Waterplane Area - Simpson's 1st Rule

Integrate a waterplane or any symmetrical area using Simpson's 1st rule over an odd number of equally-spaced half-breadths.

StabilityHydrostaticsSimpson

Half-breadths (comma separated, m)m11 half-breadths for Simpson's 1st rule (count must be odd).Spacing hm

Waterplane area A_w: 4,162.7m²

Changing the inputs requires JavaScript. The calculator above shows its default inputs and result. The formula, symbols, and regulatory sources are shown in the Formula section below.

Formula, assumptions, and limits

A_w = 2 \cdot \frac{h}{3} \left(y_0 + 4 y_1 + 2 y_2 + 4 y_3 + \ldots + y_n\right)

Symbol	Meaning	Unit
$y_i$	Half-breadth at station i	m
$h$	Common station spacing	m
$A_w$	Waterplane area	m²

Source: Derrett & Barrass Ch.5 - Simpson's rules; SNAME PNA Vol I

In short

Integrate a waterplane or any symmetrical area using Simpson's 1st rule over an odd number of equally-spaced half-breadths.

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