# Swimming stability

Under the floating stability is meant the behavior of a floating body with respect to its location to a liquid surface .

A body on top of a liquid dips into it, displacing the liquid surrounding the body. This creates a buoyancy force . The buoyancy force distributed over the body acts as if it were pulling vertically upwards in its entirety in the spatial center of the immersed part of the body. On the other hand, the weight force distributed over the volume of a body always acts as if it were concentrated vertically downwards in its entirety in the center of gravity of the body.

## regulate

### Swim, float, or sink

A body in a liquid will sink as long as the mass of the displaced liquid is less than the mass of the body. This is the Archimedean principle . If the weight of the submerged body and the buoyancy force are the same and a part of the body still protrudes from the water level, a state of swimming occurs as equilibrium. The part protruding from the water causes the buoyancy force to increase with every further minimal immersion and thus keeps the body floating.

When the mass of the completely submerged body and the weight of the displaced liquid are exactly the same, a state of suspension is established . Even the slightest change in volume due to changes in temperature or pressure leads to an ascent or sinking. This is exploited by the Cartesian diver . If the mass of the fully immersed body is greater than the weight of the displaced liquid, the body will sink.

### Geometric position to the liquid level

This floating body with a triangular cross-section protrudes about halfway out of the water. If its specific weight is increased, it sinks deeper into the water, whereby the angle of inclination also changes.
On the left a cuboid in a stable equilibrium position on the liquid level. The right picture shows the shift of the diving volume center point and the buoyancy force.

• The immersion depth in equilibrium is determined by the mass of the immersion body and the density of the liquid.
• In a liquid, the center of gravity of a body tends to be in the lowest possible position.
• The geometric swimming position is determined by the shape of the immersed body, its weight and its distribution as well as the density of the carrier liquid.

### dynamic behaviour

Irregular float with irregularly distributed weight. In the left picture the body has a stable position, in the right picture (with theoretical equilibrium) on the other hand an extremely unstable position.

A cube-shaped floating body placed on edge has points of application that are significantly further apart for the weight force and the buoyancy force. The swimming position is therefore very unstable.

• If a floating body is brought out of its stable swimming position, the center of the immersed volume always shifts, while the body's center of gravity remains the same for unchangeable bodies.
• If the points of application for the weight force and the buoyancy force are not perpendicular on a vertical axis, a torque arises between the two forces that rotates the body until the points of force application are in a common vertical line.
• The further the point of application for the weight force lies above the point of application for the buoyancy force, the more unstable a "state of equilibrium" is, which only refers to the vertical position of the center of gravity and the center of the diving volume. Even with a slight tilt, these points move against each other and turn the body until it is in a stable position on the liquid level.

## Quantitative description

A quantitative description is based on the conceptual construction of a “ metacenter ” at the intersection of the shifted lines of force and the “metacentric height” derived from it.