Ship Lines Plan: Hull Geometry Reference

The lines plan is the primary geometric document of a ship. It depicts the three-dimensional hull surface as three mutually consistent orthogonal projections drawn on two-dimensional paper (or screen): the body plan, the sheer plan, and the half-breadth plan. Every downstream calculation performed on a vessel, from displacement to block coefficient to Bonjean curves to GZ righting arm, depends on the coordinates defined by the lines plan. The hull form design process begins with the lines plan and the naval architecture coefficients that characterize its shape. The wetted surface area extracted from it drives frictional resistance estimation.

The lines plan is also the geometric reference for structural drawings, steel-cutting programs, and the lofting of construction templates. It is the document frozen in the newbuild contract to establish the agreed-upon hull geometry. When a vessel is modified in service, updated lines are submitted to the classification society for approval before construction begins.

The three orthogonal projections

A hull surface is a three-dimensional object. Representing it on a two-dimensional medium requires projecting it onto planes. The convention established in shipbuilding over centuries uses three mutually perpendicular planes: transverse, longitudinal-vertical, and longitudinal-horizontal. The intersections of the hull surface with families of parallel planes in each direction produce the three sets of curves.

Body plan: stations and transverse sections

The body plan is the view looking forward (or aft) along the ship’s length. The hull surface is cut by a series of transverse planes spaced along the length; each cut produces a station cross-section. Because a conventionally-shaped hull is port-starboard symmetric, only the half-section is drawn. The forward stations are plotted on the right side of the centreline; the aft stations on the left. This convention packs both halves onto a single drawing.

The number of stations is chosen based on design stage and vessel complexity. Preliminary design typically uses 11 stations (stations 0 to 10, with station 0 at the forward perpendicular and station 10 at the aft perpendicular). Detailed design uses 21 stations (0 to 20) or 41 stations (0 to 40). The midship station is the section at mid-length between the perpendiculars; its area relative to the midship-bounded rectangle is the midship section coefficient $C_M$:

where $A_M$ is the immersed midship section area, $B$ is the moulded breadth, and $T$ is the draught. Use the block coefficient calculator and prismatic coefficient calculator to verify form coefficients derived from the lines.

The body plan reveals the hull’s sectional shape evolution from bow to stern: the fine bow sections with narrow V or U shapes, the fuller midship section, and the progressive taper toward the stern. For a bulk carrier designed to maximize cargo volume, the midship sections are nearly rectangular over much of the parallel midbody. For a container ship optimized for wave-making resistance, the underwater sections are more V-shaped amidships.

Sheer plan: buttock lines and the profile

The sheer plan, sometimes called the profile plan, is the view looking at the ship from abeam. The hull surface is cut by a series of longitudinal vertical planes parallel to the centreline at standard transverse positions called buttock lines (or simply buttocks). The centreline cut, buttock 0, traces the keel, stem profile, and stern profile. Outer buttocks at 0.5 m, 1.0 m, 1.5 m (or whatever standard interval suits the vessel’s beam) trace the hull surface at each transverse offset.

The sheer plan also shows the deck line, the load waterline, and any features that define the hull in profile: the rise of floor, the inclination of the keel, the shape of the bulbous bow entry, and the form of the stern. For vessels with a raked keel, the sheer plan shows the keel baseline as a straight inclined line rather than horizontal.

The buttock lines should be smooth fair curves from bow to stern. A buttock that develops a reverse curvature or an inflection point in an unexpected location is a sign that the hull surface is not yet faired. The buttock lines also carry longitudinal curvature information that the body plan sections alone cannot reveal: a section might look fair in transverse cross-section while the longitudinal run of that section as traced along a buttock is kinked.

Half-breadth plan: waterlines

The half-breadth plan is the view looking down from above. The hull surface is cut by horizontal planes at standard vertical positions called waterlines (or load waterlines, construction waterlines). Each cut traces a curve on the hull surface; plotted as a plan view, it gives the half-width of the vessel at that height above the keel.

Waterline spacing of 0.5 m to 1.0 m is typical for the underwater body; finer spacing (0.25 m) is used near the keel and near the maximum draught waterline where curvature changes rapidly. The constructed waterline, identical to the load line used for displacement calculations, is the most important single waterline.

