UKC Calculator: Under-Keel Clearance from First Principles

A number on a screen is not clearance.
Clearance is what remains after every assumption has been tested against what the water is actually doing.

Introduction

Under-keel clearance is the vertical distance between the lowest point of a vessel’s hull and the seabed. It is a number that changes with every passing minute — with the tide, with the ship’s speed, with the trim, with the sea state, with the salinity of the water. It is not a fixed value read from a chart and subtracted from a draught. It is a dynamic, multi-variable calculation that must account for conditions as they are, not as they were predicted to be.

The industry’s persistent habit of reducing this to a single percentage — “ten per cent of draught” being the most common — has contributed to more near-misses and groundings than most casualty investigators care to count. A 10% rule gives a 14-metre-draught VLCC 1.4 metres of clearance. That is not a safety margin. That is a hope.

This article works through the full UKC calculation as it should be performed: from chart datum upward, accounting for every dynamic reduction. It is intended as a reference for passage planning and as the basis for the interactive calculator that will sit alongside it.

Contents

• 1. The Starting Point: Chart Datum and Charted Depth
• 2. Adding the Tide: Height of Tide Above Datum
• 3. The Ship’s Side: Static Draught and Trim
• 4. Squat: The Penalty for Speed in Shallow Water
• 5. Heel: Turning, Wind, and Asymmetric Loading
• 6. Wave Response: Allowance for Vertical Motion
• 7. Water Density: The Freshwater Trap
• 8. Assembling the Calculation: A Worked Example
• 9. Minimum UKC vs. Planned UKC: The Distinction That Matters

1. The Starting Point: Chart Datum and Charted Depth

Every UKC calculation begins at the seabed — or more precisely, at what the chart says the seabed is. The charted depth is referenced to chart datum, which in most areas covered by UKHO charts is approximately the level of Lowest Astronomical Tide (LAT). This is a tidal level so low that the water will almost never fall below it under normal meteorological conditions.

This is important. Chart datum is not mean sea level. It is not the water level visible from the bridge wing. It is a reference plane chosen to be pessimistic about depth, which means that the actual water level is almost always above chart datum. The tide height published in tables or calculated by tidal prediction software is the height of the water surface above this datum.

The charted depth itself carries uncertainty. Survey age matters. In many parts of the world, the last full hydrographic survey was conducted decades ago, with equipment that could not resolve features smaller than several metres. Siltation, dredging tolerances, and uncharted wrecks are real variables. A charted depth of 15.0 metres does not mean the seabed is a flat plane at 15.0 metres below datum. It means the best available data suggested approximately that depth at the time of the last survey.

Trust the chart, but know what you are trusting.

2. Adding the Tide: Height of Tide Above Datum

The available water depth at any given moment is the charted depth plus the height of tide above chart datum. If the charted depth is 15.0 metres and the predicted tide height is 3.2 metres, the water column from surface to charted seabed is 18.2 metres.

Several corrections apply before this number is reliable:

Meteorological effects. Tide tables give astronomical predictions only. Sustained onshore winds and low barometric pressure raise actual water levels; offshore winds and high pressure reduce them. In shallow, semi-enclosed waters — the southern North Sea, the Baltic approaches, the Malacca Strait — meteorological surges can add or subtract a metre or more from predicted levels. Port VTS and harbour authorities may issue real-time corrections. These must be sought and applied.

Timing uncertainty. The transit will not occur at a single instant. The tide changes. The calculation must be performed for the time of minimum UKC along the planned track, which is not necessarily the shallowest charted depth. It is the point where the combination of charted depth, tide height, and ship dynamics produces the smallest margin. This requires checking multiple waypoints at their respective transit times.

Tidal stream vs. tidal height. These are related but different. The current flowing beneath the hull affects squat calculation. The height affects available depth. Both must be accounted for, and confusing one with the other is a common planning error.

3. The Ship’s Side: Static Draught and Trim

The draught used in UKC calculation is the maximum static draught of the vessel — the deepest point of the hull when the ship is upright and stationary in water of known density. For most merchant vessels, this is the draught aft, though trim by the bow does occur. The value must come from the loading computer confirmed against draught marks or draught survey, not from memory or the last port’s departure condition.

Trim is not merely an academic detail. A vessel trimmed 2 metres by the stern has her deepest point further aft than her midships marks suggest. If the keel is not parallel to the waterplane, the extremities may be deeper than the mid-draught reading. The maximum draught at any point along the hull length is the value that matters.

The draught that grounds the ship is not the one painted amidships.

Any projections below the keel — transducers, sonar domes, bilge keels at certain heel angles — must also be considered. On some vessel types, the lowest point of the hull is not the keel.

