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
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