The waterlines should taper gracefully from maximum beam amidships toward fine entries at bow and stern. The entry of the waterlines at the bow determines how fine or bluff the vessel is; a fine entry with small half-angles reduces wave-making resistance while a bluff bow increases it but may suit certain cargo-handling or seakeeping requirements. The ITTC 7.5-02-01-03 procedure specifies how waterplane geometry is measured and reported for model tests.

Comparison of the three views

The three views are not independent. Every point on the hull surface must appear at the same position when read from any two of the three views. This consistency requirement is what makes fairing the lines a constrained problem rather than a free-form drawing exercise.

The grid: stations, waterlines, buttocks, and diagonals

The reference grid

The reference grid establishes the coordinate system. The three principal reference planes are:

• The baseline: the horizontal plane at the underside of the keel. All vertical measurements (waterlines, draught) are measured from the baseline upward.
• The amidships transverse plane: the plane perpendicular to the length at the midpoint between the perpendiculars. Longitudinal positions are often quoted as distances forward or aft of amidships.
• The centreplane (also called the plane of symmetry): the vertical longitudinal plane on the centreline. Half-breadth measurements are taken horizontally from the centreplane.

Stations are longitudinal positions along the length between perpendiculars. The forward perpendicular (FP) is station 0; the aft perpendicular (AP) is station 10, 20, or 40 depending on subdivision. The perpendiculars are defined by the ITTC and by Lloyd’s Register as follows: the FP is the vertical line through the intersection of the design waterline with the forward side of the stem; the AP is the axis of the rudder stock (or the aft face of the stern post when there is no rudder stock). The length between perpendiculars $L_{PP}$ spans FP to AP.

Waterlines are designated by their height above the baseline: WL 0 at the keel, WL 0.5, WL 1.0, and so on up to the freeboard deck waterline. Buttocks are designated by their distance from the centreplane: BL 0 (the centreplane), BL 0.5, BL 1.0, and so on outward to the maximum half-breadth.

Diagonals

Diagonals are a fourth family of reference planes, inclined at an angle in the body plan. A diagonal is defined by its origin point on the centreplane and its angle to the waterplane. When drawn in the half-breadth plan, the diagonal traces the hull as a curve running fore and aft.

The purpose of diagonals is to check fairness in regions where the primary sections are nearly tangent to the hull surface. The bilge region of a round-bilge hull is a classic example: the waterlines and the buttocks both pass through this region at shallow angles, meaning that a small error in the half-breadth at the bilge appears as almost no deviation in either the waterlines or the buttock curves. A diagonal that passes through the bilge at a more nearly perpendicular angle to the surface will reveal that error as a clear kink or hump.

Diagonals do not define the hull surface; they are a fairness diagnostic tool. Once the lines plan is faired, every diagonal should be a smooth curve with no unexpected inflections.

Table of offsets

The table of offsets is the numerical companion to the graphical lines plan. It tabulates the half-breadth distance from the centreplane at every station-waterline intersection. A typical table for a 150-metre cargo vessel might have 21 stations (rows) and 12 waterlines (columns), yielding approximately 252 individual offset values. Each offset is given in metres and centimetres (or in millimetres in some conventions) to the nearest millimetre.

The offset table also commonly includes:

• The half-breadth at each deck level (freeboard deck, upper deck, tween deck) at each station.
• Heights of specific features above baseline at each station: top of keel, top of flat keel, turn of bilge inner edge, turn of bilge outer edge, and deck edge.
• Knuckle line offsets where the hull surface has a hard chine or a structural discontinuity.

For computational purposes, the offset table is the primary input to hydrostatic integration programs. Integrating the immersed section areas across the stations at a given waterline elevation gives the submerged volume using Simpson’s rule or the trapezoidal rule. The Simpson’s first rule displacement calculator and waterplane area calculator implement this integration directly from the offset data.

The area of the waterplane at a given draught is:

where $y(x)$ is the half-breadth at longitudinal position $x$ along the load waterline, $h$ is the station spacing, and the bracket is the Simpson’s first-rule approximation. The waterplane area coefficient $C_{WP}$ normalizes this by the rectangle $L_{PP} \cdot B$:

Use the waterplane area coefficient calculator for this computation. The waterplane area Simpson coarse calculator handles the case where only a coarse station grid is available.