4. Squat: The Penalty for Speed in Shallow Water

Squat is the bodily sinkage and change of trim a vessel experiences when moving through water of restricted depth. As the hull moves forward, water accelerates beneath it to fill the space. The resulting drop in pressure pulls the hull downward. In a channel of limited width, the effect intensifies further — this is the confined water or canal effect.

Squat increases approximately with the square of speed through the water. Doubling speed roughly quadruples squat. This is the single most controllable variable in the entire UKC equation, and it is the one most often underestimated.

Two widely-used empirical formulae:

Barrass (simplified, open water):

Squat (m) = Cb × (V_k)² / 100

Where Cb is the block coefficient and V_k is speed through the water in knots.

Barrass (confined channel):

Squat (m) = Cb × (V_k)^2.08 / 30 × S^0.81

Where S is the blockage factor (the ratio of the ship’s midships cross-section to the channel cross-section). This version produces significantly higher values in narrow, shallow channels.

For a bulk carrier with a Cb of 0.82 making 10 knots through the water in open shallow water, the Barrass open-water formula gives a squat of approximately 0.82 metres. At 12 knots the same vessel squats 1.18 metres. The extra two knots cost 0.36 metres of clearance.

Speed is not free in shallow water. Every knot costs depth.

In practice, the choice of squat formula matters and should align with the geometry of the waterway. The IMO and many port authorities specify which formula or method to use. Where a port provides its own squat tables for a particular channel, those take precedence over generic formulae.

5. Heel: Turning, Wind, and Asymmetric Loading

When a vessel heels, the lowest point of the hull moves outboard and downward. The additional draught caused by heel is a function of beam and heel angle. For small angles, the increase in draught due to heel is approximately:

ΔT (m) = (B / 2) × sin(θ)

Where B is the beam in metres and θ is the angle of heel.

For a vessel with a beam of 32 metres heeling just 2 degrees:

ΔT = 16 × sin(2°) = 16 × 0.0349 = 0.56 m

Over half a metre from a heel barely perceptible on the bridge. At 5 degrees — a moderate turn or a beam wind on a high-sided vessel — the increase is 1.39 metres.

Sources of heel in pilotage waters include course alterations (rudder-induced heel), beam winds on container ships and car carriers, and residual list from asymmetric loading. The latter should be zero if the loading computer is correct, but it is not always correct.

A vessel does not need to be listing to heel. She only needs to be turning.

The passage plan must identify points where course alterations coincide with minimum charted depths and ensure the UKC calculation at those points includes the heel component.

6. Wave Response: Allowance for Vertical Motion

In any seaway, the hull moves vertically. Heave is bodily rise and fall. Pitch is rotation about the transverse axis. Roll is rotation about the longitudinal axis. All three contribute to the instantaneous draught being greater than the static draught.

The wave response allowance is the most difficult component to calculate precisely. It depends on the vessel’s response characteristics (length, beam, natural periods of roll and pitch), the wave height, period, and direction, and the speed and heading of the vessel relative to the sea.

For practical passage planning, empirical allowances are used. Common methods include:

• Taking half the significant wave height as the vertical motion allowance. This is crude but widely accepted for swell conditions.
• Using response amplitude operators (RAOs) from the vessel’s hull design data, if available.
• Applying port authority published allowances for specific channels, which are often derived from vessel motion studies for that waterway.

In sheltered pilotage waters with minimal swell, the wave allowance may be small — 0.1 to 0.3 metres. In an exposed approach in the North Sea or the Bay of Biscay, it can exceed a metre. The value must reflect the actual conditions expected during the transit, not fair-weather assumptions.

7. Water Density: The Freshwater Trap

A vessel’s draught in the loading computer is typically calculated for salt water of density 1.025 t/m³. If the vessel enters water of lower density — a river approach, an estuarine channel, a port fed by significant freshwater runoff — she will sink deeper.

The fresh water allowance (FWA) is given by:

FWA (m) = Displacement / (4 × TPC × 1.025)

The dock water allowance for intermediate densities is proportional:

DWA (m) = FWA × (1.025 – ρ_dw) / 0.025

Where ρ_dw is the actual dock water density.

For a vessel with an FWA of 0.30 metres transiting water of density 1.010:

DWA = 0.30 × (1.025 – 1.010) / 0.025 = 0.30 × 0.6 = 0.18 m

This 18 centimetres is real. It is there every second the ship is in that water. It is often forgotten because the draught marks were read in salt water at the berth, and the channel two miles upriver is brackish.

The water does not care what the draught marks said at the pilot station.

