Page 72 - Introduction to Naval Architecture

FLOTATION AND STABILITY 59

The maximum force on the fore poppet will be the difference
between the weight and the buoyancy at the moment the ship pivots
about the fore poppet which occurs when the moment of buoyancy
equals the moment of weight about the fore poppet. The ship becomes
fully waterborne when the buoyancy equals the weight. To ensure the
ship does not tip about the after end of the ways, the moment of
buoyancy about that point must always be greater than the moment of
weight about it. If the ship does not become waterborne before the fore
poppet reaches the after end of the ways it will drop at that point. This
is to be avoided if possible. If it cannot be avoided there must be
sufficient depth of water to allow the ship to drop freely allowing for the
dynamic 'overshoot'. The stability at the point of pivoting can be
calculated in a similar way to that adopted for docking. There will be a
high hogging bending moment acting on the hull girder which must be
assessed. The forces acting are also needed to ensure the launching
structures are adequately strong.
The ship builds up considerable momentum as it slides down the
ways. This must be dissipated before the ship conies to rest in the water.
Typically chains and other energy absorbing devices are brought into
action during the latter stages of travel. Tugs are on hand to manoeuvre
the ship once afloat in what are usually very restricted waters.

STABILITY AT LARGE ANGLES OF INCLINATION

Atwood's formula
So far only a ship's initial stability has been considered. That is for small
inclinations from the vertical. When the angle of inclination is greater
than, say, 4 or 5 degrees, the point, M, at which the vertical through the
inclined centre of buoyancy meets the centreline of the ship, can no
longer be regarded as a fixed point. Metacentric height is 110 longer a
suitable measure of stability and the value of the righting arm, GZ, is
used instead.
Assume the ship is in equilibrium under the action of its weight and
buoyancy with W 0Lo and WjLj the waterlines when upright and when
inclined through <p respectively. These two waterlines will cut off the
same volume of buoyancy but will not, in general, intersect on the
centreline but at some point S.
A volume represented by WgSWj has emerged and an equal volume,
represented by LoSLj has been immersed. Let this volume be u Using
the notation in Figure 4.22, the horizontal shift of the centre of
buoyancy, is given by:

This expression for GZ is often called Atwood 's formula.