Fairing the lines

What fairing means

Fairing is the process of making the three views mutually consistent and the hull surface geometrically smooth. A raw set of offset values, even one computed from a well-intentioned parametric formula, will typically not be perfectly consistent across the three views. At any given point on the hull, the half-breadth read from the half-breadth plan waterline must equal the half-breadth read from the body plan cross-section at the same station. The height on the sheer plan buttock at any station must equal the height of the surface point at that station and buttock offset as read from the body plan.

In practice, the three sets of curves are drawn simultaneously on the lines plan. The naval architect adjusts individual offset values iteratively until the three views agree at every intersection. This is not a simple linear system: adjusting one offset to achieve consistency in two views may introduce a discrepancy in a third view that is constrained by adjacent offsets. The process converges when all three views are simultaneously consistent.

Beyond consistency, the hull must be smooth. A hull surface that passes through all required offsets but has a local hollow or hump between offsets will produce separation of the boundary layer, increased drag, and in extreme cases, noise and vibration. Smoothness is assessed by drawing the curves themselves and inspecting them: the line of a waterline curve or a buttock curve should have no kinks, no inflections that are not required by the design intent, and no reverse curvature in the run. The diagonal curves provide a further check on regions not well-resolved by the primary views.

Traditional fairing on the mould loft floor

Before 1970, fairing was performed at full scale on the mould loft floor. The mould loft was a large flat room, typically on the top floor of the shipyard building shop, with a floor area equal to the full length and half-beam of the vessel. The offset values from the scaled lines plan were plotted on the floor at full scale. Through these points, loftsmen stretched thin flexible wooden battens (called splines in some traditions) held in place by lead weights and metal dogs. The natural shape taken by the batten under the weights was a fair curve, approximating a cubic spline. The loftsmen faired the offsets by adjusting individual points until the batten ran smoothly through the grid.

From the faired full-scale curves, wooden templates were cut for the transverse frames, and the plate expansion for the shell plating was developed on the floor. This work was highly skilled and physically demanding. A team of six to ten loftsmen might spend three to six weeks on a single large vessel.

Photographic and numerical lofting

Photographic lofting, introduced commercially in the 1950s, photographically scaled the full-size floor work back to a manageable sheet size, enabling photographic reproduction of the templates. This did not eliminate the full-scale floor work but allowed its results to be preserved and communicated more easily.

Numerical lofting, appearing in commercial practice in the late 1970s and accelerating through the 1980s, replaced the physical spline batten with a mathematical spline. A cubic spline through the offset values produces a smooth interpolating curve that satisfies the boundary conditions at each end. The parametric cubic Bezier and later the NURBS (Non-Uniform Rational B-Spline) formulation extended this to full surface modeling. By the mid-1990s, all major shipyards had adopted computer-aided design for lines plan development, and the mould loft floor was retired.

Computer fairing and NURBS surfaces

Modern hull design begins with a 3D NURBS surface model rather than a 2D lines plan. A NURBS surface is defined by a rectangular grid of control points, a knot vector in each parametric direction, and a set of rational basis functions. The surface interpolates or approximates the control polygon; moving a control point produces a smooth, locally-limited deformation of the surface. Multiple NURBS patches are joined with continuity constraints (tangent-continuous or curvature-continuous, termed G1 and G2 continuity) to cover the full hull from keel to deck.

The key advantage of NURBS modeling is that a faired hull is defined not by 200 discrete offset values but by a compact set of perhaps 80 to 150 control points. Adjusting a control point re-fairs a region of the hull globally, rather than requiring individual offset-by-offset corrections. The three 2D projection drawings are extracted automatically from the 3D model as slices at the standard station, waterline, and buttock positions. The table of offsets is extracted by querying the surface model at each grid intersection.

Commercial hull design packages that implement this workflow include NAPA Designer, AVEVA Marine Initial Design, Friendship Framework (CAESES), Maxsurf (Bentley Systems), and Rhinoceros with the Orca3D plugin. Each produces the complete lines plan and offset table as output from the 3D model.

Relationship to hydrostatics and form coefficients

The lines plan is the geometric input to all hydrostatic calculations. The connection runs through the station cross-sectional areas.

Submerged volume and displacement

At a given waterline height $T$, the submerged volume is:

where $A(x)$ is the immersed cross-sectional area at longitudinal position $x$. The immersed area at each station is itself obtained by integrating the half-breadths from the keel up to the waterline:

where $y_i(z)$ is the half-breadth at station $i$ and height $z$. Both integrations are performed numerically using Simpson’s rule on the offset table values.

The moulded displacement is $\Delta = \rho \nabla$, where $\rho$ is the water density. The block coefficient relates the displacement volume to the enclosing rectangular block:

Bonjean curves

The Bonjean curve at station $i$ is the function $A_i(T)$: the immersed cross-sectional area as a function of waterline height. Each station contributes one curve to the Bonjean set. Collectively, the Bonjean curves allow the displacement and the longitudinal position of the centre of buoyancy to be computed for any combination of draught and trim without re-integrating from the original offset data. The hydrostatics and Bonjean curves article covers this in detail.

The Bonjean curves are particularly important in trim and stability calculations and in the determination of still-water bending moments. The latter requires knowing the buoyancy force distribution along the length: the upward buoyancy per unit length at station $i$ at trim $t$ is $\rho g A_i(T_i)$, where $T_i$ is the local draught at station $i$ accounting for trim. Integrating the difference between the weight distribution and this buoyancy distribution twice gives the hull-girder bending moment.

Form coefficients from the lines plan

All four principal form coefficients follow directly from the integrated lines plan geometry:

The relationship $C_B = C_P \cdot C_M$ holds exactly from these definitions. The naval architecture coefficients article gives the design significance of each coefficient and the typical values for ship types ranging from fine-form fast ferries ($C_B \approx 0.45$) to full-form bulk carriers ($C_B \approx 0.84$).

Diagonals in detail: the fairness check

Drawing diagonals

A diagonal is specified by two parameters in the body plan: the point where it crosses the centreplane (typically a point at or near the bilge) and its angle to the baseline. Once specified, the diagonal is a straight line in the body plan. The intersection of this line with each station section gives one point of the diagonal trace in the body plan. These points are then transferred to the half-breadth plan where they are plotted at the appropriate station positions at a measured diagonal distance from the centreplane (measured along the inclined line, not horizontally). The result is a diagonal curve running fore and aft in the half-breadth plan.

The same points can also be plotted in the sheer plan at their station positions and their heights above baseline. The diagonal thus appears as a curve in all three views.

Interpreting fairness

A fair diagonal should be a smooth curve that is consistent with the station spacing. An inflection point in the diagonal that does not correspond to a designed feature (such as the transition from the parallel midbody to the run) indicates that the hull surface in that region needs further fairing. The typical correction is to adjust one or two offsets in the region of the inflection and re-check consistency with the other two views.

ITTC Recommended Procedures 7.5-02-01-03 specifies that model geometry used in resistance tests must be faired to within 0.1% of the model length as a maximum local deviation. At a model scale of 1:40, this corresponds to about 0.5 mm on a 2-metre model, which is the practical precision limit of the machining used to produce the physical model.

The lines plan in the design spiral

The ship design process is iterative, converging in a sequence of passes through the same design elements. This process, codified by J. Harvey Evans at MIT in 1959, is called the design spiral. The lines plan participates at each pass.

First-pass lines: parent ship method

In early design, there is no original lines plan. The designer begins with a parent ship: an existing vessel whose principal dimensions and form are close to the design target. The parent ship’s lines are scaled and distorted (stretched or compressed in one or more dimensions) to match the target dimensions. This approach, called the parent ship method, produces a first-pass set of lines from which preliminary hydrostatic and resistance estimates can be made within hours of starting the design.

The SNAME systematic hull series data (the Taylor Standard Series, the Series 60, the Wigley hull) provide empirical resistance data for families of geometrically-related hull forms parameterized by $C_B$, $B/T$ ratio, and $L/B$ ratio. These data allow the designer to estimate resistance at the first pass before any CFD analysis is performed.

Second-pass lines: form parameters optimization

At the second pass, the designer has established the principal dimensions from the first iteration of the design spiral and can now optimize the form parameters. The key decisions are:

Sectional area curve: the plot of immersed cross-sectional area $A(x)$ against the longitudinal position $x$ is the most useful single indicator of a hull’s hydrodynamic character. Its integral is the displaced volume. Its rate of change at bow and stern determines the fineness of entry and run. For minimum wave-making resistance at a given Froude number $F_n = V/\sqrt{gL}$, the wave-making theory (Michell thin-ship theory) predicts an optimal sectional area curve shape; for typical cargo ship Froude numbers in the range 0.15 to 0.25, this produces a nearly sinusoidal area curve. For vessels with a long parallel midbody, the sectional area curve has a flat central section flanked by sloped entry and run regions.

Bow form: bulbous, straight, raked, or spoon. The bulbous bow generates a wave system that partially cancels the bow wave of the hull, reducing wave resistance. Its effectiveness depends on the Froude number and on the relative size of the bulb expressed as the cross-sectional area of the bulb at the forward perpendicular divided by the midship section area (the bulb area ratio). See bulbous bow retrofits for the performance and limitations of this feature.

Stern form: transom, cruiser, elliptical, or hydrodynamic. For displacement speeds ($F_n < 0.30$), a relatively narrow transom emerging just above the load waterline reduces the stern wave resistance. For higher speeds, a wider transom becomes beneficial. The stern form also determines propeller clearances, wake uniformity, and the vibration excitation from propeller pressure pulses.

Third-pass lines: CFD refinement

By the third design spiral pass, a detailed set of lines exists and CFD analysis can be applied. The CFD workflow takes the 3D surface model (NURBS or equivalent) as input and computes the pressure distribution and the wave pattern at the design speed and draught. From these, the wave-making resistance, the viscous pressure resistance, and the appendage resistance are computed. The frictional resistance is estimated from the wetted surface area using the ITTC 1957 ship-model correlation line:

where $Re = VL/\nu$ is the Reynolds number based on ship length and service speed. The ITTC friction coefficient calculator computes this directly. The total resistance coefficient is:

where $(1+k)$ is the form factor and $C_R$ is the residuary resistance coefficient from model tests or CFD. The resistance correlation allowance calculator handles the model-to-ship correlation step, and the hull wetted surface area estimator provides the wetted surface for resistance calculations from the lines geometry.

A CFD-driven hull optimization at this stage will typically explore 200 to 500 candidate hull forms by varying 10 to 30 shape parameters around the baseline form, selecting the form that minimizes a composite of calm-water resistance and seakeeping performance within the cargo capacity, stability, and classification constraints. This work is performed by organizations like MARIN (Maritime Research Institute Netherlands), HSVA (Hamburg Ship Model Basin), and similar towing tanks.

Lines plan and production

Shell expansion

The shell expansion is derived from the lines plan by developing the hull surface (unrolling it flat, section by section). It shows the flat dimensions of each steel plate, the positions of the seams and butts (the welded joints between adjacent plates), and the required plate curvature. The shell expansion is the document given to the steel fabrication shop.

On a modern double-curved hull surface, plates cannot be expanded to a flat sheet without distortion. The expansion computes the best-fit flat development, and the residual double curvature is introduced by line heating (flame heating one side of the plate to induce controlled thermal distortion) or by cold pressing in a plate-bending machine.

Frame drawings and lofted templates

Each transverse frame is defined by its body plan section shape at its longitudinal position. For ships with frames at regular spacing (typically 600 mm to 1,000 mm for large vessels), the full set of frame sections is interpolated from the station sections in the lines plan. Each frame section is used to cut a wooden or metal template from which the steel frame is bent and the frame face flat (the connecting flange) is trimmed.

In modern practice, CNC bending machines replace the manual template: the lofted coordinates of each frame section are transmitted directly to the machine in a DXF or IGES file derived from the 3D hull model. The machine bends flat bar or bulb flat to the required section shape without a physical template. This is the direct successor to the manual mould loft floor, eliminating one complete handoff from geometry to production.

CNC cutting and IGES files

The shell plates are cut to shape by automated cutting machines (plasma, laser, or water-jet) guided by CNC programs. The cutting paths are derived from the shell expansion, which is computed from the 3D hull model. IGES (Initial Graphics Exchange Specification) and STEP (Standard for the Exchange of Product Data) are the file formats for transmitting the 3D geometry between the design office and the shipyard.

For classification society approval purposes, the lines plan is submitted as 2D drawings (either paper or PDF) at a defined drawing scale (typically 1:100 or 1:200 for the lines plan itself). Class approval is required before steel cutting begins on a newbuild. DNV, Lloyd’s Register, and other classification societies review the lines plan as part of their design approval process to verify that the hull geometry is consistent with the stability calculations submitted in the trim and stability booklet.

Lines plan in service and modification

The trim and stability booklet

The lines plan, or a sufficient summary of the hull geometry, forms part of the approved trim and stability booklet that every vessel must carry under SOLAS Chapter II-1 Reg.5 (cargo ships) and the IGF Code or IS Code for specialized vessel types. The booklet contains the hydrostatic curves, cross curves of stability, and capacity plans derived from the lines plan, along with the approved loading conditions. The lines plan coordinates underpin all the tabulated data in the booklet.

Hull modification

When a vessel is jumboized (cut athwartships and a new section inserted to increase length and cargo capacity), an updated lines plan must be prepared, approved by the classification society, and incorporated into a revised trim and stability booklet before the vessel re-enters service. The same process applies to a bulbous bow retrofit, an alteration to the stern frame, or the installation of an air lubrication system requiring inlet openings in the flat bottom.

For a bulbous bow addition, the modification lines plan is usually a partial plan showing only the bow region forward of about station 1, appended to the existing lines plan for the unmodified hull. The class society checks dimensional consistency at the junction, verifies that the added buoyancy of the bulb is accounted for in the revised hydrostatic data, and approves the modification.

As-built versus as-designed

The as-built hull always deviates from the as-designed lines plan by some amount. Fabrication tolerances for large steel structures allow plate positions to vary by up to 5 mm from the theoretical surface. For most vessels, this difference is negligible for hydrostatic and resistance purposes. For high-speed vessels or research vessels where small resistance differences are commercially significant, an as-built survey using either a coordinate measuring arm or a structured-light 3D scanner can capture the actual hull surface. The as-built surface is then compared against the as-designed surface to quantify the deviations and recompute the hydrostatic data.

Modern computational hull definition

From 2D to 3D

The transition from 2D lines plan to 3D surface model did not change the geometric concepts: the same stations, waterlines, and buttocks that were drawn on paper are now cross-sections extracted from a parametric surface. What changed is the workflow. A designer working in NAPA Designer or CAESES defines the hull surface by placing control points on a NURBS patch and adjusting their positions interactively. The software automatically maintains fairness constraints (G2 continuity) at patch boundaries. The complete lines plan is regenerated at any cross-section location on demand.

The 3D model also enables direct integration with downstream analysis tools. The resistance CFD solver (SHIPFLOW, OpenFOAM, or STAR-CCM+) reads the NURBS surface directly, eliminating the step of re-entering geometry from the 2D lines plan. The structural FEA mesh is generated by mapping a mesh onto the hull surface model. The same NURBS surface drives the CNC cutting files for production.

Parametric hull generation and series data

For vessels that fall within the range of established systematic series, the lines plan can be generated parametrically from the principal form coefficients without starting from a physical parent ship. The Taylor Standard Series (1933), revised by Gertler (1954), provides resistance data for fine-form vessels ($C_B$ from 0.48 to 0.80) parameterized by $B/T$ and displacement-length ratio. The Series 60 (1954 to 1960) covers cargo ship forms. The BSRA (British Ship Research Association) trawler series and the Wigley hull are other well-documented reference series. The resist-taylor-gertler-series calculator implements the Taylor-Gertler residuary resistance lookup.

Modern parametric generation goes beyond scaling and distorting these historical series. A parametric hull modeler such as CAESES defines a hull surface by equations, with each parameter (bow half-angle, stern waterline angle, bilge radius distribution, parallel midbody length) independently controllable. This allows a systematic exploration of the design space that would be impractical by manual fairing.

IGES, STEP, and data exchange

The ISO standard for 3D geometry exchange between different CAD systems is STEP (ISO 10303, Standard for the Exchange of Product Data). For shipbuilding, the application protocol AP218 (Ship Structures) and AP232 (Technical Data Packaging) are the relevant subsets. IGES (ANS Y14.26M) is an older format that remains in widespread use for backward compatibility.

