Unfortunately the data displayed in the
boat selection dialog box is a mixture of imperial (ft) and metric (m and kg)
units, thus being confusing to everybody. For the majority who are used to the
metric system, all-metric measurements would be desirable, while virtual
sailors from the USA might want to see the old imperial units. It would be easy
to do this with a simple ‘units mode’ switch in one of VS’s preference dialogs.
*Nautical miles* (a minute of arc along a latitude) and *knots*
(nm/h) are exceptions that are universally used and understood.

In what follows, I shall use metric
measurements since (a) everyone outside the USA uses them and (b) they are a
consistent system for calculations.

Each floating ship displaces its own
weight of water when at rest. In other words the weight of water equal to the
volume of its submerged hull is the same as the weight of the vessel. So if we
know the weight (mass *M*) of the vessel from the cfg file we know what
the underwater volume (call it *V*) of its hull should be. Roughly 1 kg of
water = 1 litre = 10^{-3} cubic metres, though the slightly greater
density of seawater and its variation with temperature and salinity cause
variations of a few %.

A VS cfg file contains two other relevant
parameters: the length of the vessel (*L*) and its cross-sectional area (*A*).
The former may be the length overall (end to end) but generally will not be too
much different from the waterline length. The area is presumably the maximum
area of any cross-section, or perhaps the cross-sectional area amidships (halfway
between stem and stern). We expect that *L*x*A* should be bigger than
*V*, but by how much? That is where the prismatic coefficient (call it *k*)
comes in; we define *k* = *V*/(*L*x*A*).

Suppose a vessel has the same underwater
cross-section along its entire length, perhaps like a rectangular punt or a
raft. Then *V*=*L*x*A*, and *k*=1. The underwater shape is
mathematically classified as a ‘prism’, hence the name prismatic coefficient. *Prismatic
coefficients larger than 1 are not possible.*

Suppose the vessel is much finer (more
‘pointy’) and is made up of two pyramids butted up. The volume of the two
pyramids is *L*x*A*/3, so *k*=1/3=0.33. A Hobie Cat hull
approaches this shape underwater. You can’t get lower values of *k*
without substantial concave sections.

Real vessels are in between. Consider a
vessel whose underwater hull is parallel (a prism) for its middle half, and has
two pyramids stuck on the two outer quarters. A bit of algebra gives *k*=2/3=0.67. Actually, most real displacement sailboats
have k between 0.49 (a bit fine, will develop a large quarter wave) and 0.55
(probably slow). Large ships usually have *k* between 0.52 and 0.62;
planing powerboats might go up to 0.70. So we have established that a normal
vessel probably has a prismatic coefficient of about 0.5-0.7, could be up to
1.0 or down to 0.4 but these are exceedingly rare.

How do VS vessels match up? Look at the survey report for a real shock! These are not
real vessels or the data is very wrong.

No. Most ships have pretty standard hull
shapes. Long in the direction they want to go, and about twice as wide as deep,
disregarding little bits sticking out like keels and rudders. Their prismatic
coefficients are stock-standard. Extreme prismatic coefficients generally only
occur in very small vessels. Punts and rafts at one end of the scale, and
canoes and racing catamarans at the other. Even a half-sphere vessel (like an
Irish coracle) has *k*=0.67.

The displacement principle continues to
apply to a submerged vessel (submarine or submersible) if they are stopped or
cruising slowly at stable depth.

While most vessels rely on displacement to
support their weight even when they are moving, some derive lift (just like an
aeroplane) from their speed and the shape of their hulls (usually flat or a
flattish Vee from midships aft). Examples are racing dinghies, windsurfers,
runabouts, and at an extreme hydrofoil boats that lift themselves right out of
the water on underwater wings. When any boat supports itself in this way, of
course its underwater volume will be much reduced, and the prismatic
coefficient becomes less relevant. Without huge power, this is restricted to
small vessels. A hovercraft and a
seaplane are special cases too complex to discuss here; they have air lift as
well.

Slightly. The hulls still have to support
the weight of the vessel and have similar shapes. However twin-hull boats trade
off more wetted area (and more frictional drag) in their two hulls for very
fine and thin hulls with low wave-making resistance, usually giving them lowish
but not abnormal *k*. Here is an *Incat* Tasmanian-built
wave-piercing catamaran ferry on speed trials past my home. We export them all
over the world from Japan and China to the English Channel and the Baltic Sea.
One of them holds the *Blue Riband* for the fastest crossing of the North
Atlantic by a commercial passenger-carrying vessel.