Stability in Flotation

Show why objects float in a prefered orientation and why one hull shape is more stable than another.

What it Shows:

Place a wooden stick or board into a fish tank in some random orientation and it will flip over and float in its prefered orientation. This demonstration helps explain why. As an example of the principles involved, you can show why putting a load on the deck of a boat can make for a completely unstable situation. Adding ballast in the bottom helps. Contrast how different hull shapes can exacerbate or alleviate the problem.

How it Works:

The line of action of the upward buoyant force runs through the center of gravity of the displaced water. The line of action of the downward gravitational force is through the center of gravity of the floating object. If the center of gravity of the object is below the center of buoyancy, the floating object is stable—a push from equilibrium produces a pair of forces (called a torque couple) that act to restore the object's original orientation. It's unstable if the object's center of gravity lies above the center of buoyancy—the torque couple causes the object to roll over and the boat fills with water.

Two different model boats are used to demonstrate this principle. One has a semicircular hull shape (in cross section) for which the center of buoyancy does not shift when the boat rolls. The center of gravity shifts by very little in a roll and thus there is very little torque to right the boat back up again.

Diagram of a stable boat.

Contrast this to a rectangular shaped hull for which the center of buoyancy can shift considerably, creating a torque couple that tends to right the boat and results in very stable floatation.

Schematic of an unstable boat.


The "boats" are plastic containers that float in an aquarium. The semicirular shaped hull is a gallon jug sliced in half lengthwise, and the rectangular shaped hull is a 6"x11"x3" food container. Both boats can be loaded with up to five 1-lb dumbbells placed in the bottom of the hull. Point out to the students that the mass of 1/2 gallon (≈ 2 liters) displaced water is about 2 kg, or roughly 4.5 lbs in weight, and thus that is the maximum weight the boat and its contents can be.

Floating rectangular hull with weight placed inside. Add a dumbbell to the boat.

The boats can be fitted with a styrofoam "deck." Placing a load on the deck raises the center of gravity above the center of buoyancy. The semicircular shaped hull becomes completely unstable in this situation and it is impossible to place even one 1-lb dumbbell on deck without the boat immediately capsizing. The rectangular shaped hull, on the other hand, can handle three dumbbells without capsizing.

If you wish, you can show how to "fix" the problem with the unstable semicirular hull by placing two dumbbells in the bottom for ballast. With the ballast in place, the boat can now handle one dumbbell on deck without capsizing.

Comments: You can use these principles to discuss the maneuverability of fish vis-à-vis the position of their swim bladders, or extrapolate to the flight maneuverability and stability (or lack of) of fighter jets.