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

Exam Question

The 1/2 ordinates of a waterplane 120 m long are as follows: (16)

Section AP 1/2 | 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:

(a) Waterplane area

(b) Distance of centroid from midships.

Reference Answer

### Surveyor-Grade Answer
#### Principle
This problem involves calculating the waterplane area and the longitudinal position of its centroid (LCF) using ordinates that are not uniformly spaced. To solve this, the waterplane must be divided into sections where Simpson's First Rule can be applied. The rule requires an odd number of ordinates (or an even number of equal intervals).
The given ordinates are spaced such that we can divide the 120m length into three distinct sections:

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