# Stability (hull)

Heel is the inclination of a ship around its longitudinal axis (x)

In shipbuilding and nautical science, the term stability refers to the property of a floating body , for example a ship, to maintain an upright swimming position or to straighten up independently in response to a heeling torque.

## Stability of seagoing vessels

### Influencing factors

The following factors determine the individual stability of a ship.

Further operating conditions to be considered are:

### Physical basics

Position of the center of gravity (G), center of lift (B) and metacenter (M) when the ship is upright or heeled

The fundamental parameters of the stability of a ship are the center of gravity and the center of lift (also form or displacement center of gravity ), as well as the resulting metacentric height . In the center of gravity you can imagine the entire downward weight of the ship concentrated on one point. If the ship is heeled, the center of gravity remains in its position within the ship as long as all the masses in the ship remain in place (for example, if cargo passes over, this also changes the center of gravity). One can imagine the total upward weight of the displaced water in the buoyancy center. It changes its position if it heels because the "shape" of the displaced water changes.

When the ship is in an upright position, the center of gravity and the center of buoyancy are perpendicular to each other. If the ship is heeled by an external influence, the center of gravity remains in place in relation to the ship, but moves overall to the side of the heel. The center of buoyancy migrates to the same side, namely into the center of the now displaced water. If the center of gravity and the center of buoyancy are no longer perpendicular and the center of gravity is below the initial metacenter of the ship, a so-called “righting lever arm” is created, which returns the ship to its original position when the heeling influence is removed.

### Identification and evaluation

Lever arm curve. GZ corresponds to the righting lever arm

The key parameters for evaluating the stability of a ship are the metacentric initial height, the range of stability and the area under the lever arm curve. The metacentric height is a parameter for the righting lever arm. The scope of stability denotes the calculated heeling of the ship in degrees up to the overturning point and the righting lever arm curve is a graphic representation of the righting lever arm over the full heeling range up to the overturning point. The lever arm grows stronger with increasing heel, then weaker and weaker and becomes smaller again with even stronger heel, until it finally reaches the capsizing point when the center of gravity migrates beyond the center of lift. With the area under the righting arm curve, not only can the fulfillment of the minimum stability be proven, but also an undesirably high stability can be proven.

### Statutory Regulations

Several IMO resolutions are decisive for the stability of ships . The most important of these are the resolutions A.749 (18) and MSC.267 (85) ( 2008 IS Code ) for the intact stability of ocean-going vessels or, accordingly, the SOLAS regulation for passenger ships. Even if the requirements formulated therein are not binding, many flag states and z. For example, the EU has also adopted the IMO regulations in its own stability regulations. Merchant ships flying the German flag must, however, also comply with the stricter regulations of the See-Berufsgenossenschaft , now BG Verkehr.

Typical stability requirements are, for example:

• Minimum size of the metacentric height , the distance between the center of gravity and the metacenter.
• Area under the righting lever curve.
• Angle of the maximum of the lever arm curve.
• Righting moment at a defined heel angle is checked using the acting lever arm.

The stability is already taken into account in the design phase of a ship. a. examined on the basis of specified standard loading cases. Today, the stability is usually verified by means of an on-board computer, which calculates all loading and stability criteria in advance. The ship's center of gravity is determined experimentally in a heeling test. The invoice is checked by a classification society authorized by the flag state and is considered accepted if all stability regulations applicable to the ship in question are complied with. The checked stability documents are part of the on-board documents.

### Practical considerations

The rolling behavior of ships with a large righting lever arm is called stiff , that of ships with a small righting lever arm is called soft and a ship with only a very small righting lever arm is called rank .

Ship types such as container ships or ferries often have an undesirably high center of gravity due to their load and design, which would result in insufficient stability. To ensure sufficient stability, a high load on deck is therefore balanced out with large ballast water capacities, mainly in double bottom tanks. The opposite situation can be found, for example, with ore ships , which usually have an extremely low center of gravity when loaded. A ship with undesirably high stability has a very short roll period with small roll angles which, due to the high accelerations that occur, favor the cargo being passed over or personal injury and would put a great deal of stress on the ship's formations. Here, the center of gravity is shifted upwards by absorbing ballast water in high tanks in order to improve this behavior.

