Class 4 (4th Engineer) SC&S 📅 Jun 2024

Exam Question

The 1/2 ordinates of a waterplane 120m long are as follows:

Section: AP ½ 1 1½ 2 3 4 5 6 7 8 8½ 9 9½ FP

½ ord 1.2 3.5 5.3 6.8 8.0 83 8.5 8.5 8.5 84 8.2 7.9 6.2 3 5 0m

Calculate: (16)

(a) Waterplane area

(b) Distance of centroid from midships.

Reference Answer

### Principle of Calculation
This problem requires the calculation of the waterplane area (WPA) and the longitudinal position of its centroid (LCF) using Simpson's First Rule. The provided half-ordinates are not spaced at a single common interval throughout the length of the waterplane. Therefore, the waterplane must be divided into sections where Simpson's rule can be applied with a constant common interval within each section. The total area and total moment are found by summing the results from each section.
**Methodology:**
1. **Divide the Waterplane:** The 120m waterplane is divided into three sections based on the spacing of the given ordinates:

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