Block coefficient

Metrics

1. Block coefficient (C_b) is the volume (V) divided by the L_WL × B_WL × T_WL. 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. $${\displaystyle C_{b}={\frac {V}{L_{WL}\cdot B_{WL}\cdot T_{WL}}}}$$
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. $${\displaystyle C_{m}={\frac {A_{m}}{B_{WL}\cdot T_{WL}}}}$$
3. Prismatic coefficient (C_p) is the volume (V) divided by L_WLx 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. $${\displaystyle C_{p}={\frac {V}{L_{WL}\cdot A_{m}}}}$$
4. Waterplane coefficient (C_w) is the waterplane area divided by L_WL x B_WL. 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. $${\displaystyle C_{w}={\frac {A_{w}}{L_{WL}\cdot B_{WL}}}}$$