Page 114 - statbility for masters and mates

102 Ship Stability for Masters and Mates
x AGH d/3 AGED
1 d V/A d
2 d 3 AGED
AGED 1 d V/A d
2d 3 16 d V/A
The new vertical distance of the centroid below AD will now be given by: 1V1 V
DistancebelowAD 2A 6 d A 13 AV 16 d
1 d V 32A
Therefore the distance of the centre of buoyancy below the load waterline is given by the formula:
Distance below LWL 1 d V 32A
This is known as Morrish's or Normand's formula and will give very good results for merchant ships.
To ®nd Transverse BM
The Transverse BM is the height of the transverse metacentre above the centre of buoyancy and is found by using the formula:
BM V1
1 The second moment of the water-plane area about the centre line,
and
V The ship's volume of displacement
The derivation of this formula is as follows:
Consider a ship inclined to a small angle (y) as shown in Figure 12.3(a) Let `y' be the half-breadth.
where