# Metacentric height

The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of gravity of a ship and its metacentre. A larger metacentric height implies greater initial stability against overturning. The metacentric height also influences the natural period of rolling of a hull, with very large metacentric heights being associated with shorter periods of roll which are uncomfortable for passengers. Hence, a sufficiently, but not excessively, high metacentric height is considered ideal for passenger ships.

Ship stability diagram showing centre of gravity (G), centre of buoyancy (B), and metacentre (M) with ship upright and heeled over to one side.
As long as the load of a ship remains stable, G is fixed. For small angles M can also be considered to be fixed, while B moves as the ship heels.

## Metacentre

Whenever a floating body in a liquid is given a small angular displacement, it will start oscillating about some point, called the metacentre.

When a ship heels, the centre of buoyancy of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is the metacentre. The metacentre remains directly above the centre of buoyancy by definition.

In the diagram, the two Bs show the centres of buoyancy of a ship in the upright and heeled conditions, and M is the metacentre. The metacentre is considered to be fixed for small angles of heel; however, at larger angles of heel, the metacentre can no longer be considered fixed, and its actual location must be found to calculate the ship's stability.
The metacentre can be calculated using the formulae:

${\displaystyle KM=KB+BM}$
${\displaystyle BM={\frac {I}{V}}\ }$

Where KB is the centre of buoyancy (height above the keel), I is the Second moment of area of the waterplane in metres4 and V is the volume of displacement in metres3. KM is the distance from the keel to the metacentre.[1]

Stable floating objects have a natural rolling frequency, just like a weight on a spring, where the frequency is increased as the spring gets stiffer. In a boat, the equivalent of the spring stiffness is the distance called "GM" or "metacentric height", being the distance between two points: "G" the centre of gravity of the boat and "M", which is a point called the metacentre.

Metacentre is determined by the ratio between the inertia resistance of the boat and the volume of the boat. (The inertia resistance is a quantified description of how the waterline width of the boat resists overturning.) Wide and shallow or narrow and deep hulls have high transverse metacenters (relative to the keel), and the opposite have low metacenters; the extreme opposite is shaped like a log or round bottomed boat.

Ignoring the ballast, wide and shallow or narrow and deep means that the ship is very quick to roll and very hard to overturn and is stiff. A log shaped round bottomed means that it is slow to roll and easy to overturn and tender.

"G", is the center of gravity. "GM", the stiffness parameter of a boat, can be lengthened by lowering the center of gravity or changing the hull form (and thus changing the volume displaced and second moment of area of the waterplane) or both.

An ideal boat strikes a balance. Very tender boats with very slow roll periods are at risk of overturning, but are comfortable for passengers. However, vessels with a higher metacentric height are "excessively stable" with a short roll period resulting in high accelerations at the deck level.

Sailing yachts, especially racing yachts, are designed to be stiff, meaning the distance between the centre of mass and the metacentre is very large in order to resist the heeling effect of the wind on the sails. In such vessels, the rolling motion is not uncomfortable because of the moment of inertia of the tall mast and the aerodynamic damping of the sails.

## Different centres

Initially the second moment of area increases as the surface area increases, increasing BM, so Mφ moves to the opposite side, thus increasing the stability arm. When the deck is flooded, the stability arm rapidly decreases.

The centre of buoyancy is at the centre of mass of the volume of water that the hull displaces. This point is referred to as B in naval architecture. The centre of gravity of the ship is commonly denoted as point G or VCG. When a ship is at equilibrium, the centre of buoyancy is vertically in line with the centre of gravity of the ship.[2]

The metacentre is the point where the lines intersect (at angle φ) of the upward force of buoyancy of φ ± dφ. When the ship is vertical, the metacentre lies above the centre of gravity and so moves in the opposite direction of heel as the ship rolls. This distance is also abbreviated as GM. As the ship heels over, the centre of gravity generally remains fixed with respect to the ship because it just depends on the position of the ship's weight and cargo, but the surface area increases, increasing BMφ. Work must be done to roll a stable hull. This is converted to potential energy by raising the centre of mass of the hull with respect to the water level or by lowering the centre of buoyancy or both. This potential energy will be released in order to right the hull and the stable attitude will be where it has the least magnitude. It is the interplay of potential and kinetic energy that results in the ship having a natural rolling frequency. For small angles, the metacentre, Mφ, moves with a lateral component so it is no longer directly over the centre of mass.[3]

