## USCG Masters Captains License 25/50/100 Ton Upgrade

# SHIP CONSTRUCTION - Trim and Stability

## Ship Construction - Module 2

# Trim and Stability

*Stability* is the tendency of a vessel to remain upright. An object is stable if when tilted (inclined) from its upright position by an outside force it will return when the inclining force is removed. The stability of a vessel is very important to the safety of the crew and cargo, and it is important to understand this concept. The two forces that affect stability of a floating vessel are weight and buoyancy. Weight is the downward force due to gravity. Buoyancy is an upward force on a vessel in the water. The interaction of these two forces affects a vessel’s stability.

Box A has *positive stability *because if it is inclined up to a certain angle it will right itself. Cone B has *negative stability* because if it is inclined it will not return to an upright position. Ball C has *neutral stability* because an outside force will cause it to assume a new position. It neither falls over nor returns to its original position. Box A has a stability limit because if it is tilted beyond 45 degrees from the horizontal it would develop negative stability and fall over. Therefore its range of stability is zero to 45 degrees.

The *center of gravity* (G) of an object is the point through which the entire downward force of gravity acts on its weight. If weight is distributed evenly, G will be at the geometric center of the object.

If Box A and B are identical, then A would be harder to tip because the center of gravity is lower and is has a broader base.

Box B has been filled with sand and placed on its broader base. Now B would be harder to tip because B is heavier, even though both of their center of gravities are the same.

In this diagram, while A and B are positioned the same, the center of gravity in A has been lowered by putting weight in the bottom. A is now harder to tip and is said to have greater stability.

In this diagram A and B both have the same center of gravity. B is more stable because the breadth of the base is greater. Three things, the weight, center of gravity or distribution of weight, and the shape of the object affect stability. While shape is not a factor that can be altered, the weight and distribution of that weight need to be controlled.

Any time a vessel is loaded or unloaded the operator should calculate the change in “G” up or down, forward or aft. The height of the center of gravity is measured from the keel (K), or baseline. Because it is a vertical measurement it is sometimes called KG or VCG for *vertical center of gravity.*

The *transverse (sideways) center of gravity* (TCG) is measured so many feet port or starboard of the fore and aft centerline of a vessel.

*The longitudinal center of gravity* (LCG) is measured lengthwise.

The most important of the three measurements is the height of the center of gravity (KG or VCG). The lower the KG the more stable the vessel. As the KG increases the vessel becomes less stable and becomes top heavy.

**There are three rules to remember regarding movement of the center of gravity.**

- The center of gravity will always move toward an added weight. When weight is added above the center of gravity (G), the center moves up toward it to a new position (nG). When weight is added below the center of gravity (G), the center moves down toward it to a new position (nG).

- The center of gravity will move away from an offloaded weight. If a weight is removed from below the original G, the center of gravity will move away (up) from the location of the removed weight. If a weight is removed from above the original G, the center of gravity will move away (down) to the new position (nG).

- The center of gravity will always move in the same direction as a shifted weight.

Liquids on board a vessel that are free to slosh around as the vessel moves is said to have *free surface.* This would include water in the bilge, water collected on deck, or the contents of tanks that are neither completely full nor pumped completely empty. Free surface liquids always reduce stability. In a tank, free surface affects the vessel as if the center of gravity of the liquid in the tank had moved up. This increases the overall KG, thereby reducing stability.

A large amount of weight high in a vessel will produce a slow, lazy roll, indicating a high center of gravity. A vessel with a long *rolling period *is said to be *tender* or top heavy. Stability can be improved by shifting weights to a lower point in the vessel, filling a tank low in a vessel, and reducing from surfaces. A winged tank has *free communication*.

# Center of Buoyancy

Just as the force of gravity acting downward on the vessel is concentrated at one point call the *center of gravity *(G), the force of buoyancy which pushes the vessel up is concentrated at a point called the *center of buoyancy *(B). The forces of gravity and buoyancy are equal and act in exactly opposite directions, gravity down, buoyancy up. The height of B is measured up from the keel or baseline and is abbreviated KB or VCB. It’s fore and aft locations abbreviated LCB and is measured from one of the perpendiculars. B is the geometric center of the submerged part of the hull. Figuring the location of B in various conditions is done by the designer and provided to the vessel operator in a set of tables or curves.

Once the vessels load is set, the center of gravity stays the same until the next operation. In contrast, B moves every time the vessel changes draft, rolls, pitches, heels or trims. KB (VCB) increases as draft increases, and decreases as draft decreases.

B always moves toward the low side (or end) as the vessel inclines. That’s what keeps the vessel upright. The movement of B creates a righting arm.

Look at a vessel in the upright position. G is on the centerline because the vessel is loaded properly. The forces of gravity and buoyancy are equal, opposite, and in line. As the wind or a wave inclines the vessel, B moves toward the low side. Now the force of buoyancy is out of line. The force of buoyancy is trying to push the vessel back upright and has leverage equal to the horizontal distance between GZ. GZ is called the *righting lever* or *righting arm.*

How does the righting arm (GZ) change? The displacement (weight) of the vessel multiplied by the length (distance) of the righting arm (GZ) will give us the force being exerted to push the vessel to an upright position. In this case, the product is call the *righting moment*. The displacement doesn’t change from one minute to the next, so the energy available to right the vessel depends on the length of the righting arm (GZ). The longer GZ is, the more righting energy you have. The diagram below shows how GZ can change.

In a wide vessel, B will move farther from the centerline at a given angle of roll, therefore developing a longer righting arm and greater stability. It’s obvious that a swimming raft is harder to tip than a canoe.

The length (and strength) of the *righting arm* also depends on the location of G. As the center of gravity is lowered, the righting arm increases. Conversely, the higher the center of gravity, the smaller the righting arm, as the following drawings indicate.

This is an empty vessel inclined to show the initial length of GZ.

When a load is added above the original G, the center of gravity moves up toward it, reducing the length of GZ.

If a load is added below the original G, the center of gravity moves down toward it, increasing the length of GZ.

GZ also increases with the angle of the heel, but up to only a certain critical angle. Roll her beyond that angle and the righting arm starts to decrease and eventually disappear, as the following drawings indicate.

As a vessel inclines the movement of B increases the length of GZ…Until the vessel inclines to the point where B is directly under G. There is now no righting arm, which means the vessel has neutral stability.

What is *metacentric height?* For a given displacement the stability or righting tendency of the vessel depends entirely on the length of the righting arm, GZ. That is true, but calculating GZ for different KG’s and angles of heel is rather complicated. It is much simpler for a vessel operator to calculate stability by using the *metacentric height* (GM).

As the drawing indicates, the intersection of a vertical line drawn upward from B with the centerline is call the *metacenter* (M). The distance from G to M (GM) is called *metacentric height*. The larger GM is, the longer GZ gets. If GM is zero, no righting arm exists, and the vessel would be in a state of neutral stability.

If G got above M, GZ would go in the opposite direction. It would be an upsetting arm instead of a righting arm. This condition is called *negative GM*, resulting in a *negative righting arm*, which would give you *negative stability*. The vessel wouldn’t necessarily capsize, but it would certainly list until the center of buoyancy moved far enough to start developing a righting arm. It could capsize. **G must be kept below M!**

Remember that the distance from the center of gravity (G) to the metacenter (M) is the *metacentric height* (GM). The distance from the keel (K) to the metacenter is the *height of the metacenter* (KM). This distance of KM may be given in a problem that asks that GM be found. If KM was 72’ and KG was 67’ you could find GM by subtracting KG from KM. GM = KM – KG The GM in this example would be 5 feet.

Metacentric height (GM) is a measure of stability. The larger the GM, the more stable the vessel. Reducing the GM reduces the ability of the vessel to right itself.

The *rolling period* of a vessel is the time (in seconds) required for one complete roll, which is from all the way to one side, over to the opposite side and back. The rolling period is an indication of stability. A stable ship (with a large GM) will have a fast, snappy roll (short rolling period). A vessel in this condition is said to be *stiff*. One with a small GM (less stable) will roll slowly, and is said to be *tender* or *crank.*

The rolling period for a vessel can be calculated using the following formula (this formula does not need to be memorized).**Practical Exercise: **Your vessel’s beam is 60 feet and your roll period is 20 seconds. What is your metacentric height?

*Empirical means this formula does not depend on theory, but was figured out by actually timing the rolling periods of vessels of known beam and GM.*Trim* is a relative term that refers to the way the boat sets in the water in relationship to the vessel’s stability and buoyancy.

Design features that affect the stability of a vessel would be the size and shape of the hull, trim and draft of the vessel, displacement, non-watertight compartments, and the size, shape and weight of the superstructure. Some factors that influence stability are wind and waves, damage that affects loss of buoyancy, and adding, removing or shifting weight on the vessel.