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

Exam Question

The ½ 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 8.3 8.5 8.5 8.5 8.4 8.2 7.9 6.2 3.5 0 m

Calculate: (16)

(a) Waterplane area

(b) Distance of centroid from midships.

Reference Answer

### Concept
This problem requires the calculation of the waterplane area and the longitudinal position of its centroid (Longitudinal Centre of Flotation - LCF). The provided half-ordinates are not at a constant interval along the entire length of the waterplane. Therefore, Simpson's First Rule for numerical integration must be applied by dividing the waterplane into sections where a common interval (`h`) exists.
The waterplane is divided into three sections:
1. **Section 1:** AP (Stn 0) to Stn 2, with a common interval `h₁ = 6 m`.

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