The righting couple on the ship is proportional to the horizontal distance between two equal forces. These are gravity acting downwards at the centre of mass and the same magnitude force acting upwards through the centre of buoyancy, and through the metacentre above it. The righting couple is proportional to the metacentric height multiplied by the sine of the angle of heel, hence the importance of metacentric height to stability. As the hull rights, work is done either by its centre of mass falling, or by water falling to accommodate a rising centre of buoyancy, or both.

For example, when a perfectly cylindrical hull rolls, the centre of buoyancy stays on the axis of the cylinder at the same depth. However, if the centre of mass is below the axis, it will move to one side and rise, creating potential energy. Conversely if a hull having a perfectly rectangular cross section has its centre of mass at the water line, the centre of mass stays at the same height, but the centre of buoyancy goes down as the hull heels, again storing potential energy.

When setting a common reference for the centres, the molded (within the plate or planking) line of the keel (K) is generally chosen; thus, the reference heights are:

KB – to Centre of Buoyancy
KG – to Centre of Gravity
KMT – to Transverse Metacentre

### Righting arm

Distance GZ is the righting arm: a notional lever through which the force of buoyancy acts

The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel. Beyond that range, the stability of the vessel is dominated by what is known as a righting moment. Depending on the geometry of the hull, naval architects must iteratively calculate the center of buoyancy at increasing angles of heel. They then calculate the righting moment at this angle, which is determined using the equation:

${\displaystyle RM=GZ\cdot \Delta }$

Where RM is the righting moment, GZ is the righting arm and Δ is the displacement. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel. The righting arm (known also as GZ — see diagram): the horizontal distance between the lines of buoyancy and gravity.[3]

${\displaystyle GZ=GM\cdot sin\phi }$ [2] at small angles of heel

There are several important factors that must be determined with regards to righting arm/moment. These are known as the maximum righting arm/moment, the point of deck immersion, the downflooding angle, and the point of vanishing stability. The maximum righting moment is the maximum moment that could be applied to the vessel without causing it to capsize. The point of deck immersion is the angle at which the main deck will first encounter the sea. Similarly, the downflooding angle is the angle at which water will be able to flood deeper into the vessel. Finally, the point of vanishing stability is a point of unstable equilibrium. Any heel lesser than this angle will allow the vessel to right itself, while any heel greater than this angle will cause a negative righting moment (or heeling moment) and force the vessel to continue to roll over. When a vessel reaches a heel equal to its point of vanishing stability, any external force will cause the vessel to capsize.

Sailing vessels are designed to operate with a higher degree of heel than motorized vessels and the righting moment at extreme angles is of high importance.

Monohulled sailing vessels should be designed to have a positive righting arm (the limit of positive stability) to at least 120° of heel,[4] although many sailing yachts have stability limits down to 90° (mast parallel to the water surface). As the displacement of the hull at any particular degree of list is not proportional, calculations can be difficult, and the concept was not introduced formally into naval architecture until about 1970.[5]

## Stability

### GM and rolling period

The metacentre has a direct relationship with a ship's rolling period. A ship with a small GM will be "tender" - have a long roll period. An excessively low or negative GM increases the risk of a ship capsizing in rough weather, for example HMS Captain or the Vasa. It also puts the vessel at risk of potential for large angles of heel if the cargo or ballast shifts, such as with the Cougar Ace. A ship with low GM is less safe if damaged and partially flooded because the lower metacentric height leaves less safety margin. For this reason, maritime regulatory agencies such as the International Maritime Organization specify minimum safety margins for seagoing vessels. A larger metacentric height on the other hand can cause a vessel to be too "stiff"; excessive stability is uncomfortable for passengers and crew. This is because the stiff vessel quickly responds to the sea as it attempts to assume the slope of the wave. An overly stiff vessel rolls with a short period and high amplitude which results in high angular acceleration. This increases the risk of damage to the ship and to cargo and may cause excessive roll in special circumstances where eigenperiod of wave coincide with eigenperiod of ship roll. Roll damping by bilge keels of sufficient size will reduce the hazard. Criteria for this dynamic stability effect remain to be developed. In contrast, a "tender" ship lags behind the motion of the waves and tends to roll at lesser amplitudes. A passenger ship will typically have a long rolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a rolling period of 6 to 8 seconds.

