, it will take a lot less energy for the boat to right itself with water ballast than without, so she should right herself more quickly with the water ballast. The difference is that without water ballast she can go either way from inverted to upright but with water ballast she has to go full circle.

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