Midship Coefficient (CM)

What is the Midship Coefficient (CM)?

The midship coefficient (CM) is a dimensionless hull-form parameter that describes how full the ship’s midship section is relative to a rectangle defined by the moulded beam and draft. It reflects the transverse shape of the hull at midship.

Definition

CM is defined as the ratio between the immersed midship section area and the product of the moulded beam and draft:

CM = A_M / (B × T)

where A_M is the underwater midship section area, B is the moulded beam, and T is the moulded draft at midship.

Relationship with other hull coefficients

The midship coefficient is closely related to the block coefficient (CB) and prismatic coefficient (CP) through the relationship:

CM = CB / CP

This relationship highlights how CM isolates the transverse fullness of the hull, while CB represents overall volume fullness and CP reflects longitudinal volume distribution.

Typical CM values

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

• Fine or rounded midship sections: 0.85 – 0.90
• General cargo vessels: 0.90 – 0.96
• Bulk carriers and tankers: 0.95 – 0.99
• Boxy or slab-sided sections: up to ≈ 1.00

Engineering significance

CM is primarily a geometric parameter and is used to describe the shape of the midship section rather than overall hull performance. Higher CM values indicate fuller, more rectangular sections, while lower values correspond to finer, more rounded forms.

During preliminary design, CM is often selected based on construction method, structural arrangement, and cargo requirements, and later refined using body plans or sectional offsets.

Limitations and correct use

• CM alone does not determine resistance or powering.
• It should be evaluated together with CB and CP.
• Values depend on the definition of moulded beam and draft.
• Estimated CM values should be validated using actual midship geometry.

Related calculators

The midship coefficient is typically evaluated together with the following hull-form parameters:

• Block Coefficient (CB) – overall hull fullness indicator.
• Prismatic Coefficient (CP) – longitudinal volume distribution.
• Displacement Calculator – converts geometry into displacement.
• Wetted Surface Area (WSA) – required for resistance estimation.