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roll periods are known as “tender” and lag behind the waves. These vessels generally
heel farther over but are more comfortable for passengers.
Pitch
Likewise, there is a pitch period that measures the speed at which the vessel responds
to a wave. This is highly dependent on the length of a ship and can be estimated as
follows:
T = (2π / g 1/2 )(k/(GM) 1/2 )
Where k is the radius of gyration and is commonly taken as 30% of the beam. Note that
pitch period is normally one-third to one-half that of roll period, so that the bow of a
vessel will rise and fall with the wave more in phase than in a roll event.
Coupled Motions
The real trick to getting motions to look right is to understand that for most boats the
motions are coupled. For instance, heave and pitch are strongly coupled. This means
that if a wave causes your boat to heave, it will most likely also cause it to pitch. This is
because the distribution of buoyancy along the hull is not constant. If the waterline is
raised some constant value, there is usually more buoyancy provided aft than there is
forward for the same change in waterline. This will cause the vessel to pitch forward to
move the center of buoyancy to the longitudinal location of the center of gravity. Sim‐
ilarly, a pitch event will cause the vessel to heave because if the stern is lifted from the
water, there is usually a loss of total buoyancy, and the boat will sink farther into the
water.
Resistance and Propulsion
Resistance is the amount of force it takes to move a body through the water. Propulsion
is the method by which you create that force.
General Resistance
In Chapter 3 , we discussed drag forces on objects moving through a fluid. Specifically,
we discussed frictional and pressure drag. Ships moving on the water's surface experi‐
ence these drag forces; however, at the air-water interface, there are other drag compo‐
nents that you have to consider. If you were to write an equation breaking up the total
resistance acting on a ship into its three main components, that equation would look
something like this:
R total = R friction + R pressure + R waves
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