Page 148 - statbility for masters and mates

136 Ship Stability for Masters and Mates
where
L the length of the vessel, and Hence, BML is independent
of ships Br. Mld.
12 12 L B d
L2
BML 6d ; so again is independent of Br. Mld.
It should be noted that the distance BG is small when compared with BML or GML and, for this reason, BML may, without appreciable error, be substituted for GML in the formula for ®nding MCT 1 cm.
The Moment to Change Trim one centimetre (MCT
1 cm or MCTC)
The MCT 1 cm, or MCTC, is the moment required to change trim by 1 cm, and may be calculated by using the formula:
MCT 1 cm W GML 100L
where
W the vessel's displacement in tonnes
GML the longitudinal metacentric height in metres, and L the vessel's length in metres.
The derivation of this formula is as follows:
Consider a ship ¯oating on an even keel as shown in Figure 15.3(a). The
ship is in equilibrium.
Now shift the weight `w' forward through a distance of `d' metres. The
ship's centre of gravity will shift from G to G1, causing a trimming moment of W GG1, as shown in Figure 15.3(b).
The ship will trim to bring the centres of buoyancy and gravity into the same vertical line as shown in Figure 15.3(c). The ship is again in equilibrium.
Let the ship's length be L metres and let the tipping centre (F) be l metres from aft.
The longitudinal metacentre (ML) is the point of intersection between the verticals through the centre of buoyancy when on an even keel and when trimmed.
d the draft of the vessel For a triangular prism:
BML IL V
BL3