Ship Lines Plan

The lines plan is the principal geometric specification of a ship’s hull, depicting the hull surface in three orthogonal projections: the body plan (transverse cross-sections at standard longitudinal positions called stations); the sheer plan (longitudinal centreline-parallel sections at standard transverse positions called buttocks); and the half-breadth plan (horizontal sections at standard vertical positions called waterlines, drawn as half-views due to the assumption of port-starboard symmetry). The lines plan is the input to all hydrostatic, stability, resistance, seakeeping and structural calculations; the foundation of every subsequent design and construction drawing; and the geometric reference frozen in the newbuild contract. The lines plan is generated at the design stage by parametric hull-form software (NAPA Designer, AVEVA Marine, Friendship Framework), refined through CFD optimisation and model testing, validated by classification society review, and used by the shipyard to generate the construction drawings, the steel-cutting CNC programs, and the lofting templates. Modern shipyard practice maintains the lines plan as a 3D surface model (typically NURBS-based) from which the traditional 2D drawings are extracted; the 2D representation remains the standard documentation format for Class approval and for ship operator reference. ShipCalculators.com hosts the principal computational tools: the hull form coefficients calculator, the naval architecture coefficients calculator, the hydrostatics calculator, the Bonjean curve interpolation calculator and the GZ curve calculator. A full listing is available in the calculator catalogue.

Contents

Background

Purpose

The lines plan answers the basic question: what is the shape of the hull? Every downstream calculation (displacement, block coefficient, GZ curve, resistance, seakeeping RAOs) depends on integrating quantities over the hull surface defined by the lines plan. The lines plan is therefore the most fundamental document in ship design.

Three orthogonal projections

A 3D hull surface is depicted on 2D drawings by projecting it onto three orthogonal planes:

Body plan: transverse cross-sections (looking forward or aft). The standard projection uses 11, 21 or 41 stations along the length, drawn at half-scale on each side of the centreline (forward stations on right, aft stations on left).
Sheer plan (also profile plan or longitudinal plan): longitudinal sections parallel to the centreline. Conventionally drawn at the centreline (showing the keel, stem, and stern profile) plus several buttock cuts at standard transverse offsets.
Half-breadth plan: horizontal sections at standard waterline elevations. Drawn as a half-view (port side reflected to give the visual symmetry).

The three views together fully define the hull geometry: any point on the hull surface can be located by reading the matching coordinates from any two of the three views.

Stations, waterlines, buttocks

The standard reference grid:

Stations: longitudinal positions at which transverse cross-sections are drawn. Conventionally numbered from the forward perpendicular (FP, station 0) to the aft perpendicular (AP, station 10 or 20 or 40) depending on the chosen subdivision (typically 10 for early-design, 20 for general, 40 for detailed design). The midship station is at 5 (or 10 or 20).
Waterlines (WL): horizontal positions at which half-breadth sections are drawn. Conventionally numbered from the baseline (WL 0) at the keel to the freeboard deck waterline at the top, with intermediate waterlines at standard intervals (typically 1 m, 0.5 m for finer detail).
Buttocks (BL): transverse positions at which sheer-plan sections are drawn. Conventionally numbered from the centreline (BL 0) outward to the maximum half-breadth, at standard intervals (typically 1 m or 0.5 m).

Diagonals

In addition to the three principal projections, diagonals are sometimes drawn to verify the fairness of the hull surface in regions where the principal sections are nearly parallel to the surface (which makes small geometric errors undetectable in those views). Diagonals are oblique sections drawn at user-specified angles to expose any local unfairness.

History and tradition

Lofting

Before computer-aided design, the lines plan was used to loft the hull at full scale on the mould loft floor (a large flat space with marked grid lines). Skilled loftsmen used wooden battens and weights to draw smooth full-scale curves through the lines plan offset points; from these full-scale curves the steel-plate templates and the wooden hull-form moulds were taken.

Lofting was a high-skill craft activity that could occupy a team of loftsmen for weeks per vessel. The transition to photographic lofting (1950s) and then to computer lofting (1980s) progressively eliminated the manual loft floor, while preserving the underlying geometric concepts.

