The Seabed Joins the Flow

Every speed-power curve a ship owns was drawn in water that might as well be bottomless. The towing tank is deep by design. A sea trial is run in deep water by rule, and if the site is not quite deep enough the analysis corrects the result back to deep water before anyone sees it. A monitoring system's reference curve inherits all of that without ever writing the assumption down. Deep water is the default so completely that it has no name.

Then the ship leaves it. A river approach, a canal, a shelf sea twenty metres deep, an anchorage roads with a metre and a half under the keel. The hull does not know it has crossed into a different regime; the physics does. This lesson is about what changes, why, and the two numbers that let you say how much.

One Cause, Five Effects

Start with a ship moving through water that is very deep and very wide. Every second she displaces a volume of water equal to her underwater cross-section times her speed, and that water has to get out of her way. In open water it does so with elegance: it flows under the keel, around the bilges, outward to either side, with the whole ocean available as a return path. The velocities involved are modest, the pressure changes along the hull are modest, and the resistance that results is the calm-water resistance our Ship Resistance Fundamentals course takes apart: friction, viscous pressure, wave making.

Now bring the seabed up. Nothing about the ship changes: same hull, same speed, same volume of water to be pushed aside per second. What changes is the room available for that water to pass. The cross-section beneath and beside the hull shrinks, and a fixed volume per second through a smaller area means one thing: the flow accelerates. This is continuity, the most elementary law in fluid mechanics, and every shallow-water effect in this course descends from it.

Faster flow under the hull has three immediate consequences, and they are the skeleton of the next seven lessons.

The pressure under the hull falls. Bernoulli's relation says that where a flow speeds up its pressure drops, and the pressure under a ship is what holds her up. Lower it, and she sinks bodily and, because the pressure field is not symmetric fore and aft, she trims as well. This is squat, lesson 2: a safety problem first, a resistance problem always.

The friction rises. Frictional resistance goes with the square of the velocity past the plating. The accelerated return flow along the bottom and bilges of the hull is exactly that velocity, raised, and the ship pays for it on every square metre of wetted surface the bottom is near. This is the quiet term, the one with no drama and no diagram, and in moderate depths it is most of the bill.

The wave system deforms. A ship's waves are made by the pressure field she drags along with her, and that field has just been distorted. Worse, waves in shallow water have a speed limit, the square root of gravity times depth, and as the ship approaches it her wave system cannot get out of her way. That is critical speed, lesson 4, the effect that turns depth into a hard ceiling on speed.

Put a bank on one side and the squeeze becomes asymmetric: the bank effect of lesson 3, a turning moment rather than a sinking force. Put banks on both sides and the waves she makes come back at her off the walls while the water alongside physically drops: the canal of lesson 5. Put a layer of fluid mud on the bottom, and the seabed itself stops being a surface: lesson 6. Five effects, one cause, which is why a course and not a checklist.

The Two Numbers

Depth on its own tells you nothing. Twenty-four metres of water is deep for a feeder and dangerously shallow for a laden tanker, and it is critical-speed territory for a fast container ship while the tanker, in the same water, never comes near it. Two dimensionless numbers carry the information, and the discipline of this course is to compute both before saying anything.

The depth-to-draught ratio, h/T, measures how close the bottom is in the only units that matter to the hull: her own draught. It governs the constriction effects, squat, backflow friction and bank interaction, because it sets how much of the return path the seabed has taken away. As a first orientation:

• h/T above about 3: the bottom is felt, faintly. A per cent or two of resistance on a full ship; hard to see in service data.
• h/T between 2 and 3: measurable. Several per cent of power at service speed; a trial standard will correct for it rather than accept the run.
• h/T between 1.5 and 2: substantial. The squat is now a safety quantity; resistance increases of ten per cent and more at ordinary speeds.
• h/T below 1.5: the constriction dominates. Pilots reduce speed for squat rather than for time, and the power to hold any given speed climbs steeply.

The depth Froude number, Frh, measures speed against the fastest a wave can travel in water that deep:

Frh = V / √(g · h)

with V the ship's speed through the water in metres per second, g the acceleration of gravity and h the water depth. The denominator is the long-wave speed limit: in water of depth h, no gravity wave can propagate faster than √(g·h) (lesson 4 derives it). The ship's own wave system has to keep pace with the ship, so as Frh rises toward 1 the waves she generates cannot escape ahead of her and the pattern piles up. Below about 0.6 the effect on the wave system is small; between 0.7 and 1 resistance climbs steeply; at 1 it peaks in the wall that gives critical speed its name.