The period of roll can be estimated from the following equation[2]

${\displaystyle T={\frac {2\pi \,k}{\sqrt {g{\overline {GM}}}}}\ }$

where g is the gravitational acceleration, k is the radius of gyration about the longitudinal axis through the centre of gravity and ${\displaystyle {\overline {GM}}}$ is the stability index.

### Damaged stability

If a ship floods, the loss of stability is caused by the increase in KB, the centre of buoyancy, and the loss of waterplane area - thus a loss of the waterplane moment of inertia - which decreases the metacentric height.[2] This additional mass will also reduce freeboard (distance from water to the deck) and the ship's angle of down flooding (minimum angle of heel at which water will be able to flow into the hull). The range of positive stability will be reduced to the angle of down flooding resulting in a reduced righting lever. When the vessel is inclined, the fluid in the flooded volume will move to the lower side, shifting its centre of gravity toward the list, further extending the heeling force. This is known as the free surface effect.

## Free surface effect

In tanks or spaces that are partially filled with a fluid or semi-fluid (fish, ice, or grain for example) as the tank is inclined the surface of the liquid, or semi-fluid, stays level. This results in a displacement of the centre of gravity of the tank or space relative to the overall centre of gravity. The effect is similar to that of carrying a large flat tray of water. When an edge is tipped, the water rushes to that side, which exacerbates the tip even further.

The significance of this effect is proportional to the cube of the width of the tank or compartment, so two baffles separating the area into thirds will reduce the displacement of the center of gravity of the fluid by a factor of 9. This is of significance in ship fuel tanks or ballast tanks, tanker cargo tanks, and in flooded or partially flooded compartments of damaged ships. Another worrying feature of free surface effect is that a positive feedback loop can be established, in which the period of the roll is equal or almost 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 has been significant in historic capsizes, most notably the MS Herald of Free Enterprise and the MS Estonia.

## Transverse and longitudinal metacentric heights

There is also a similar consideration in the movement of the metacentre forward and aft as a ship pitches. Metacentres are usually separately calculated for transverse (side to side) rolling motion and for lengthwise longitudinal pitching motion. These are variously known as ${\displaystyle {\overline {GM_{T}}}}$ and ${\displaystyle {\overline {GM_{L}}}}$, GM(t) and GM(l), or sometimes GMt and GMl .

Technically, there are different metacentric heights for any combination of pitch and roll motion, depending on the moment of inertia of the waterplane 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.

## Measurement

The metacentric height is normally estimated during the design of a ship but can be determined by an inclining test once it has been built. This can also be done when a ship or offshore floating platform is in service. It can be calculated by theoretical formulas based on the shape of the structure.

The angle(s) obtained during the inclining experiment are directly related to GM. By means of the inclining experiment, the 'as-built' centre of gravity can be found; obtaining GM and KM by experiment measurement (by means of pendulum swing measurements and draft readings), the centre of gravity KG can be found. So KM and GM become the known variables during inclining and KG is the wanted calculated variable (KG = KM-GM)

## References

1. ^ Ship Stability. Kemp & Young. ISBN 0-85309-042-4
2. ^ a b c d Comstock, John (1967). Principles of Naval Architecture. New York: Society of Naval Architects and Marine Engineers. p. 827. ISBN 9997462556.
3. ^ a b Harland, John (1984). Seamanship in the age of sail. London: Conway Maritime Press. p. 43. ISBN 0-85177-179-3.
4. ^ Rousmaniere, John, ed. (1987). Desirable and Undesirable Characteristics of Offshore Yachts. New York, London: W.W.Norton. p. 310. ISBN 0-393-03311-2.
5. ^ U.S. Coast Guard Technical computer program support accessed 20 December 2006.
1746 in science

The year 1746 in science and technology involved some significant events.

