September 25, 2020
A Lesson on The Free Surface Effect
As a captain, you can make a number of decisions that affect a boat’s stability. My first article on stability briefly mentioned how arranging your cargo or rigging can change the location of your boat’s center of gravity. Consumables also can have a large effect, specifically liquids such as fuel, water, liquid cargo, or water in your bilge. This is called the Free Surface Effect.
To start, I’m going to treat the fuel as a separate entity with its own center of gravity (F). As with the boat, the fuel’s center of gravity is in the average location of its mass.
Figure 1: Point G shows the location of the Center of Gravity of the hull and point F shows that of the fuel.
When the boat is stable, its center of gravity (G) is directly above the buoyancy point (B), as is the center of gravity of the fuel. Gravity acts downward on both the boat and the fuel, while buoyancy acts upwards.
Figure 2: Points G and F mark the centers of gravity for the hull and fuel, respectively, from which the forces of gravity act downward. Point B shows the center of buoyancy, from which the buoyancy force acts upward.
Now imagine the boat heels quickly. For an instant, the fuel stays where it was because of its momentum. This means the center of gravity of the fuel remains on the keel side of the boat, while the buoyancy point moves outboard. For an instant, both the force of gravity of the fuel and the buoyancy force act in a direction to right the boat.
Figure 3: The buoyancy force (B) causes a righting motion or torque since it is outboard of the boat’s center of gravity. The force of gravity of the fuel (F) also causes a righting force for this instant, since it is on the keel side of the boat’s center of gravity.
But the problem with liquids is that they move and slosh quite easily. So an instant after the boat heels, that fuel is going to move in order to settle and remain level due to gravity. In that motion, it sloshes to the outboard side of the tank (just like my coffee does and why I often spill it everywhere). This moves the fuel’s center of gravity outboard, putting it on the same side of the boat’s center of gravity as the buoyancy force. Here’s where the trouble lies: The buoyancy force is still acting upward, trying to right the boat, but now the fuel’s center of gravity has moved so that the force of gravity on the fuel is acting to capsize the boat. Essentially, the sloshing fuel’s force of gravity is subtracting from the buoyancy force’s effective ability to right the boat.
Figure 4: When the fuel sloshes, its center of gravity (F) moves outboard from the boat’s center of gravity (G). This causes the fuel’s force of gravity to reduce or counteract the buoyancy force’s (B) ability to right the boat.
Sloshing can have an additive effect over time. If the boat gets rolling, the repetitive motion can cause the liquid to move further to each side or with more energy each time. I’m not going to get into the hydrodynamics in this post, but I think we can all agree that water is pretty good at building up momentum. It likes to keep doing whatever it was trying to do. Repetitively sloshing tanks, or taking a big wave aboard, can really cause problems for a boat’s stability, even to the point of causing her to capsize.
Another way to look at it is to consider the fuel’s effect on the location of the boat’s center of gravity. Instead of treating the boat and fuel separately, we can determine the boat’s center of gravity including the fuel. Then, when the fuel moves its mass, it causes the boat’s center of gravity to relocate. This moves the boat’s center of gravity outboard, shortening the righting arm or distance between the center of gravity and the line of the buoyancy force. The shorter the righting arm, the less affect the buoyancy force has in righting the boat.
Figure 5: Point G shows the new location of the center of gravity of the hull and the fuel combined. Since it moved outboard, it shortens the righting arm (r), reducing the buoyancy force’s effectiveness.
Remember that partially full fuel or water tanks will behave this way, as well as any water in your holds or bilge. Separate tanks or ones with baffles or subdividers reduce the space that the liquid has to slosh around, and therefore reduces its free surface effect on your stability. Keep your bilge dry and your tanks full!