- The Longitudinal Centre of Gravity (LCG) is the point along the length of the vessel where the total weight of the ship is considered to act vertically downward.
- It represents the balance point of the ship's weight distribution and is measured as a distance forward or aft of the midship.
Longitudinal Centre of Buoyancy (LCB):
- The Longitudinal Centre of Buoyancy (LCB) is the point along the length of the vessel through which the total buoyant force, acting vertically upward, is considered to act.
- It represents the balance point of the underwater volume of the ship and is also given as a distance forward or aft of the midship.
$$Common \space interval \space (h) \space = \space {{L} \over h} \space = \space {{120} \over 10} \space = \space 12 $$
Cross-sectional area | SM | Product of volume | Lever | Product of 1st moment |
2 | 1 | 2 | +5 | +10 |
40 | 4 | 160 | +4 | +640 |
79 | 2 | 158 | +3 | +474 |
100 | 4 | 400 | +2 | +800 |
103 | 2 | 206 | +1 | +206 |
| | | | ΣMA = +2130 |
104 | 4 | 416 | 0 | 0 |
104 | 2 | 208 | -1 | -208 |
103 | 4 | 412 | -2 | -824 |
97 | 2 | 194 | -3 | -582 |
58 | 4 | 232 | -4 | -928 |
0 | 1 | 0 | -5 | 0 |
| | Σ∇ = 2388 | | ΣMF = -2542 |
$$Displacement \space = \space \rho \times {{h} \over 3} \times \sum ∇ \space tonne $$
$$=1.025\times{{12}\over3}\times2388$$
$$Displacement \space = \space 9790.8 tonne$$
Centre of buoyancy from midship (LCB)
$$LCB\:=\:h\times({{\sum M_{A}+\sum M_{F}}\over\sum\nabla})$$
$$=12\times({{2130-2542}\over2388})$$
$$LCB \space = \space -2.07m fwd$$
