Game Development Reference

In-Depth Information

For a ship, the viscous boundary layer can be quite thick, up to several feet near the end

of the ship depending on its length, and the mass of water that gets accelerated is sig‐

nificant. Therefore, when doing any sort of analysis that involves the acceleration of the

ship, you need to consider added mass, too. The calculation of added mass is beyond

the scope of this topic. We should also point out that, unlike mass, added mass is a tensor

—that is, it depends on the direction of acceleration. Further, added mass applies to

both linear and angular motion.

Added mass is typically expressed in terms of an added mass coefficient, which equals

the added mass divided by the mass of the ship. Some methods actually integrate over

the actual hull surface, while others approximate the hull as an ellipsoid with proportions

matching the ship's. Using this approximation, the ellipsoid's length corresponds to the

ship's length while its width corresponds to the ship's breadth. For longitudinal motion

(that is, linear motion along an axis parallel to the ship's length), the added mass coef‐

ficient varies nearly linearly from 0.0 at a breadth-to-length ratio of 0 (the ship is in‐

finitely thin) up to 0.5 at a breadth-to-length ratio of 1 (a sphere).

When the added mass coefficient is expressed as a percentage of the ship's mass, virtual

mass can be calculated as
mv
=
m
(1 +
xa
), where
m
is mass, and
xa
is the added mass

coefficient—for example, 0.2 for 20%. For typical displacement ship proportions, the

longitudinal added mass ranges from about 4% to 15% of the mass of the ship. Con‐

servative estimates generally use 20%.

Guidance speeds

To provide some guidance,
Table 16-1
provides common ship types and appropriate

speed ranges. This will help guide you in properly simulating the resistance of your

vessel.

Table 16-1. Some vessels and their speeds

Vessel type

Speed (knots)

Horsepower (hp)

Aircraft carrier

31.5

260,000

Cruiser

30

80,000

Oil tanker

15-20

20,000-60,000

Containership

21

100,000

200-foot yacht

15.5

4,000

35-foot recreational boat

30

420

35-foot speedboat

70

1,200

40-foot sailboat

8.5

N/A

Note that at a certain speed, for non-planing hulls, there is a theoretical limit to how

fast a boat can go. This speed is called the
hull speed
. At the hull speed the bow and stern

waves reinforce each other, and there is a rise in wave-making resistance. This can be a