Length, beam, draft, displacement & key hull coefficients — formulas, empirical ranges, and practical guidance.
If you strip a ship down to its essentials, what you're left with is a handful of numbers. Length, beam, draft, displacement — and a few coefficients that don't look like much at first. But these values quietly control almost everything a ship does. Before resistance calculations, propulsion estimates, or stability checks begin, these parameters already define what the vessel can and cannot do.
What makes them useful isn't just that they describe a ship — it's that they allow comparison. A bulk carrier and a patrol vessel might be entirely different in purpose, but once reduced to the same set of parameters, their design intent becomes straightforward to read.
This article covers each parameter in practical terms: definition, formula, typical empirical ranges for different vessel types, common relationships between parameters, and the kind of judgment that experience builds over time.
"Length" sounds like one number, but in practice naval architects work with at least three distinct definitions — and confusing them in calculations leads to errors.
Length has a fundamental relationship with wave-making resistance through the Froude number, which is the non-dimensional form of the speed–length ratio:
A vessel sailing at its "hull speed" operates at approximately Fn ≈ 0.4. Wave-making resistance rises steeply above this. Longer vessels can reach higher absolute speeds before hitting this barrier — this is why container ships are long and slender, while harbour tugs are not.
| Vessel Type | Typical LBP Range (m) | Design Fn |
|---|---|---|
| Harbour tug | 20 – 40 | 0.20 – 0.28 |
| General cargo | 80 – 150 | 0.18 – 0.23 |
| Bulk carrier | 150 – 300 | 0.14 – 0.18 |
| Container ship | 200 – 400 | 0.22 – 0.26 |
| Naval frigate | 100 – 150 | 0.35 – 0.45 |
| Patrol vessel | 30 – 80 | 0.35 – 0.60 |
| VLCC tanker | 300 – 340 | 0.13 – 0.16 |
Two slenderness ratios involving length appear frequently in early-stage design:
Beam (B) is the maximum breadth of the hull at the design waterline or at midships, depending on context. It carries consequences for stability, resistance, cargo capacity, and port access.
In most contexts, beam refers to moulded beam — measured to the inside of the shell plating. For external clearances (locks, berths), the full outer breadth is used.
The initial metacentric height (GM), which governs stability at small angles of heel, depends strongly on the second moment of the waterplane area — which scales with beam cubed:
Doubling the beam has an enormous effect on transverse stability — it raises the metacentre dramatically. This is why barge-like vessels (high B/T ratios) are extremely stiff, and why narrow sailing yachts need deep keels.
| Vessel Type | Typical B/T | Notes |
|---|---|---|
| Ocean-going tanker | 2.4 – 3.0 | Relatively deep draft, moderate stability |
| Container ship | 2.8 – 3.5 | High deck loads require good stability |
| River barge | 4.0 – 6.0 | Shallow water, maximise beam for stability |
| Naval frigate | 3.0 – 4.0 | Balance of seakeeping and stability |
| Sailing yacht (monohull) | 2.5 – 4.5 | Relies on ballast keel, not form stability |
Draft (T or d) is the vertical distance from the keel to the waterline. It sets displacement for a given hull form and determines operational access to ports, canals, and shallow waters.
Ships operate across a range of drafts depending on loading condition:
The change in displacement per unit change in draft is called the Tonnes Per Centimetre Immersion (TPC):
TPC is a key number for loading officers. For a large Panamax bulker with Awp ≈ 12,000 m², TPC is around 123 t/cm — meaning loading 1,230 tonnes sinks the vessel by approximately 1 cm.
Many important waterways impose hard draft restrictions:
| Waterway / Route | Max Draft Constraint |
|---|---|
| Suez Canal (laden) | ≈ 20.1 m |
| Panama Canal (Neopanamax locks) | ≈ 15.2 m |
| Panama Canal (old Panamax locks) | ≈ 12.0 m |
| English Channel (TSS) | Effectively unrestricted for most merchant vessels |
| Typical coastal port | 8 – 14 m (varies widely) |
| Major river terminal | 5 – 10 m |
Depth (D) is measured from the keel to the uppermost continuous deck (the freeboard deck) at the vessel's side. It is a structural and geometric dimension, not a hydrodynamic one.
Freeboard is a reserve of buoyancy. Insufficient freeboard makes a vessel susceptible to shipping water on deck in a seaway, which affects both safety and structural loads. The required freeboard depends on ship type, length, and block coefficient.
Displacement (Δ or W) is the weight of water displaced by the hull. By Archimedes' principle, this equals the total weight of the vessel at that draft.
| Displaced volume: | ∇ = 180 × 28 × 10 × 0.78 = 39,312 m³ |
| Displacement (seawater): | Δ = 1.025 × 39,312 ≈ 40,295 tonnes |
Total displacement is divided into:
The ratio DWT/Δ varies by vessel type: tankers and bulk carriers achieve 0.80–0.87, container ships 0.55–0.70, naval vessels 0.30–0.50.
You can calculate displacement directly using the Displacement Calculator.
Cb expresses how much of the bounding box (L × B × T) is actually filled by the hull. It is the single most influential coefficient in preliminary design.
