Final answer:
To calculate the new draft forward and aft after loading a 50-tonne container onto a ship, we use the waterplane area, longitudinal moment of inertia, and the center of floatation's location. Change in trim and change at the draft marks are then calculated and applied to the initial drafts to get the new drafts, considering the principles of ship stability and moments.
Step-by-step explanation:
To determine the new draft forward and draft aft of the ship after loading a 50 tonnef (tonne-force) container of circus equipment, we need to apply the concept of ship stability and use the known quantities of the ship. We're given the waterplane area (4300 m²), the longitudinal moment of inertia about the midships (1.43 ×10⁶ m⁴), and the location of the center of floatation. The initial forward (5.1 m) and aft (6.5 m) drafts are given. We also know the container's position relative to the FP (15 m aft of the FP).
To calculate the new drafts, we first work out the change in trim using the following formula:
Change in Trim = × Lever Arm / Moment of Inertia
The Lever Arm is the distance from the center of flotation to the location where the weight is added. In this case, the container's center of gravity is 6 m aft of the ship's midship, which means it is 12 m from the center of floatation. The moment of inertia is given, and we can calculate the trim change due to the additional weight. Using the trim change, we then find the change at the draft marks. We use the known distances from the FP and AP to the draft marks to distribute the trim change to the forward and aft, based on the principle of moments. Finally, the new drafts can be calculated by adding or subtracting the trim change from the initial drafts.
Remember that the ship's weight and buoyancy distribution might change after adding weight, which could affect the draft readings. Normally we would also need to calculate the change in mean draft due to this added weight, which is not detailed in this response.