Prismatic coefficient (Cp) is a dimensionless number describing how a ship’s underwater volume is distributed along its length — specifically, how much the hull tapers toward the bow and stern compared to its fullest (midship) section.
The Actual Formula
Cp = ∇ / (Am × L)
Where:
- ∇ (nabla) = volume of displacement
- Am = midship section area (the cross-sectional area at the ship’s widest, fullest point)
- L = length (typically length between perpendiculars)
In plain terms: it compares the ship’s actual volume to the volume of an imaginary prism with the same length as the ship and a constant cross-section equal to the midship area throughout.
Prismatic Coefficient vs Block Coefficient: The Key Difference
Both describe hull “fullness,” but relative to different reference shapes:
- Block coefficient (Cb) — compares volume to a rectangular block using length, breadth, AND draft
- Prismatic coefficient (Cp) — compares volume to a prism using length and the midship section area (which already incorporates breadth and draft at that one section)
Cp specifically isolates how the hull’s shape changes along its length — a ship can have identical block coefficient to another vessel but different prismatic coefficient, if one hull tapers more sharply toward the bow/stern while the other maintains fullness over more of its length.
What Cp Tells You Practically
- Lower Cp — hull volume is concentrated more toward the midship section, with sharper tapering toward the ends; generally associated with better performance at higher speeds
- Higher Cp — volume is distributed more evenly along the length, with less tapering; generally suited to slower, more cargo-capacity-focused vessels
Naval architects select prismatic coefficient specifically based on the vessel’s design speed — this is a genuine, real design parameter that directly affects powering requirements, not just an abstract number checked after the fact.
Why This Matters Beyond Design
Prismatic coefficient’s relevance to a working officer is mostly indirect — understanding it helps make sense of why different vessel types (a fast container ship versus a slow bulk carrier) have genuinely different hull shapes even at similar overall dimensions, not just different block coefficients.
Exam Relevance
Prismatic coefficient’s correct formula and its distinction from block coefficient are core Naval Architecture topics tested in senior deck and engineering officer competency exams.