Offset tables

The lines plan is supported by offset tables: tabulations of half-breadth offsets at every station-waterline intersection. The offset table is a numerical specification of the hull geometry, used as the computational input alternative to the graphical lines plan.

A typical offset table has 21 stations (rows) and 10 to 15 waterlines (columns), for a total of approximately 200 to 300 offset values. For a complex hull with significant longitudinal and vertical variation, the offset table is supplemented by knuckle line offsets (where the hull surface has discontinuities) and bilge offsets (the curved transition from bottom to side).

Standardised offset format

For ITTC model testing and for some Class approval purposes, offset tables are submitted in standardised formats:

ITTC offset format: standard column ordering and dimensional convention.
STEP and IGES: international standards for 3D geometry interchange (1990s onwards).
STL (stereolithography): triangulated surface format, used principally for CFD model preparation.

Modern parametric design

Surface representation

Modern hull-form design uses 3D surface modelling rather than 2D lines plan. The hull surface is typically represented as:

NURBS (Non-Uniform Rational B-Spline) surfaces: the dominant standard. Each NURBS surface patch is defined by a control polygon and basis functions; multiple patches join with continuity constraints to form the complete hull.
Bezier surfaces: simpler than NURBS but less common in ship design.
Subdivision surfaces: emerging, used in some modern ship design tools.

The 2D lines plan is automatically extracted from the 3D model as needed for Class approval, contract documentation, and ship operator reference.

Parametric hull-form generation

Modern hull design begins with a parametric template: a hull form whose shape is controlled by a small number of parameters (principal dimensions, block coefficient, prismatic coefficient, bow form choice, stern form choice, etc.). The designer iterates by adjusting the parameters and observing the effect on the resulting performance.

The principal commercial parametric hull-design tools:

NAPA Designer (Helsinki, Finland): the dominant commercial product.
AVEVA Marine Initial Design: integrated with the wider AVEVA Marine suite.
Friendship Framework / CAESES (Friendship Systems, Berlin): widely used for CFD-driven optimisation.
Maxsurf (Bentley Systems): widely used for smaller vessels and yachts.
Rhinoceros + Orca3D: NURBS-based, widely used in custom and small-vessel design.
ShipFlow Design (FLOWTECH, Sweden): integrated with the ShipFlow CFD code.

CFD-driven hull optimisation

Once the parametric template is established, CFD-driven optimisation explores the design space:

Define the design variables: typically 10 to 30 parameters (bow form, stern form, bilge radius, sectional area distribution, etc.).
Define the objective function: typically calm-water resistance at design speed (or fuel consumption, or composite of resistance and seakeeping).
Define the constraints: cargo capacity, stability, classification requirements, structural feasibility.
Run the optimisation: typically a genetic algorithm or differential evolution exploring approximately 100 to 1,000 candidate hull forms.
CFD evaluation of each candidate.
Select the optimum within the constraints.

Modern CFD-driven hull optimisation can deliver 5 to 15% reduction in calm-water resistance compared to an experienced naval architect’s manual design, particularly for vessels operating in the high Froude-number range.

Model testing validation

The CFD-optimised hull is typically validated by physical model testing at one or more model basins. The principal model basins are:

MARIN (Maritime Research Institute Netherlands, Wageningen).
HSVA (Hamburg Ship Model Basin, Germany).
SSPA (Sweden).
NMRI (National Maritime Research Institute, Tokyo).
Krylov (St. Petersburg, Russia).
MOERI (Maritime and Ocean Engineering Research Institute, Korea).

Model tests typically include resistance tests, propulsion tests, manoeuvring tests and seakeeping tests, conducted at scale ratios of 1:20 to 1:60. The model test results validate the CFD predictions and provide the contractually-binding power-speed curves for newbuild contracts.

Lines plan applications

Hydrostatic calculations

The lines plan is the input to all hydrostatic calculations:

Displacement at any draught (by integrating the underwater volume).
Centre of buoyancy position (by computing the volume centroid).
Waterplane area (the integrated horizontal area at the waterline).
Transverse and longitudinal moments of inertia of the waterplane (for metacentric height calculation).
Block coefficient, prismatic coefficient, midship coefficient, waterplane coefficient (the principal naval architecture coefficients).

