Game Development Reference
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test data where results from the model test are extrapolated to approximate drag on the
full-size ship.
Just like pressure drag, wave drag is difficult to compute, and we usually rely on model
testing in practice. Wave drag is due to the energy transfer, or momentum transfer, from
the ship to the fluid, or in other words, it's a function of the work done by the ship on
the surrounding fluid to generate the waves. The visible presence of wave resistance is
evident in the large bow wave that builds up at the front of the ship as well as the wave
system that originates at the stern of the ship as it moves through the water. These waves
affect the pressure distribution around the ship and thus affect the pressure drag, which
makes it difficult for us to separate the wave drag component from pressure drag when
performing an analysis.
When scale model tests are performed, pressure drag and wave drag are usually lumped
together in what's known as residual resistance . Analogous to the coefficient of frictional
drag, you can determine a coefficient of residual resistance, such that:
R r = R pressure + R wave = (1/2) ρ V 2 S C r
Here R r is the total residual resistance, and C r is the coefficient of residual resistance.
There are many resistance estimation methods available that allow you to estimate the
coefficient of residual resistance for a ship; however, they are usually presented for
specific ship types. For example, one method might give empirical formulas for C r for
destroyer-type ships, while another might give formulas for C r for large oil tankers. The
trick, of course, is to choose a method appropriate for the type of ship you are analyzing.
1 Generally, C r increases as the displacement and speed of the ship increase. A typical
range for C r for large displacement hulls is from 1.0e-3 to 3.0e-3.
While these three resistance components—friction, pressure, and wave—are the most
important for typical displacement-type ships, they aren't the only ones. Since a ship
operates at the air-water interface, a large part of its structure is above the water surface,
exposed to the air. This means that the ship will also experience air resistance. You can
approximate this air resistance using the following formula:
R air = (1/2) ρ V 2 A p C air
Here, C air is the coefficient of air resistance, ρ is the density of air, V is the speed of the
ship, and A p is the projected transverse (profile) area of the ship. C air typically ranges
from 0.6 to 1.1, depending on the type of ship. Tankers and large cargo ships tend to be
near the upper end of the range, while combatant ships tend to be near the lower end.
1. These methods are quite involved and there are far too many to discuss here, so we've included some references
in the Bibliography for you.
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