Longitudinal Centre of Buoyancy (LCB)

Two modes: (A) from hydrostatic moment, (B) from sectional areas with Simpson’s rule.

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

A) Hydrostatic Moment

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

LCB from AP: — m

LCB from FP: — m

LCB from Midship (aft + / fwd −): — m

LCB (% of LPP from AP): — %

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

A) Hydrostatic Moment: \( \mathrm{LCB} = \dfrac{\int x\,dV}{\nabla} \). Input the first moment about the selected datum (AP or FP). We also report distances from AP, FP and midship, and % of LPP from AP.

B) Stations via Simpson: We use equal-spacing composite Simpson’s rule on A(x) to obtain \( \nabla \approx \int A(x)\,dx \) and on \( xA(x) \) to obtain the first moment \( \int xA(x)\,dx \). Then \( \mathrm{LCB} = \dfrac{\int xA(x)\,dx}{\int A(x)\,dx} \).

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