A Naval Architect derives the hydrostatic curves of a ship from the lines drawing designs. The hydrostatic curve is a calculation of the underwater volume of the hull that supports buoyancy so the ship can float freely on the surface of the water. The immersed underwater volume of the hull of the ship displaces a volume of water in cubic meters and the said displaced volume of water creates a buoyant force that pushes the underwater volume of the hull to float in a stable equilibrium. The hydrostatic curve is a tool of ship officers to help with stability and trim management, especially stability prediction before loading, and identifying location and weight of cargoes pre-boarding. Cargo handling affects projections of stability and trim of the ship for the following reasons:

• Weight added or deducted from the ship.
• Location of the cargoes must be symmetrical for balance and to have a counter weight.
• Height of the location of cargoes from the keel
• Cargo weight movement, from one point to another, either in transverse or longitudinal position.
• Others.

The total ship characteristic, motion behavior, and ship response to internal and external forces of nature are manifested, and the effects can be predicted in the hydrostatic curves.

Fig. 1 Examples of Lines Drawing of a Ship’s Hull

Fig. 2 Examples of The Hydrostatic Curves The Characteristics of a vessel can be interpreted; while stability and trim of the Hull can be predicted by the following parameters.

1. Displacement (D) – the volume of water occupied and displaced by the underwater hull envelope. Said displaced water has an equivalent force called buoyancy that pushes the hull of the ship upward. Both volume and density are presumed at 30oC more or less as explained in the theory and the principles of Archimedes. The principles state that any solid matter immersed in liquid is buoyed by a force of the immersed solid upward that then causes the solid matter to float in the liquid.
2. Center of Buoyancy (B) – the centroid of the underwater volume of the ship immersed in the water and the point through which the total force of buoyancy can be assumed to concentrate. This is defined as:
3. Center of Gravity (G) – the point located vertically and horizontally through which the total weight of the ship is assumed to concentrate. This is defined as:
4. Longitudinal Center of Floatation (LCF) – the centroid of the area of the waterplane through which the center of floatation is concentrated.
5. Tons per Centimeter (TPC) of a waterplane – the weight required to effect change in the mean draft of the hull at the waterline by sinkage of 1cm. Area of waterplane (A) x 1/100 x 1.025 Where A is the area of waterplane.
6. Moment to Trim per 1 Cm (MCTC) – the expression describes the moment that needs to be exerted on a given ship to change trim by 1cm. This is shown in the formula: MCT 1 cm = 7 (TPC)2 tons meters B.
7. Metacentric Height (GM) – the predicted location of GM is calculated through inclining experiment of a newly constructed or outfitted vessel in relation to metacenter KM or height of the location of M from the keel as shown in Fig. 3 below. The location of “G” results from inclining and the experiments must be always below “M”.

Fig. 3 Diagram of Metacenter

The analogy in ship stability is demonstrated in the diagram showing how the vessel behaves.

Conclusions

The calculation of trim and stability threshold of a vessel  of the Navy, Coast Guard, Merchant Marine Ship, and others depend on the configuration of the lines drawing and hydrostatic curves. The calculations made by the Naval Architects and Shipbuilders are just based on assumptions. The forces of nature interfering with the vessels at sea vary and are difficult to predict as weather and climate frequently change.

A “PROVEN DESIGN VESSEL” is a vessel that has been tested through the forces of nature at sea in various mission situations for long years of operational experience, that only the wisdom of our great GOD could provide us with evidence through the existence of several tested vessels built of the same class, having been proven seaworthy by the forces of nature. In this scenario, GOD is our mighty Naval Architect.

References:

• Muckle, W. (2013). Naval Architecture for Marine Engineers. Oxford, UK. Publisher: Butterworth-Heinemann.
• Derret, Capt. D.R. & Barrass, Bryan. (2012). Ship Stability for Masters and Mates. Oxford, UK. Publisher: Elsevier Science & Technology