The stability assessment of a ship relates not only to the hull alone, but also to different conditions that vary during operation. This mainly includes the loading of the ship, which has to take into account, for example, the special regulations for grain cargoes (which can easily slide as bulk cargo ) or small heel angles for heavy goods colli on deck. Furthermore, the changing conditions during operation, in particular due to the consumption of bunkers, operating materials and fresh water, as well as changes in the amount of ballast water from the beginning to the end of the journey must be calculated in advance. The influence of different external operating conditions, such as wind pressure, swell, water absorption by the deck cargo and water accumulation on deck, or icing in cold regions must also be taken into account. Last but not least, consideration must also be given to internal influences, such as putting hard rudders at full speed or the possible situation that all passengers move to one side of the passenger ship.

Further so-called dynamic stability loads can arise during a trip due to wind and swell. Mainly it is about the influences of strong wind gusts, the sea behavior of the ship in swell and swell, as well as occurring roll period resonances. Since these phenomena cannot simply be put into formulas due to the highly complex energy balances on which they are based, their assessment is still largely left to the nautical experience of the ship's command. In the event of leaks, the weight distribution as well as the buoyancy can change considerably, so that a ship capsizes even though it is still fully buoyant. From all of the above it follows that the assessment of the stability of ships is more difficult, the more complex it is and the more variable the operating conditions are.

### Ship stabilizers

In larger ships, especially in passenger ships , systems are often used with which the movement of a ship on the longitudinal axis dampen, or such. B. with fin stabilizers, can be actively controlled.

## Pleasure craft area

In contrast to commercial and naval vessels , pleasure craft are often more simply constructed. They often consist essentially of a hollow hull, possibly with a mast and sails. In practice, it is therefore sufficient to consider a few aspects: average torso cross-section, center of gravity and / or an additional stabilization weight.

### Sailing ships

Sailboats and ships are worth a special look. Since their sails offer a very large surface area for the wind to attack, they would simply tip over at low wind strengths without suitable countermeasures.

The stability of a sailboat depends largely on the shape of the hull and weight distribution of the boat (including the crew). There are two components that can be used to compensate for heeling. Except in a few special cases (purely dimensionally stable boats), stability is always made up of two righting components:

• Weight stability - a low-lying ballast keel forces the boat back into an upright position ( stand-up principle).
• Dimensional stability - the shape of the trunk favors a return to the starting position.

#### Weight stability

Weight stability

In sailing ships and yachts, the keel acts as a counterweight to counteract heeling . This contains up to 50% of the mass of the ship and thus causes a righting moment. A certain heeling - depending on the design of the ship and wind strength of 20 to 45 ° - is normal in these ships and does not pose any risk to the ship. Since strong heeling, high waves running in opposite directions can usually be expected - the largest Heeling occurs when sailing on an upwind course - the equipment should be well secured and the crew wear lifebelts so as not to be washed overboard in a gust or a wave, as well as life jackets in case this does happen.

In the adjacent picture, G is the center of gravity (center of gravity of the boat) and A is the center of gravity of shape (center of gravity of the displaced water mass). In these points one can think of the weight or buoyancy forces as a unit. The position of G is decisive for weight stability: With increasing heel, the center of gravity moves outwards and thus increases the righting torque .

The stronger the heel, the stronger the righting moment of the keel becomes due to the lever law (principle of the standing man ). Monohull sailing ships straighten themselves up to a heel of 120 ° or more, so they can actually capsize only in very high waves, i.e. remain lying with the keel up. Keelboats are therefore considered to be overturned safe. However, if waves hit the ship's interior, they fill up and can sink. In the very unfortunate and rare event that a keel yacht loses its keel at sea, it is in fact lost.

#### Dimensional stability

Dimensional stability

In contrast to keel yachts, most dinghies are largely dimensionally stable. The (usually fold-out) light sword of a dinghy has no righting effect worth mentioning. Also catamarans or trimarans due to their width have a high dimensional stability.

