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Class 4 (4th Engineer) SC&S 📅 Mar 2025

Exam Question

The ½ ordinates of a waterplane 120 m 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

Calculate: (16)

(a) waterplane area

(b) distance of centroid from midships.

Exam question diagram

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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