A- and B-class destroyer

The A- and B-class destroyers were a group of 18 destroyers built for the Royal Navy during the late 1920s, with two additional ships built for the Royal Canadian Navy. The British ships were divided into two flotillas of eight destroyers, each with a flotilla leader.

Angle of list

The angle of list is the degree to which a vessel heels (leans or tilts) to either port or starboard.A listing vessel is stable and at equilibrium, but the distribution of weight aboard (often caused by uneven loading or flooding) causes it to heel to one side.

By contrast, roll is the dynamic movement from side to side caused by waves.

If a listing ship goes beyond the point where a righting moment will keep it afloat, it will capsize and potentially sink.

Angle of loll

Angle of loll is the state of a ship that is unstable when upright (i.e. has a negative metacentric height) and therefore takes on an angle of heel to either port or starboard.

When a vessel has negative metacentric height (GM) i.e., is in unstable equilibrium, any external force applied to the vessel will cause it to start heeling. As it heels, the moment of inertia of the vessel's waterplane (a plane intersecting the hull at the water's surface) increases, which increases the vessel's BM (distance from the center of Buoyancy to the Metacenter). Since there is relatively little change in KB (distance from the Keel to the center of Buoyancy) of the vessel, the KM (distance from Keel to the Metacenter) of the vessel increases.

At some angle of heel (say 10°), KM will increase sufficiently equal to KG (distance from the keel to the center of gravity), thus making GM of vessel equal to zero. When this occurs, the vessel goes to neutral equilibrium, and the angle of heel at which it happens is called angle of loll.

In other words, when an unstable vessel heels over towards a progressively increasing angle of heel, at a certain angle of heel, the center of buoyancy (B) may fall vertically below the center of gravity (G). Angle of list should not be confused with angle of loll. Angle of list is caused by unequal loading on either side of center line of vessel.

Although a vessel at angle of loll does display features of stable equilibrium, this is a dangerous situation and rapid remedial action is required to prevent the vessel from capsizing.It is often caused by the influence of a large free surface or the loss of stability due to damaged compartments. It is different from list in that the vessel is not induced to heel to one side or the other by the distribution of weight, it is merely incapable of maintaining a zero heel attitude.

Eclipse-class cruiser

For the 1867 class of sloop (later corvette) see: Eclipse-class sloopThe Eclipse-class cruisers were a class of nine second-class protected cruisers constructed for the Royal Navy in the mid-1890s.

Florida-class battleship

The Florida-class battleships of the United States Navy comprised two ships: Florida and Utah. Launched in 1910 and 1909 respectively and commissioned in 1911, they were slightly larger than the preceding Delaware class design but were otherwise very similar. This was the first US battleship class in which all ships received steam turbine engines. In the previous Delaware-class, North Dakota received steam turbine propulsion as an experiment while Delaware retained triple-expansion engines.

Both ships were involved in the 1914 Second Battle of Vera Cruz, deploying their Marine contingents as part of the operation. Following the entrance of the United States into World War I in 1917, both ships were deployed to Europe. Florida was assigned to the British Grand Fleet and based in Scapa Flow; in December 1918 she escorted President Woodrow Wilson to France for the peace negotiations. Utah was assigned to convoy escort duty; she was based in Ireland and was tasked with protecting convoys as they approached the European continent.

Retained under the Washington Naval Treaty of 1922, both ships were modernized significantly, with torpedo bulges and oil-fired boilers installed and other improvements made, but were demilitarized under terms of the 1930 London Naval Treaty. Florida was scrapped, Utah converted into first a radio-controlled target ship, then an anti-aircraft gunnery trainer. She served in the latter role until sunk by the Japanese during the attack on Pearl Harbor on 7 December 1941. Her hull, never raised, remains on the bottom of the harbor as a war memorial.

