Waterplane Coefficient (CWP)

What is the Waterplane Coefficient (CWP)?

The waterplane coefficient (CWP) is a dimensionless hull-form parameter that describes how full the ship’s waterplane area is relative to a rectangle defined by the length and breadth at the waterline. It reflects the planform shape of the hull at a given draft.

Definition

CWP is defined as the ratio between the actual waterplane area and the area of a rectangle formed by the length and breadth at the same waterline:

CWP = A_WP / (L_WL × B_WL)

where A_WP is the waterplane area at the selected draft, L_WL is the length on the waterline, and B_WL is the corresponding maximum breadth.

Engineering significance

The waterplane coefficient plays an important role in hydrostatic behavior, particularly in relation to tons per centimeter immersion (TPC), trim, and initial stability. Fuller waterplanes (higher CWP) generally result in higher TPC values and greater resistance to changes in draft.

Because the waterplane shape changes with draft, CWP is always draft-specific and should be evaluated at the operating waterline of interest.

Typical CWP values

Typical CWP values depend primarily on the hull planform and vessel type. The following ranges are indicative for conventional displacement ships:

• Fine or tapered waterplanes: 0.70 – 0.80
• General cargo and container vessels: 0.80 – 0.88
• Bulk carriers and tankers: 0.85 – 0.95
• Box-shaped or barge-like hulls: up to ≈ 1.00

Relation to hydrostatics

The waterplane area is directly related to tons per centimeter immersion (TPC) through water density, making CWP a useful normalized indicator when comparing hulls of different sizes. Changes in waterplane geometry also affect trim behavior and transverse metacentric height (GM).

Limitations and correct use

• CWP is valid only for the selected draft and waterline.
• It does not describe longitudinal or transverse volume distribution.
• Polygon and Simpson methods require consistent station spacing.
• Results should be cross-checked against hydrostatic tables when available.

Related calculators

The waterplane coefficient is typically evaluated together with the following hydrostatic and hull-form parameters:

• Displacement Calculator – converts waterplane and draft into displacement.
• Block Coefficient (CB) – overall hull fullness indicator.
• Prismatic Coefficient (CP) – longitudinal volume distribution.
• Metacentric Height (GM) – initial stability influenced by waterplane geometry.
• Trim Calculator – evaluates trim response to loading changes.