The hydrostatic curves are plotted as a function of draught and constitute the second-most-fundamental design document after the lines plan itself.

Bonjean curves

Bonjean curves are derived from the lines plan: at each station, the immersed cross-section area is plotted as a function of waterline. The Bonjean curves are used to compute:

Longitudinal weight-buoyancy distribution (for hull strength calculations).
Trim and parallel sinkage at any loaded condition.
Damage stability with selected compartments flooded.

Cross curves of stability and KN tables

The cross curves of stability and KN tables are computed from the lines plan by integrating the underwater volume and centroid at each (heel angle, displacement) pair across the design grid. These provide the rapid GZ-curve generation used by the operational loading computer.

Resistance and propulsion

Ship resistance and powering calculations use the lines plan to:

Compute the wetted surface area (for frictional resistance).
Compute the wave-making resistance from CFD on the hull surface.
Compute the appendage resistance for additional appendages.
Provide the geometric input to bulbous bow, bilge keel, rudder, and propeller integration analysis.

Seakeeping

Seakeeping and ship motion calculations use the lines plan to compute the strip-theory or 3D potential-flow added mass and damping coefficients, and the wave-induced exciting forces.

Structural design

Hull strength calculations use the lines plan to define the hull cross-section at each station, from which the section modulus, the longitudinal bending strength, the buckling strength and the ultimate strength are derived.

Construction

The lines plan is the basis for the construction drawings:

Shell expansion: the hull surface unrolled flat for steel-plate cutting.
Frame drawings: the cross-section of each transverse frame.
Plate seams and butts: the locations of the welded joints between adjacent plates.
CNC cutting templates: the digital files for automated steel cutting (typically delivered in DXF or IGES format).

Lines plan management in service

Operator reference

Once the vessel is delivered, the lines plan is preserved as a static reference document, included in the trim and stability booklet that the vessel must carry. It is used for:

Hull repair planning (steel renewal).
Modification design (lengthening, bulbous bow retrofit, air lubrication installation).
Resale documentation (verifying that the as-built hull matches the contracted geometry).
Marine casualty investigation (reconstructing the hull condition).

Modifications

When a vessel undergoes major hull modification, the lines plan must be updated:

For minor modifications (e.g. bulbous bow retrofit): the existing lines plan is amended with the new bow geometry.
For major modifications (e.g. lengthening): a new lines plan is generated for the modified hull.

The updated lines plan is approved by the Class society and incorporated into the trim and stability booklet.

As-built vs as-designed

The as-built lines plan may differ slightly from the as-designed lines plan due to fabrication tolerances. For Class approval purposes, the as-designed lines plan is normally used; for very high-precision applications (e.g. specialised research vessels) an as-built survey may be undertaken to capture the actual geometry.

References

Lewis, E. V. (editor). Principles of Naval Architecture, Volume I: Stability and Strength. SNAME, 1988.
Tupper, E. C. Introduction to Naval Architecture. Butterworth-Heinemann, 5th edition, 2013.
Watson, D. G. M. Practical Ship Design. Elsevier, 1998.
Schneekluth, H. and Bertram, V. Ship Design for Efficiency and Economy, 2nd edition. Butterworth-Heinemann, 1998.
Bertram, V. Practical Ship Hydrodynamics. Butterworth-Heinemann, 2nd edition, 2012.
Larsson, L. and Eliasson, R. E. Principles of Yacht Design. Adlard Coles Nautical, 4th edition, 2013.
Rawson, K. J. and Tupper, E. C. Basic Ship Theory. Butterworth-Heinemann, 5th edition, 2001.
IACS. Common Structural Rules for Bulk Carriers and Oil Tankers (CSR BC and OT). International Association of Classification Societies, 2024 edition.
DNV. DNV Rules for Classification of Ships, Pt 3 Hull. DNV, 2024 edition.
Lloyd’s Register. Rules and Regulations for the Classification of Ships, Part 3 Ship Structures. Lloyd’s Register Group, 2024 edition.
ITTC. Recommended Procedures and Guidelines: Ship modelling and reporting. International Towing Tank Conference, 2017.