Game Development Reference

In-Depth Information

Stability and Sinking

If you have boats in your video game, the first step to making them realistic physically

is allowing them to sink if they become damaged. To understand why boats sink and

how they do so, you must first understand
stability
.

Stability

Most boats are least stable about their longitudinal axis—that is, they are easier to heel

port and starboard than they are to flip end over end. If the vessel heels over so far that

it is upside down, this is called capsizing. This is how most boats sink due to wind, waves,

or in some cases of side damage. One of the most famous examples of a sinking ship,

the
Titanic
, shows that when a boat is sinking from damage, it can sink end over end,

sometimes with the ship breaking in two. We'll discuss both here so that you can animate

realistic sinking in your simulation.

In
Chapter 3
we introduced the concept of buoyancy and stated that the force on a

submerged object due to buoyancy is a function of the submerged volume of the object.

Archimedes's principle states that the weight of an object floating in a fluid is equal to

the weight of the volume of fluid displaced by the object. This is an important principle.

It says that a ship of a given weight must have sufficient volume to displace enough

water, an amount equal to the weight of the ship, in order for it to float. Further, this

principle provides a clever way of determining the weight of a ship: simply measure or

calculate the amount of water displaced by the ship and you can calculate the weight of

the ship. In the marine field, displacement is synonymous with the weight of the ship.

As discussed in
Chapter 3
, we can calculate the buoyant force on any object by using

the following formula:

F
B
= ρ g ∇

Here, ∇ is the submerged volume of the object, ρ is the density of the fluid within which

the object is submerged, and
g
is the acceleration due to gravity. Since buoyancy is a

force, it has both magnitude and direction, and always acts straight up through the

center of buoyancy. The center of buoyancy is the geometric center of the submerged

part of the object.

When a ship is floating in equilibrium on the surface of the water, its center of buoyancy

must be located directly below the ship's center of gravity. The weight of the ship, a force,

acts straight down through the center of gravity, opposing the force due to buoyancy.

When the ship is in equilibrium, these two forces, weight and buoyancy, are equal in

magnitude and opposite in direction.

Now, when an external force causes the ship to roll or pitch, the portion of the hull below

the water is changed and the center of buoyancy moves to the new geometric centroid