8. Assembling the Calculation: A Worked Example

Consider a loaded bulk carrier approaching a port. The parameters:

• Charted depth at the critical point on track: 16.5 m (below chart datum)
• Predicted tide height at time of transit: +2.8 m above datum
• Available water depth: 16.5 + 2.8 = 19.3 m

Ship data:

• Maximum static draught (aft): 14.2 m (in salt water at load port)
• Block coefficient (Cb): 0.83
• Beam: 32.2 m
• FWA: 0.28 m
• Planned speed through the water in the channel: 8 knots

Environmental and dynamic conditions:

• Dock water density in channel: 1.015 t/m³
• Significant wave height on approach: 0.6 m (sheltered channel)
• Maximum anticipated heel during course alteration at the critical point: 3 degrees

Step 1 — Dock water allowance:

DWA = 0.28 × (1.025 – 1.015) / 0.025 = 0.28 × 0.4 = 0.11 m

Adjusted static draught: 14.2 + 0.11 = 14.31 m

Step 2 — Squat (Barrass, open water):

Squat = 0.83 × 8² / 100 = 0.83 × 64 / 100 = 0.53 m

Step 3 — Heel allowance:

ΔT = (32.2 / 2) × sin(3°) = 16.1 × 0.0523 = 0.84 m

Step 4 — Wave response allowance:

0.6 / 2 = 0.30 m (half significant wave height)

Step 5 — Total dynamic draught:

14.31 + 0.53 + 0.84 + 0.30 = 15.98 m

Step 6 — Calculated UKC:

19.3 – 15.98 = 3.32 m

Step 7 — Apply safety margin:

The safety margin is separate from the calculated UKC. It is the buffer retained against the uncertainties that the calculation cannot resolve: charted depth inaccuracy, tide prediction error, unexpected trim changes, transient squat effects from meeting traffic, and the possibility that one or more input values are simply wrong.

A safety margin of 0.5 to 1.0 metres is common in well-surveyed, sheltered waters. In poorly surveyed areas or exposed approaches, more is required.

With a 1.0-metre safety margin, the net UKC is 3.32 – 1.0 = 2.32 m.

That is the planned clearance after every known reduction has been applied and a buffer has been held for the unknowns.

Now compare this with the “10% of draught” rule: 10% of 14.2 = 1.42 m. That single number makes no distinction between squat, heel, waves, density, or survey uncertainty. It does not tell the navigator what is consuming the clearance or where the risk can be controlled. It is a number that appears safe because it has always been used.

It is not a calculation. It is an incantation.

9. Minimum UKC vs. Planned UKC: The Distinction That Matters

Minimum UKC is the lowest acceptable clearance — the hard limit below which the transit does not proceed or the ship reduces speed, alters course, or waits for more tide. It is defined by the port authority, the company SMS, or the master’s standing orders, and it exists to ensure that even if conditions deteriorate from the plan, the ship does not touch the bottom.

Planned UKC is the clearance the passage plan is built to achieve. It should always exceed the minimum by a meaningful margin. If the planned UKC equals the minimum UKC, there is no room for anything to go wrong.

Something always goes wrong.

The tide arrives twelve minutes late. The speed over ground creeps up because the current was stronger than predicted. The loading computer rounds a trim figure. The chart is based on a survey from 1987. The wind picks up and the vessel heels three degrees instead of two. Each of these is individually small. Together, they consume the margin that was supposed to be there.

The relationship between planned and minimum UKC is the difference between a passage plan and a hope. A competent plan identifies the critical points along the track, calculates UKC at each one for the expected transit time, and demonstrates that the planned clearance exceeds the minimum clearance with room for the variables that cannot be predicted.

If that demonstration cannot be made, the transit parameters must change. Slower speed. Different tide window. Lighter draught. There is no third option.

Port authorities increasingly mandate dynamic UKC management — real-time monitoring of actual draught, actual tide, actual squat — rather than accepting a static pre-departure calculation. This is progress. But the pre-departure calculation remains the foundation, because it determines whether the transit should be attempted at all.

The minimum is not the target. The target is comfort above the minimum. The minimum is the abort point.

Closing Reality

Under-keel clearance is not a single number and it is not a percentage. It is the sum of a series of physical phenomena — tidal height, vessel sinkage, rotational motion, density effects — each of which must be quantified separately, because each behaves differently and each responds to different controls.

Speed can be reduced to cut squat. Timing can be adjusted to gain tide. Heel can be managed by limiting rudder angles at critical points. Wave allowance can be addressed by choosing a different weather window. These are operational decisions. They require a calculation that exposes the individual components, not a rule of thumb that buries them.

A vessel that transits a channel with 10% of draught as clearance and arrives safely has not validated the rule. She has been lucky. Luck is not a navigation aid.

The calculation presented here is the minimum standard. It should be performed for every port approach where depth is a constraint, checked against real-time data during the transit, and revisited whenever any input changes. The interactive UKC calculator, when available alongside this article, will automate the arithmetic. It will not automate the judgement of what values to put into it.

That part remains the navigator’s problem.