Game Development Reference

In-Depth Information

We'll describe each of these components and give you some empirical formulas in just

a moment. First, however, we want to qualify the material to follow by saying it is very

general in nature and applicable only when little detail is known about the complete

geometry of the particular ship under consideration. In the practice of ship design, these

formulas would be used only in the very early stages of the design process to approximate

resistance. That said, they are very useful for getting in the ballpark, so to speak, and

(sometimes more importantly) in performing parametric studies to see the effects of

changes in major parameters.

The first resistance component is the frictional drag on the underwater surface of the

hull as it moves through the water. This is the same as the frictional drag that we dis‐

cussed in
Chapter 3
. However, for ships there's a convenient set of empirical formulas

that you can use to calculate this force:

R
friction
= (1/2) ρ V
2
S C
f

In this formula, ρ is the density of water,
V
is the speed of the ship,
S
is the surface area

of the underwater portion of the hull, and
C
f
is the coefficient of frictional resistance.

You can use this empirical formula to calculate
C
f
:

C
f
= 0.075 / (log10 Rn - 2)2

Here,
Rn
is the Reynolds number, as defined in
Chapter 6
, based on the length of the

ship's hull. This formula was adopted in 1957 by the International Towing Tank Con‐

ference (ITTC) and is widely used in the field of naval architecture for estimating fric‐

tional resistance coefficients for ships.

To apply the formula for R
friction
, you'll also have to know the surface area,
S
, of the

underwater portion of the hull. You can directly calculate this area using numerical

integration techniques, similar to those for calculating volume, or you can use yet an‐

other empirical formula:

S = C
ws
√(∇L)

In this formula, ∇ is the displaced volume,
L
the length of the ship, and
C
ws
is the wetted

surface coefficient. This coefficient is a function of the ship's shape—its breadth-to-draft

ratio—and statistically it ranges from 2.6 to 2.9 for typical displacement hull forms.

The pressure drag experienced by a ship is the same as that experienced by projectiles

as discussed in
Chapter 3
. Remember, this drag is due to the viscous effects causing a

region of relatively low pressure behind the ship. Quantifying this force is difficult for

ships of arbitrary geometry. We can use computational fluid dynamics algorithms to

approximate this force, but this requires detailed knowledge of the hull geometry and

a whole lot of time-consuming computations. An alternative is to rely on scale-model