A raft is made from two cylinders each 1.5 m diameter and 6 m long. The distance between the centres of the cylinders is 3 m. If the draught is 0.75 m, calculate the transverse BM.

A raft is made from two cylinders each 1.5 m diameter and 6 m long. The distance between the centres of the cylinders is 3 m. If the draught is 0.75 m, calculate the transverse BM.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.4

 

Solution:

 

Moment of inertia (I) = I₁ – I₂

                                    = 1/12 *LB₁³ – 1/12 * LB₂³

                                    = 1/12 L * (B₁³ – B₂³)

                                    = 1/12 * 6 * (4.5³ – 1.5³)

                                    = 43.875 m⁴

Volume of displacement (∇) = 2* π*(d/2)² * h * 0.5

                                                     = 2 * 3.1416 * (1.5/2)² * 6 * 0.5

                                                      = 10.603 m³

BM = I/∇

        = 43.875/10.603

        = 4.138 m