Determine the longitudinal position of the buoyancy centre using hydrostatic moments or sectional areas with Simpson’s rule.
LCB from AP: — m
LCB (% LPP from AP): — %
LCB from AP: — m
LCB (% LPP from AP): — %
The longitudinal centre of buoyancy (LCB) is the fore-and-aft position of the centroid of the underwater volume of a ship. It represents the point through which the resultant buoyant force acts in the longitudinal direction.
LCB is defined as the first longitudinal moment of the displaced volume divided by the total displacement volume:
LCB = ∫x dV / ∇
where x is measured from a chosen longitudinal datum, typically the aft perpendicular (AP) or forward perpendicular (FP).
When hydrostatic data is available, LCB can be calculated directly from the longitudinal first moment of displacement volume. This method is commonly used during detailed design and stability analysis.
If sectional area data is available along the ship length, LCB may be determined by integrating sectional areas and their longitudinal positions using Simpson’s rule. This approach is suitable for preliminary design and fairing studies.
The longitudinal position of buoyancy has a direct influence on trim and longitudinal equilibrium. Differences between LCB and the longitudinal centre of gravity (LCG) result in trimming moments.
LCB is commonly reported as a distance from AP, from FP, or as a percentage of LPP. Consistent use of datum and sign convention is essential when comparing values.
Tip: Always ensure that LCB and LCG are referenced to the same datum and loading condition when performing trim calculations.