Hull (watercraft) - Metrics

Metrics

Hull forms are defined as follows:

• Block measures that define the principal dimensions. They are:

• Length overall (LOA) is the extreme length from one end to the other.
• Length at the waterline (LWL) is the length from the forwardmost point of the waterline measured in profile to the stern-most point of the waterline.
• Length between perpendiculars (LBP or LPP) is the length of the summer load waterline from the stern post to the point where it crosses the stem. (see also p/p)
• Beam or breadth (B) is the width of the hull. (ex: BWL is the maximum beam at the waterline)
• Depth or moulded depth (D) is the vertical distance measured from the top of the keel to the underside of the upper deck at side.
• Draft (d) or (T) is the vertical distance from the bottom of the keel to the waterline.
• Freeboard (FB) is depth plus the height of the keel structure minus draft.

• Form derivatives that are calculated from the shape and the block measures. They are:

• Volume (V or ∇) is the volume of water displaced by the hull.
• Displacement (Δ) is the weight of water equivalent to the immersed volume of the hull.
• Longitudinal centre of buoyancy (LCB) is the longitudinal distance from a point of reference (often midships) to the centre of the displaced volume of water when the hull is not moving. Note that the longitudinal centre of gravity or centre of the weight of the vessel must align with the LCB when the hull is in equilibrium.
• Vertical centre of buoyancy (VCB) is the vertical distance from a point of reference (often the baseline) to the centre of the displaced volume of water when the hull is not moving.
• Longitudinal centre of floatation (LCF) is the longitudinal distance from a point of reference (often midships) to the centre of the area of waterplane when the hull is not moving. This can be visualized as being the area defined by the water's surface and the hull.

• Coefficients help compare hull forms as well:

1) Block coefficient (C_b) is the volume (V) divided by the LWL x BWL x T. If you draw a box around the submerged part of the ship, it is the ratio of the box volume occupied by the ship. It gives a sense of how much of the block defined by the L_WL, beam (B) & draft (T) is filled by the hull. Full forms such as oil tankers will have a high C_b where fine shapes such as sailboats will have a low C_b.

2) Midship coefficient (C_m or C_x) is the cross-sectional area (A_x) of the slice at midships (or at the largest section for C_x) divided by beam x draft. It displays the ratio of the largest underwater section of the hull to a rectangle of the same overall width and depth as the underwater section of the hull. This defines the fullness of the underbody. A low C_m indicates a cut-away mid-section and a high C_m indicates a boxy section shape. Sailboats have a cut-away mid-section with low C_x whereas cargo vessels have a boxy section with high C_x to help increase the C_b.

3) Prismatic coefficient (C_p) is the volume (V) divided by L_pp x A_x. It displays the ratio of the immersed volume of the hull to a volume of a prism with equal length to the ship and cross-sectional area equal to the largest underwater section of the hull (midship section). This is used to evaluate the distribution of the volume of the underbody. A low or fine C_p indicates a full mid-section and fine ends, a high or full C_p indicates a boat with fuller ends. Planing hulls and other highspeed hulls tend towards a higher C_p. Efficient displacement hulls travelling at a low Froude number will tend to have a low C_p.

4) Waterplane coefficient (C_w) is the waterplane area divided by L_pp x B. The waterplane coefficient expresses the fullness of the waterplane, or the ratio of the waterplane area to a rectangle of the same length and width. A low C_w figure indicates fine ends and a high C_w figure indicates fuller ends. High C_w improves stability as well as handling behavior in rough conditions.

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