In the adjacent picture, G is the center of gravity (center of gravity of the boat) and A is the center of gravity of shape (center of gravity of the displaced water mass). In these points one can think of the weight or buoyancy forces as a unit. The position of A is decisive for the dimensional stability.

When the boat is upright, the same amount of water is displaced on both sides of the hull. A is then in the middle of the fuselage cross-section, there is no torque. With increasing heel (see picture), water is mainly displaced on one side of the hull. As a result, A moves outwards, creating a torque. The wider the boat, the further A moves outward and the stronger the righting torque. If the heel becomes too great, however, the torque decreases again because the broad trunk is then tilted and A is closer to the center again. A slight heel is therefore compensated for by the powerful righting torque ("water resistance"), while too much heel leads to the boat capsizing. Catamarans capsize when the heel reaches 90 °.

There are even examples of completely dimensionally stable boat types with negative initial stability. These do not have an upright swimming position when at rest.

#### Countermeasures in the event of great heel

A sailor hangs in the trapeze to balance the catamaran.

In keel boats, catamarans and dinghies, the heel can be reduced by having the crew "sit on the high edge", that is, sit on the railing on the windward side , or by reducing the sail area ( reefing ). When sailing dinghies , the crew hangs in a trapeze to be able to ride further to windward. When sailing dinghies for sport, capsizing can happen. In return, they are equipped with floating bodies so that they do not sink despite capsizing. Nevertheless, dinghies are not suitable for the high seas and even good dinghy sailors will no longer cast off when the announced wind strengths of more than 6.

The heel automatically reduces the effective sail area, and the shape of the hull also prefers a certain heel angle at which the ship can reach the highest speed. Therefore, the ship slows down due to strong heeling, and staying on board becomes more uncomfortable. There is also an increased risk that excessive heeling will result in a so-called sun shot and the ship “gets out of hand” and “shoots into the wind”. It is even worse if the main boom's nock is submerged in the water, which can cause serious damage to the rig . Therefore, by reefing in good time - despite the reduced sail area - the speed can increase.

### Motor boats

Typical motor yacht with a steering position on the roof
The aircraft carrier Ronald Reagan heels during rowing tests.

Motor boats for pleasure boating are almost exclusively dimensionally stable boats, they have a wide and flat hull with a relatively low center of gravity. Motor boats can overturn when making tight turns at high speed. In strong lateral winds, they typically offer a larger surface area to attack than a sailing yacht without a sail, as they have several decks. If there are corresponding waves, it also becomes dangerous for a motor yacht.

### Capsize angle

Depending on how a certain boat behaves at different heel angles, one speaks of high initial or final stability . The dynamic capsize angle , from which the angle increases even without external moments such as wind pressure, relates to the final stability . The center of lift moves under the center of gravity. With stable keel yachts this capsizing angle is usually between 110 ° and 160 °, with dinghies, on the other hand, it is usually less than 90 °, whereby the latter easily remain stable in the water with the sword pointing upwards, while keel yachts usually capsize quickly.

## Individual evidence

1. a b seamanship , page 163
2. ^ Seamanship , page 162.
3. “Getting out of hand” means that the rudder is stalled because it is no longer being washed around properly or is protruding completely out of the water. This makes steering impossible.
4. Seamanship , page 270 - For safety reasons, boats are usually designed to be easily luffed, so that if the rudder is lost, the boat will luff up and control will return.

## literature

• Helmers, Walter (ed.): Müller-Krauss, manual for ship management . Volume 3, seamanship and ship technology, part B. Springer Verlag, Berlin 1980, ISBN 3-540-10357-0 .
• Hermann Kaps: Stability, Trimm, Strength In: Knud Benedict (Hrsg.), Christoph Wand (Hrsg.): Manual Nautics II - Technical and operational ship management . Seehafen Verlag (DVV Media Group), Hamburg 2011, ISBN 978-3-87743-826-8 , pp. 65–153.
• Werner Voss: Stability. including various attachments (trim and loading plans, diagrams, stability and resonance sheets etc.) (publisher), Seafaring School Bremen, edition 1963.