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

Exam Question

A ship 120 meters long at the waterline has equidistantly spaced half-ordinates commencing from forward as follows: 0, 3.7, 5.9, 7.6, 7.5, 4.6 and 0.1 meters respectively. Find the area of the waterplane using Simpson's Second rule and the TPC at this draft. Water density is 1.025 t/m3. (16)

Reference Answer

### **Objective**
To calculate the waterplane area (A_w) of a ship using Simpson's Second (3/8th) Rule and subsequently determine the Tonnes Per Centimetre Immersion (TPC) at the given draft.
### **Part 1: Principle of Simpson's Rules**
Simpson's Rules are numerical integration methods used to find the area under an irregular curve. For a ship's hull, the waterplane is an irregular shape whose area is essential for stability and hydrostatic calculations.

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