Another association of the free surface effect is that a positive feedback loop can be established, in which the period of the roll is equal to the period of the motion of the centre of gravity in the fluid, resulting in each roll increasing in magnitude until the loop is broken or the ship capsizes.
This is a further compounding factor should the Waratah have been taking on water.
There is also a similar consideration in the movement of the metacentre forward and aft as a ship pitches.
Technically, there are different metacentric heights for any combination of pitch and roll motion, depending on the moment of inertia of the water plane area of the ship around the axis of rotation under consideration, but they are normally only calculated and stated as specific values for the limiting pure pitch and roll motion.
The metacentric height is normally estimated during the design of a ship but can be determined by an 'heeling test' once it has been built.
This was the experiment or test that Captain Ilbery missed and Mr Barrie oversaw. Did Captain Ilbery have reservations about the outcome?
The angle(s) obtained during the inclining experiment are directly related to GM (metacentric height) and establishing the vessel's centre of gravity.
The inclining test is usually done inshore in calm weather, in still water, and free of mooring restraints to achieve accuracy. The vessel should also be without free water in ballast tanks. Free water would cause shifts in the centre of gravity.
The GM position is determined by moving weights transversely to produce a known overturning moment in the range of 1-4 degrees if possible. Knowing the restoring properties (buoyancy) of the vessel from its dimensions and floating position and measuring the equilibrium angle of the weighted vessel, the GM can be calculated.
Mr Sawyer quoted the Waratah listing to an angle of 45 degrees. This seems highly unlikely considering the figures quoted and even 4.5 degrees would have been beyond the range.
'Inclinings' can be performed in service by averaging out the effects of motions caused by waves. As in a new ship test, the weight shifts have to be known and the angles of tilt measured. The effects of any mooring can be calculated and deducted. A series of weight (usually ballast) movements are used to obtain an average and variance for GM.
Referring back to Mr Barrie's closing statement:
"On the 21st October, 1908, a load line certificate was issued by Lloyd's. The centre of the disc was to be 8 feet 1 inch below the spar deck line."
To further explain this statement:
A hull is the watertight body of a ship or boat. Above the hull is the superstructure and/or deck house, where present. The line where the hull meets the water surface is called the waterline.
Baseline is an imaginary reference line used to measure vertical distances from.
Waterline is an imaginary line circumscribing the hull that matches the surface of the water when the hull is not moving.
Plimsoll Mark or Load Line Disc are a disc marked amidships below the deck line which is 12 inches in diameter and intersected by a horizontal line 18 inches in length and 1 inch in breadth, the upper edge of which passes through the center of the disc.
The Plimsoll Line is the line where the hull of a ship meets the surface of the water, in concept or reality.
Specifically, it is also the name of a special marking, also known as the International Load Line or water line (positioned amidships), that indicates the draft of the ship and the legal limit to which a ship may be loaded for specific water types and temperatures in order to safely maintain buoyancy, particularly with regard to the hazard of waves that may arise.
The purpose of a load line is to ensure that a ship has sufficient freeboard (the height from the water line to the main deck) and thus sufficient reserve buoyancy.
The freeboard of commercial vessels is measured between the lowest point of the uppermost continuous deck at side and the waterline and this must not be less than the freeboard marked on the Load Line Certificate issued to that ship.
All commercial ships, other than in exceptional circumstances, have a load line symbol painted amidships on each side of the ship.
This symbol must also be permanently marked, so that if the paint wears off it remains visible.
The load line makes it easy for anyone to determine if a ship has been overloaded. The exact location of the load line is calculated and/or verified by a Classification Society and that society issues the relevant certificates.
This marking was invented in the 1870s by Samuel Plimsoll
Waratah had a freeboard of 8 ft. max. draught, which was 3.6 ft. short of the ideal freeboard for a vessel of this size.
NB - SEE: