Hull Form Characteristics

The hull form characteristics applicable to the profile view of a ship have already been discussed. However, there are a number of others which are relevant to a view of the ship from the bow or stern.

As mentioned previously, the keel is at the bottom of the ship. The bottoms of most ships are not flat. Distances above the keel are usually measured from a constant reference plane, the base-plane. The keel is denoted by "K" on diagrams with the distance above the keel being synonymous with the distance above the baseline.

Depth (D), Draft (T) and Beam (B)

The depth of the hull is the distance from the keel to the deck. Sometimes the deck is cambered, or curved, so the depth may also be defined as the distance from the keel to the deck at the intersection of deck and side or the “deck at edge”. The symbol used for depth is "D". The depth of the hull is significant when studying the stress distribution throughout the hull structure.

The draft (T) of the ship is the distance from the keel to the surface of the water. The mean draft is the average of the bow and stern drafts at the perpendiculars. The mean draft is the draft at amidships.
Freeboard is the difference between “D” and “T”.

The beam (B) is the transverse distance across each section. Typically when referring to the beam of a ship, the maximum beam at the DWL is implied.

Figure below shows the dimensions of these terms on a typical midship section of a ship.

Figure: Hull Form Characteristics

Flare and Tumblehome

The forward sections of most ships have a bow characteristic called flare. On a flared bow, the half-breadths increase as distance above the keel increases. Flare improves a ship's performance in waves, and increases the available deck space.

Tumblehome is the opposite of flare. It is uncommon on modern surface ships. However, sailing yachts and submarines do have tumblehome. Figure below shows flare and tumblehome.

Figure: Ships with Flare and Tumblehome

Centroids

A centroid is defined as the geometric center of a body.

The center of mass is often called the center of gravity and is defined as the location where all the body’s mass or weight can be considered located if it were to be represented as a point mass.
If the object has uniform density and thickness, then the centroid will be coincident with the body’s center of mass.

Conceptually, and in their application to ships, there is a big difference between a centroid and a center of mass.

Both centroids and centers of mass can be found by doing weighted averages as discussed in chapter one. For example, Figure below is a two dimensional uniform body with an irregular shape. The “Y” location of the centroid of this shape can be found by breaking the area up into little pieces and finding the average “Y” distance to all the area. This can be repeated for the “X” location of the centroid. This will result in the coordinates of the centroid of the area shown with respect to the arbitrary coordinate system chosen.

Figure: Showing the Calculation of a Centroid of an Irregular Plane Area

Two Very Important Centroids - The Center of Flotation and The Center of Buoyancy

The concept of a centroid is important in Naval Engineering because it defines the location of two extremely useful points in the analysis of the statical stability of a ship.

Center of Flotation (F)

The centroid of the operating waterplane is the point about which the ship will list and trim. This point is called the center of flotation (F) and it acts as a fulcrum or pivot point for a floating ship.

The distance of the center of flotation from the centerline of the ship is called the “transverse center of flotation” (TCF). When the ship is upright the center of flotation is located on the centerline so that the TCF = 0 feet.

The distance of the center of flotation from amidships (or the forward or after perpendicular) is called the “longitudinal center of flotation” (LCF). When writing a LCF distance you must state if it’s from midships or from one of the perpendiculars so the person reading the value will know where it’s referenced from. If the reference is amidships you must also indicate if the distance is forward or aft of midships. By convention, a negative sign is used to indicate distances aft of midships.

The center of flotation is always located at the centroid of the current waterplane. When the ship lists to port or starboard, or trims down by the bow or stern, or changes draft, the shape of the waterplane will change, thus the location of the centroid will move, leading to a change in the center of flotation.

Center of Buoyancy (B)

The centroid of the underwater volume of the ship is the location where the resultant buoyant force acts. This point is called the center of buoyancy (B) and is extremely important in static stability calculations.

The distance of the center of buoyancy from the centerline of the ship is called the “transverse center of buoyancy” (TCB). When the ship is upright the center of buoyancy is located on the centerline so that the TCB = 0 feet.

The vertical location of the center of buoyancy from the keel (or baseplane) is written as “VCB” or as "KB" with a line over the letters “KB” indicating it is a line segment from point “K” to point “B”.

The distance of the center of buoyancy from amidships (or the forward or after perpendicular) is called the “longitudinal center of buoyancy” (LCB). When writing a LCB distance you must state if it’s from midships or from one of the perpendiculars so the person reading the value will know where it’s referenced from. If the reference is amidships you must also indicate if the distance is forward or aft of midships. Recall that a negative sign is used to indicate distances aft of midships.

The center of buoyancy is always located at the centroid of the submerged volume of the ship. When the ships lists to port or starboard, or trims down by the bow or stern, or changes draft, the shape of the submerged volume will change, thus the location of the centroid will move and alter the center of buoyancy.