GZ

GZ or gz may refer to:

.gz, the file extension for gzip files (GNU zip, an open source file compression program)

GZ, an HCPCS Level II modifier meaning an item or service is expected to be denied as not reasonable or necessary

GZ, the "righting moment" or "righting arm" acting to restore a tilting ship to vertical; see metacentric height

Galaxy Zoo, a crowdsourced astronomy project

Gaza Strip (FIPS PUB 10-4 territory code)

Gestrichener Zellstoffkarton (German; DIN 19303 Code), a grade of paperboard also known as solid bleached board

Ground Zero, in military parlance

Guangzhou, capital and largest city of Guangdong Province in southeastern China

Guizhou, a province of China (Guobiao abbreviation GZ)

Air Rarotonga (IATA airline designator)

HMS Atherstone (L05)

HMS Atherstone was a Hunt-class destroyer of the Royal Navy. She was launched in late 1939 as the first of her class but was found to be unstable, and had to undergo significant modifications before entering service in March 1940.

Inclining test

An inclining test is a test performed on a ship to determine its stability, lightship weight and the coordinates of its center of gravity. The test is applied to newly constructed ships greater than 24m in length, and to ships altered in ways that could affect stability. Inclining test procedures are specified by the International Maritime Organization and other international associations.

The weight of a vessel can be readily determined by reading draughts and comparing with the known hydrostatic properties. The metacentric height (GM), which dominates stability, can be estimated from the design, but an accurate value must be determined by an inclining test.

The inclining test is usually done inshore in calm weather, in still water, and free of mooring restraints to achieve accuracy. 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.

As in a new ship test, the weight shifts have to be known and the angles of tilt measured. A series of weight (ballast) movements are used to obtain an average and variance for GM.

Metacentric

Metacentric may refer to:

Metacentric height: the distance between the center of gravity of a ship and its metacenter

Metacentric centromere: the position of a centromere on a chromatid

Pennsylvania-class battleship

The Pennsylvania-class consisted of two super-dreadnought battleships built for the United States Navy just before the First World War. The ships were named Pennsylvania and Arizona, after the American states of the same names. They constituted the United States' second battleship design to adhere to the "all or nothing" armor scheme, and were the newest American capital ships when the United States entered the First World War.

The Nevada-class battleships represented a marked increase in the United States' dreadnought technology, and the Pennsylvania-class was intended to continue this with slight increases in the ships' capabilities, including two additional 14-inch (356 mm)/45 caliber guns and improved underwater protection. The class was the second standard type battleship class to join the US Navy, along with the preceding Nevada and the succeeding New Mexico, Tennessee and Colorado classes.

In service, the Pennsylvania-class saw limited use in the First World War, as a shortage of oil fuel in the United Kingdom meant that only the coal-burning ships of Battleship Division Nine were sent. Both were sent across the Atlantic to France after the war for the Paris Peace Conference of 1919, and were then transferred to the Pacific Fleet before being significantly modernized from 1929 to 1931. For the remainder of the inter-war period, the ships were used in exercises and fleet problems. Both Pennsylvania and Arizona were present during the Japanese attack on Pearl Harbor, which brought the United States into the Second World War. Arizona was sunk by a massive magazine explosion and was turned into a memorial after the war, while Pennsylvania, in dry dock at the time, received only minor damage. After a refit from October 1942 to February 1943, Pennsylvania went on to serve as a shore bombardment ship for most of the remainder of the war. Pennsylvania was present at the Battle of Surigao Strait, the last battle ever between battleships, but did not engage. Pennsylvania was severely damaged by a torpedo on 12 August 1945, two days before the cessation of hostilities. With minimal repairs, it was used in Operation Crossroads, part of the nuclear testing at Bikini Atoll, before being expended as a target ship in 1948.

Pontoon effect

The pontoon effect refers to the tendency of a vessel whose flotation depends on lateral pontoons to capsize without warning when a lateral force is applied. The effect can be sudden and dramatic because pontoon boats usually cannot rely on the righting effect of a keel (which contains ballast).

