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Class 4 (4th Engineer) SC&S 📅 Mar 2026

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

### **Objective**
To calculate the waterplane area (Awp) and the longitudinal position of its centroid (LCF) from midships using the provided half-ordinates for a ship of 120m length.
### **Principle & Method**
This problem will be solved using Simpson's First Rule for numerical integration. The ordinates are not equally spaced throughout the length; there are half-spaced ordinates at the ends. Therefore, the waterplane will be divided into three sections, and Simpson's rule will be applied to each section individually. The results will then be summed.

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