Integrate a waterplane or any symmetrical area using Simpson’s 1st rule over an odd number of equally-spaced half-breadths.
Formula
$$ A_w = 2 \cdot \frac{h}{3} \left(y_0 + 4 y_1 + 2 y_2 + 4 y_3 + \ldots + y_n\right) $$
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $y_i$ | Half-breadth at station i | m | offsets table |
| $h$ | Common station spacing | m | body plan |
| $A_w$ | Waterplane area | m² | result |
Sources
- Derrett & Barrass Ch.5 - Simpson’s rules.
- SNAME PNA Vol I.