At early design stages, before body lines exist, Cb is estimated from speed using empirical methods. The most widely cited is the Alexander formula:
| Fn: | 7.20 / √(9.81 × 120) = 7.20 / 34.31 = 0.210 |
| Cb (Alexander): | 1.08 − 1.68 × 0.210 ≈ 0.73 |
| Vessel Type | Typical Cb | Characteristic |
|---|---|---|
| VLCC / Suezmax tanker | 0.82 – 0.88 | Very full form, slow speed |
| Bulk carrier (Capesize) | 0.78 – 0.84 | Full form, cargo-optimised |
| General cargo | 0.68 – 0.76 | Moderate fullness |
| Container ship (large) | 0.62 – 0.70 | Medium-speed, finer bow |
| RoPax / ferry | 0.55 – 0.65 | Speed and capacity trade-off |
| Naval frigate / OPV | 0.45 – 0.56 | Fine form, high speed |
| Fast patrol craft | 0.35 – 0.50 | Very fine, semi-planing |
You can calculate Cb directly using the Block Coefficient Calculator.
Cp describes how volume is distributed along the ship's length — whether the ends are full or fine relative to the midship section. It is closely tied to wave-making resistance.
Cp has a strong influence on residuary resistance, particularly wave-making at higher Froude numbers. For each Froude number, there is an optimum Cp that minimises wave-making resistance:
| Froude Number (Fn) | Optimum Cp | Interpretation |
|---|---|---|
| 0.15 – 0.18 | 0.55 – 0.62 | Slow displacement vessels — full ends acceptable |
| 0.18 – 0.22 | 0.62 – 0.70 | Medium-speed cargo ships |
| 0.22 – 0.26 | 0.70 – 0.76 | Container ships, faster RoPax |
| 0.26 – 0.32 | 0.60 – 0.65 | Resistance hump region — finer ends preferred |
| 0.32 – 0.45 | 0.55 – 0.62 | High-speed displacement vessels |
You can calculate Cp using the Prismatic Coefficient Calculator.
Cm quantifies how rectangular the midship cross-section is. It connects Cb and Cp, and has implications for both resistance and structural efficiency.
| Vessel Type | Typical Cm | Section Shape |
|---|---|---|
| VLCC / bulk carrier | 0.98 – 0.995 | Near-rectangular, tight bilge radius |
| General cargo | 0.93 – 0.98 | Moderately rounded bilge |
| Container ship | 0.95 – 0.98 | Relatively full section |
| Naval frigate | 0.75 – 0.88 | More rounded, often flared topsides |
| Sailing yacht | 0.55 – 0.72 | Deep V or fin-keel section |
For commercial vessels, Cm is rarely far from 0.98. Designers of high-speed or naval vessels have more freedom to use rounded sections for seakeeping benefits.
You can calculate Cm using the Midship Coefficient Calculator.
Cwp describes how fully the waterplane area fills its enclosing rectangle. It directly affects initial stability, trim behaviour, and seakeeping.
Cwp feeds directly into the transverse metacentric radius BM, through the second moment of waterplane area:
When the waterplane area is not yet calculated, Cwp can be estimated from Cb:
| Vessel Type | Typical Cwp |
|---|---|
| Tanker / bulk carrier | 0.85 – 0.92 |
| General cargo | 0.78 – 0.86 |
| Container ship | 0.74 – 0.82 |
| Naval frigate | 0.68 – 0.76 |
| Sailing yacht (monohull) | 0.60 – 0.72 |
| SWATH vessel | 0.15 – 0.30 |
You can check values using the Waterplane Coefficient Calculator.
Less commonly discussed but worth understanding, Cvp describes how volume is distributed vertically — whether the hull is fuller near the keel or near the waterline.
A high Cvp indicates volume concentrated near the keel (deep U-sections). A lower Cvp indicates more volume near the waterline (wide, shallow hull). This affects vertical centre of buoyancy height (KB) and roll behaviour.
The five main coefficients are not independent — they are connected by exact mathematical identities:
In practice, this means that only a subset of coefficients are truly free design variables. Once Cb, Cm, and Cwp are specified (and the main dimensions set), all others follow.
Before body lines are drawn, the L/B, B/T, and L/T ratios are used to check that the proposed main dimensions fall within the range of successful precedent vessels. Schneekluth & Bertram (2nd ed.) provide the following as general guidance:
| Ratio | General range | Notes |
|---|---|---|
| L/B | 4.5 – 8.5 | Lower for short-sea shipping; higher for fast vessels |
| B/T | 2.3 – 4.5 | Shallower draught → higher B/T |
| L/T | 15 – 30 | Extreme values indicate unusual design requirements |
| D/T | 1.20 – 1.50 | Minimum freeboard and structural depth considerations |
| L/D | 10 – 16 | Structural depth relative to hull length |
Extreme departures from these ranges are not impossible, but they require careful justification — either through detailed analysis or well-understood precedent.
When you encounter a set of hull parameters, a useful mental checklist:
These parameters form the basic language of naval architecture. Used carefully, they allow a designer to make rapid estimates, verify data, compare vessels, and spot inconsistencies — all before a single line is drawn.
In practice, they're part of an iterative process. Adjusting one parameter changes the others, often in ways that aren't obvious at first. But with a clear understanding of the formulas and the empirical ranges, the interactions become much more manageable.
The concepts covered here are treated in depth in the following standard references: