Game Development Reference

In-Depth Information

Roll, pitch, and yaw are the terms also used for airplanes. The translation degrees of

freedom are called surge, heave, and sway. Surge, sway, and yaw are not that apparent

when vessels are moving forward, so it is acceptable to limit your model to heave, pitch,

and roll. Heave is the up-and-down motion of the boat caused by the change in elevation

of the water's surface as a wave passes. If a vessel is stationary, it would be referred to as

bobbing. Pitch is the rotation about the transverse axis of the vessel due to increased

buoyancy on one end of the ship as a wave passes. This motion is most pronounced

when the waves are traveling in the same direction (or 180 degrees) from the vessel. Roll

is like pitch, but about the longitudinal axis.

Heave

As stated before, heave is displacement in the vertical direction from the static equili‐

brium draft. This degree of freedom is straightforward to model as a hydrostatic spring

acting in the vertical direction. Assuming we have a barge that is 30 meters long and 10

meters wide, we'll develop an equation that can govern our heave simulation.

Commonly, a vessel's hydrostatics include something called tons per centimeter im‐

mersion (TPCM)—that is, for every centimeter you press the boat down, a certain

number of tons of buoyancy force is created. For our barge, this is a relatively straight‐

forward calculation.

Given that the water plane area is a constant 300 square meters, 1 centimeter of im‐

mersion would result in a volume of 3 cubic meters. As 1 cubic meter of saltwater weighs

1,027 kg, 3 cubic meters would be 3,081 kg, and (assuming this boat is on Earth), would

result in a buoyant force of 3,081 kg × 9.81 m/s
2
, or 30.2 kN. Therefore, 30.2 kN per cm

would make a good starting value for a spring constant to model the heave response of

this vessel in waves.

Roll

For us to simulate realistic roll motions, it is important that the ship take time to com‐

plete the motion. This time is called the
roll period
. This defines the angular velocity

that a ship rolled to one side will experience when it recovers. We can estimate it by the

following equation:

2
πk

gxGM

T =

Where
k
is the radius of gyration and
GM
is the distance from the metacenter to the

center of gravity. A good estimate for the radius of gyration is often taken as 30% of the

beam of the vessel. A vessel with a shorter roll period will respond quicker to a wave

and try to assume the wave slope. This is known as being “stiff ” and can cause passenger

discomfort and damage via higher angular accelerations. Conversely, vessels with higher