When a design office delivers a hull surface model to a shipyard for production, the exchange format is typically IGES or STEP. The shipyard’s production CAD system (typically a specialized nesting and cutting software rather than a generic CAD platform) reads the surface and generates the cutting and bending programs.

Limitations

Accuracy of the offset table

An offset table with values to the nearest millimetre at 21 stations and 12 waterlines defines the hull at 252 points. Between these points, the hull shape is inferred by interpolation. For a smooth hull without hard chines, cubic spline interpolation between station sections introduces errors below 1 mm at mid-station, which is within fabrication tolerance. For a hull with a knuckle or a chine (a hard angular feature), the interpolation must be constrained to pass through the knuckle coordinates without smoothing them. Failure to handle knuckles correctly produces a hull with incorrect geometry at the feature and incorrect displacement in the adjoining region.

Scale model fidelity

When a model test is used to validate the lines plan, the model is machined to a scale typically between 1:20 and 1:60. At scale 1:40, the model is machined to tolerances of ±0.5 mm, corresponding to ±20 mm at full scale. Resistance test results are corrected to full scale using the ITTC 1978 performance prediction method, which applies a model-ship correlation allowance $\Delta C_F$ to account for hull roughness differences between the smooth machined model and the sandblasted painted ship. The model-ship correlation allowance calculator implements this correction per ITTC guidelines.

Trim and loading effects

The lines plan is drawn at the design draught and upright. A vessel in service operates at varying draughts, trims, and occasionally with a list. The hydrostatic data (derived from the lines) are presented as curves over the full draught range to account for draught variation. Trim effects are handled by including the trimming moment in the hydrostatic calculation, typically through the moment to change trim one centimetre (MCT1cm) derived from the second moment of the waterplane area about the centre of flotation. For large trims (exceeding about 1% of ship length), the standard small-trim corrections become inaccurate and a full oblique waterplane integration is required.

CFD limitations

While CFD analysis using the lines plan can predict calm-water wave-making resistance to within about 3 to 5% of model test values for conventional hull forms at design speed, the following effects are not well-captured by standard RANS CFD:

• Appendage resistance (rudder, bilge keels, shafting, brackets) requires separate treatment.
• Added resistance in waves is computed separately by strip theory or 3D potential flow using the seakeeping methods, not from the calm-water CFD.
• Shallow-water and canal effects alter the pressure distribution and resistance; the standard open-water lines plan gives no information about this without a separate shallow-water CFD run.
• The squat effect in restricted waters requires knowledge of the waterplane area and displacement volume from the lines plan; the squat effect article covers this in the context of underkeel clearance.

Production tolerances

CNC cutting machines maintain plate cutting accuracy to better than ±1 mm. However, the subsequent fitting, bending, and welding of plates introduces distortions that can move the final hull surface by 3 to 10 mm from the theoretical lines. These distortions are within normal class tolerances but can affect a vessel’s drag by a small amount. For a bulk carrier hull with a wetted surface area of approximately 6,000 m² and a frictional resistance coefficient of 0.0015, a 5 mm average roughness increase over the entire hull contributes roughly 1 to 2% to the total resistance. After five years of service without drydocking, this roughness penalty can grow to 10 to 15% due to biofouling.

See also

Related wiki articles:

• Hull form design
• Naval architecture coefficients
• Hydrostatics and Bonjean curves
• Wetted surface area
• Block coefficient
• GZ curve and righting arm
• Hull strength and longitudinal bending
• Cross curves of stability and KN tables
• Ship resistance and powering
• Seakeeping
• Metacentric height
• Intact stability
• Bulbous bow retrofits
• Squat effect
• Trim optimisation
• Classification society

Related calculators:

• Block coefficient calculator
• Prismatic coefficient calculator
• Waterplane area coefficient calculator
• Simpson’s rule displacement calculator
• Simpson’s rule waterplane area calculator
• GZ curve from KN tables calculator
• ITTC friction coefficient calculator
• Resistance correlation allowance calculator
• Hull wetted surface area estimator
• Wetted surface Mumford formula calculator
• Taylor-Gertler resistance series