The vessel is stable and self-righting up to the point that the centre of gravity shifts past the centre of buoyancy of the ship and the vessel rapidly capsizes.(The same term can also arise when describing a design in which the attributes of a pontoon are created without using explicit pontoons—when a design effectively incorporates pontoons. This page describes the specific phenomenon described above.)

The pontoon effect is theoretically possible whenever the vessel's entire weight exceeds the buoyancy of the pontoon(s) on either side. However, the pontoon effect is more likely in vessels with a high center of gravity and low or non-existent displacement other than the pontoons.

A pontoon vessel such as a catamaran floats in a level position when the center of gravity of the entire vessel (including its load) is above the center of buoyancy. This is the opposite of the case in a traditional or displacement hull vessel, which derives positive stability from having its center of buoyancy above the center of gravity. If the pontoon vessel tips, it will remain stable as long as the center of gravity does not move further to the side than the center of buoyancy is moved by the change in the depth (and displacement) of each pontoon. Under these conditions a "righting force" (a turning moment) acts on the vessel to push it back toward the level position.

However, if the center of gravity is high relative to the width of the vessel, and the pontoons on one side are unable to bear the vessel's complete weight, the lateral movement of the center of buoyancy will be restricted. Even a relatively small lateral force can move the center of gravity further to the side than the center of buoyancy can go. At this point, the righting force will disappear, replaced by a turning moment in the opposite direction. This can capsize the vessel at the point at which one pontoon is completely submerged.

When using twin lateral pontoons, each pontoon should have enough buoyancy to bear the load of the entire vessel on its own. If the vessel is so heavy that either pontoon is mostly submerged when no lateral force is applied, it will be vulnerable to the pontoon effect. If sufficient lateral force arises (such as wind or shifting load), the vessel can tip enough to submerge one pontoon. At this point, the sunken pontoon will provide no further buoyancy to right the vessel. As the center of buoyancy cannot move further to that side to match the center of gravity, that pontoon will continue sinking. The tipping angle will increase until the vessel capsizes. This can continue until the vessel inverts completely with the pontoons again floating on the surface but the rest of the vessel underwater. At this point, the upside-down vessel will be highly stable. If, on the other hand, the vessel is designed and loaded so that each pontoon can support the vessel's entire weight (plus any lateral forces that arise like wind), the center of gravity cannot move transversely beyond the center of buoyancy at the most extreme tipping angle, and the pontoon effect cannot occur.Note, however, that this is not the sole effect to be taken into consideration when assessing the likelihood of capsize. The change in hull windage as the vessel heels is also important. In the case of a trimaran designed for cruising, with solid wing decks (as opposed to racing-type designs with mesh or open wings), those with wide-beam floats able to support the whole weight of the vessel are more likely to capsize than those with narrow-beam floats of lesser buoyancy that can be submerged as the vessel heels. As the wide-beam float comes to take the entire weight of the heeling vessel, the centre hull lifts out of the water; this exposes the entire area of the underside of both wings to the wind, and also increases the turning moment of the wind force on the weather wing. There is now a considerable overturning force due to the wind and the vessel is very likely to capsize. In contrast, a trimaran with narrow-beam floats will simply submerge the lee float, exposing only the weather wing and that with a lesser moment. In practical sea situations the windage effect is greater than the buoyancy effect and so cruising trimarans with highly buoyant floats are more, not less, likely to capsize than those with less buoyant floats.A trimaran is best stabilised not by adding buoyancy on the lee float but adding weight to the weather float. This is the basis of the "cool-tubes" stability system invented by Tristan Jones and L. Surtees. A large-diameter pipe closed at the aft end is attached to the keel of each float and fills with water. While it remains submerged buoyancy forces cancel the weight of the trapped water and the weight of the tube is effectively zero. But if the boat heels enough to bring the weather float out of the water, this effect no longer operates and the water provides a heavy ballast weight on the float, creating a righting moment.In the abstract sense, the principles at work govern the stability of all boats and ships including those without lateral pontoons. See angle of loll and metacentric height.

Royal Sovereign-class battleship

The Royal Sovereign class was a group of eight pre-dreadnought battleships built for the Royal Navy in the 1890s. The ships spent their careers in the Mediterranean, Home and Channel Fleets, sometimes as flagships, although several were mobilised for service with the Flying Squadron in 1896 when tensions with the German Empire were high following the Jameson Raid in South Africa. Three ships were assigned to the International Squadron formed when Greek Christians rebelled against the Ottoman Empire′s rule in Crete in 1897–1898.

By about 1905–1907, they were considered obsolete and were reduced to reserve. The ships began to be sold off for scrap beginning in 1911, although Empress of India was sunk as a target ship during gunnery trials in 1913. Hood was fitted with the first anti-torpedo bulges to evaluate underwater protection schemes in 1911 before being scuttled as a blockship a few months after the start of the First World War in August 1914. Only Revenge survived to see active service in the war, during which she bombarded the Belgian coastline. Renamed Redoubtable in 1915, she was hulked later that year as an accommodation ship until she was sold for scrap after the war.

Ship stability

Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves, whether intact or damaged. Stability calculations focus on centers of gravity, centers of buoyancy, the metacenters of vessels, and on how these interact.

Stability conditions

The Stability conditions of watercraft are the various standard loading configurations to which a ship, boat, or offshore platform may be subjected. They are recognized by classification societies such as Det Norske Veritas, Lloyd's Register and American Bureau of Shipping (ABS). Classification societies follow rules and guidelines laid down by International Convention for the Safety of Life at Sea (SOLAS) conventions, the International Maritime Organization and laws of the country under which the vessel is flagged, such as the Code of Federal Regulations.

Stability is normally broken into two distinct types: Intact and Damaged

Superfiring

The idea of superfiring armament is to locate two (or more) turrets in a line, one behind the other, but with the second turret located above ("super") the one in front so that the second turret could fire over the first. This configuration meant that both forward or aft turrets could fire at any target within their sector, even when the target was in the same vertical plane as the turrets.

Thermal fluids

Thermofluids is a branch of science and engineering encompassing four intersecting fields:

Heat transfer

Thermodynamics

Fluid mechanics

CombustionThe term is a combination of "thermo", referring to heat, and "fluids", which refers to liquids, gases and vapors. Temperature, pressure, equations of state, and transport laws all play an important role in thermofluid problems. Phase transition and chemical reactions may also be important in a thermofluid context. The subject is sometimes also referred to as "thermal fluids".

USS Texas (1892)

USS Texas was a second-class battleship built by the United States in the early 1890s, the first American battleship commissioned and the first ship named in honor of the state of Texas to be built by the United States. Built in reaction to the acquisition of modern armored warships by several South American countries, Texas was meant to incorporate the latest developments in naval tactics and design. This includes the mounting of her main armament en echelon to allow maximum end-on fire and a heavily-armored redoubt amidships to ensure defensive strength. However, due to the state of U.S. industry at the time, Texas's building time was lengthy, and by the time she was commissioned, she was already out of date. Nevertheless, she and her near-sister USS Maine were considered advancements in American naval design.

Texas developed a reputation as a jinxed or unlucky ship after several accidents early in her career; she consequently earned the nickname "Old Hoodoo". These mishaps included problems during construction, a grounding off Newport, Rhode Island, and flooding shortly afterwards while at dock in New York City. In the last, she settled to the bottom with her gun deck awash and several crew members drowned. She also received significant damage to her hull in drydock after being raised. Her reputation improved with her service in the Spanish–American War, when she blockaded the coast of Cuba and fought in the Battle of Santiago de Cuba.

After the war, Texas returned to peacetime duty, interrupted by several refits. She became the station ship in Charleston, South Carolina, by 1908 and was renamed San Marcos in 1911 to allow her name to be used by a new battleship. She became a target ship that same year and was sunk in shallow water in Chesapeake Bay. She was used as a gunnery target through World War II and was finally demolished in 1959 because her remains were considered a navigational hazard.

Length