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:
W X GML
MCT 1 cm
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 floating 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 X 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 I 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.
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