Determine the longitudinal position of the waterplane centroid using waterplane moments or sectional half-breadths with Simpson’s rule.
LCF from AP: — m
LCF (% LPP from AP): — %
LCF from AP: — m
LCF (% LPP from AP): — %
The longitudinal centre of flotation (LCF) is the fore-and-aft position of the centroid of the waterplane area. It represents the point about which the ship trims when small longitudinal moments are applied.
LCF is defined as the first longitudinal moment of the waterplane area divided by the total waterplane area:
LCF = ∫x dA / AWP
where x is measured from a chosen longitudinal datum, typically the aft perpendicular (AP).
When the waterplane area and its first moment are known, LCF can be calculated directly. This method is commonly used when hydrostatic particulars are available.
If waterline offsets or half-breadths are available, LCF can be determined by integrating half-breadths along the ship length using Simpson’s rule. The resulting waterplane area and moment are used to locate the centroid.
LCF plays a critical role in trim calculations. Longitudinal moments applied about the LCF produce minimal change in trim, while moments applied away from the LCF result in trimming effects.
LCF is typically reported as a distance from AP, from FP, or as a percentage of LPP. Consistent datum usage is essential when combining LCF with trim and stability calculations.
Tip: For small trim calculations, LCF is often assumed constant over limited draft changes, but this assumption should be verified for fuller hull forms.