Longitudinal Centre of Flotation (LCF)

Two modes: (A) from waterplane first moment, (B) from waterline half-breadths with Simpson’s rule.

Choose how to compute LCF.
Reference for moment input / reporting.
Enter a positive number.

A) From Waterplane Area & First Moment

Enter a positive number.
Enter a valid number (can be 0+).
Provide the first moment about the selected datum (AP/FP). LPP is used for %LPP and AP/FP conversion.
Result

LCF from AP: — m

LCF from FP: — m

LCF from Midship (aft + / fwd −): — m

LCF (% of LPP from AP): — %

Choose a method, enter inputs, and click Calculate.
Report: Longitudinal Centre of Flotation (LCF)
Method — —
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How it works

A) Waterplane Moment: \( \mathrm{LCF} = \dfrac{\int x\,dA}{A_{WP}} \). Input the first moment about the selected datum (AP/FP). We also report AP, FP, midship references and %LPP.

B) Stations via Simpson: With equal station spacing over LPP and half-breadths \(y_i\), we compute \( A_{WP} = 2\int y\,dx \) and \( \int x\,dA = 2\int x\,y\,dx \) via composite Simpson’s rule, then \( \mathrm{LCF} = \frac{2\int x y\,dx}{2\int y\,dx} \).

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