Note what each number does not say. A laden tanker at 10 knots in 1.2 draughts of water has Frh ≈ 0.36, deeply subcritical, and is nonetheless squatting most of a metre and carrying a large resistance penalty from the constriction. A fast ship in 2.5 draughts of water may have no squat worth mentioning and be well into the transcritical range. Squat and backflow are governed by h/T; the wave effects by Frh; and most real situations carry some of both. Compute both, always.

How Deep Is Deep?

The two numbers also answer the question that hides inside every deep-water assumption: how deep does water have to be before the seabed can be forgotten? The trial standards have had to answer it in writing, and the 2015 generation, ISO 15016:2015 and the ITTC's 2017 procedure, used two criteria in the ITTC form, one for each mechanism:

h > 3 · √(B · T) and h > 2.75 · V² / g

The first is geometric: beam times draught is the order of the hull's underwater cross-section, and three times its square root is how far away the bottom has to be before the return flow around that cross-section stops feeling it. The second is kinematic: rearrange it and it reads V/√(g·h) < 1/√2.75, that is, Frh below about 0.6: the wave system kept out of the range where depth begins to deform it. A run had to clear both to count as deep water, and if it did not, the standard applied a correction, lesson 4's subject, to carry the result back to the deep condition the curve is supposed to describe, down to a floor of its own (2·√(B·T) and 2·V²/g in the ITTC's 2017 text) below which it did not. The current generation, the ITTC's 2021 procedure and ISO 15016:2025, dropped the pair: the correction is now applied to every trial, small in deep water and larger in shallow, and the depth clause that remains is a floor. The ITTC procedure (section 6.4 of its 2024 revision) says the water depth used for the correction "shall not be less than" the larger of 2.5 draughts and 2.4·V²/g, so water shallower than that is no place for a trial; ISO 15016:2025 gives water depth a clause of its own among the trial boundary conditions. The pair survives as the honest deep-water filter for performance data, which is how this course uses it.

Put a real ship through those criteria. Meet the course tanker, which will do duty throughout: length between perpendiculars 275 m, beam 48 m, laden draught 17.0 m, block coefficient 0.84, midship coefficient 0.995, displaced volume about 188,500 m³, midship section area about 812 m², and a laden service speed of 14.5 knots at about 16,000 kW of shaft power in deep water. Her geometric criterion is 3 × √(48 × 17) = 3 × 28.6 ≈ 86 metres: five times her draught. Her kinematic criterion at 14.5 knots (7.46 m/s) is 2.75 × 7.46² / 9.81 ≈ 16 metres, which the geometric one swallows whole. The seabed, for this ship, is felt from eighty-six metres down.

That figure surprises most people, and the surprise is the point. Navigational intuition is calibrated on clearance: a ship with twenty metres under her keel is, to a watchkeeper, in deep water. To her resistance she is at h/T ≈ 2.2, and measurably slower for a given power than the curve says she should be. Large parts of the North Sea, the Baltic, the Yellow Sea, the Persian Gulf, the Malacca Strait and the entire US Gulf shelf are shallower than eighty-six metres. A tanker on those trades spends a good fraction of her steaming life inside her own shallow-water criterion, and her performance record is full of it.

Why the Correction Chain Does Not Contain This

Here is the thesis of the course, stated at the point it becomes unavoidable. Every method that turns measured power into a hull-condition figure, a trial analysis, an ISO 19030 evaluation, a vendor's monitoring dashboard, works by comparing a measurement with a reference that describes calm, deep water. The weather corrections, wind, waves, current, water temperature, remove what the weather added so that the comparison is fair. Our Added Weather Resistance specialisation teaches each of those terms. Not one of them contains the depth.

So what happens to a shallow-water record? Its resistance is higher than the reference for reasons of geometry, the weather correction removes the weather, and the remainder, the geometry, is attributed to the one thing the analysis has left to blame: the hull. A ship that trades through confined water carries a one-signed error in every record collected there, and one-signed errors accumulate into trends. The river leg becomes fouling; the canal transit becomes a cleaning invoice. Lesson 7 sizes that artefact and gives the defences, and the trial standards' own answer to the problem is the subject of lesson 4.

Until then, one habit: when a performance deviation appears, ask where the ship was. Not what the weather was doing, which the corrections already asked, but how much water was under her keel and how fast she was going relative to the waves that water could carry. Two numbers. The rest of the course is what to do with them.

Go deeper: the original article Shallow Water Changes the Physics: Five Effects.