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Squat in shallow water: Barrass's formulas and the under-keel clearance

Why it matters At speed in a channel she can touch a bottom she cleared by a metre alongside; squat is the clearance the bridge can take back by slowing down.

Squat against speed: Barrass's open-water and confined-channel lines, this channel between them, and the water under the keel at restSpeed through the water along the bottom, squat up the side, both to scale. Open water: Cb × V² ÷ 100, 0.85 m at 10 kn. Confined channel: Cb × V² ÷ 50, 1.7 m at 10 kn. This channel, blockage factor 0.175: the general formula gives 1.25 m at 10 kn and 0.43 m at 6 kn. The water under the keel at rest is 2.5 m; at 10 kn 1.25 m of it is left, and squat alone would use all of it at about 14 kn.SQUAT AGAINST SPEED · TO SCALE0246810121416kn00.511.522.53m squatunder the keel at rest 15 − 12.5 = 2.5 mCb 0.85 · H/T 1.2 · S 0.175confined channel ÷ 50 · 1.7 mopen water ÷ 100 · 0.85 mthis channel · S = 0.1751.25 m at 10 kn0.43 m at 6 kn1.25 m leftunder the keeltouches at 14 kn

Words on this page

Squat
the extra sinkage of a moving ship in shallow water, because the water rushing under her presses less.
Shallow water
water less than about one and a half times the draft deep; below that, squat starts to matter.
Block coefficient (Cb)
how full the hull is: her underwater volume as a share of the box that just holds it.
Open water and confined channel
open water is wide enough that the banks do not matter, several ship-breadths each side; a confined channel is a narrow cut or canal with the banks close.
Blockage factor (S)
the share of the channel's cross-section the ship fills: her breadth × draft over the channel's width × depth.
Depth to draft ratio (H/T)
the water depth divided by the ship's draft; 1.2 means twenty per cent more water than ship.
Speed through the water
how fast the ship moves relative to the water around her, not to the ground; squat follows this one.
Static and dynamic under-keel clearance (UKC)
the water under the keel when she is stopped; and what is left of it once she moves and squats.
By the bow or by the stern
which end of the ship goes down more as she squats: the front (bow) or the back (stern).

An everyday picture

Watch a stream run between two rocks. In the narrow gap the water moves faster. Its surface there is a little lower than before and after the gap.

Under a ship in shallow water the same thing happens. The water she pushes aside must squeeze between her hull and the sea bed. So it runs faster, and its level drops. She sinks with it.

Make the stream run twice as fast, and the dip grows about four times. That is why speed is squared, and why slowing down gives so much back.

The rule

  • Decide the water. Open: the banks several ship-breadths away. Confined: a channel with the banks close.
  • Quick estimate: open water, squat ≈ Cb × V² ÷ 100; confined channel, squat ≈ Cb × V² ÷ 50. Metres, with V in knots through the water.
  • For a known channel, work the blockage factor S = (b × T) ÷ (B × H). Then use the general formula. It was fitted for H/T about 1.1 to 1.4 and S about 0.10 to 0.265.
  • Then the clearance: static UKC = depth − draft; dynamic UKC = static UKC − squat, before the other allowances. If it is thin, slow down; squat falls with the square of the speed.

Formula

  • Open water: squat (m) ≈ Cb × V² ÷ 100 · confined channel: squat (m) ≈ Cb × V² ÷ 50 (V in knots)
  • General: squat = Cb × S^0.81 × V^2.08 ÷ 20, with S = (b × T) ÷ (B × H)
  • Dynamic UKC = (depth − draft) − squat

What squat is, and what it is not

  • A ship under way in shallow water sits deeper than the same ship stopped. The water she displaces must pass under and beside her through a gap that the bottom has narrowed; it speeds up, its pressure falls, and the hull drops into the lower pressure. The ship has not got heavier and her displacement has not changed; the water level around her has.
  • It has two parts: a bodily sinkage, and a change of trim. Both grow with speed, with the fullness of the hull, and with how much of the water's cross-section the ship blocks.
  • The speed that matters is the speed through the water. A knot of current under the keel squats her exactly as a knot of engine speed does, whatever the GPS says over the ground.

Barrass's two quick formulas

  • From many model and full-scale measurements, Barrass reduced the maximum squat to one line each for the two ends of the range: open water, squat ≈ Cb × V² ÷ 100; a confined channel, squat ≈ Cb × V² ÷ 50. The answer is in metres when V is in knots.
  • Open water here means the banks are far enough away not to matter, several ship-breadths on each side; a confined channel is a dredged cut or canal with the banks close. In between, the truth lies between the two lines, and the general formula below places it.
  • Cb is the block coefficient: a laden tanker or bulk carrier is 0.80 to 0.85; a container ship or ferry 0.55 to 0.70. The fuller the hull, the more it squats at the same speed.

The general formula and the blockage factor

  • The blockage factor S is the share of the channel's cross-section the ship fills: her breadth times her draft, over the channel's width times its depth. A ship 42 m wide drawing 12.5 m in a channel 200 m wide and 15 m deep fills 525 ÷ 3000 = 0.175 of it.
  • Barrass's general formula is squat = Cb × S^0.81 × V^2.08 ÷ 20. It was fitted for depth-to-draft ratios of about 1.1 to 1.4 and blockage factors of about 0.10 to 0.265; outside that range fall back on the quick formulas or the ship's own data. Put S ≈ 0.1 into it and you are near the open-water line; S ≈ 0.25, near the confined line.
  • The exponent on V is a little above 2, so the rule of thumb holds: halve the speed and the squat falls to about a quarter.

Where she squats: bow or stern

  • A full-form ship, Cb above about 0.7, squats by the bow: the deepest point moves forward. A fine ship, Cb below about 0.7, squats by the stern. Near 0.7 she sinks about evenly.
  • This decides which draft meets the bottom first. On the UKC sum the deepest draft on arrival is the one that counts, and squat can move it to the other end of the ship.

Into the under-keel clearance

  • The next page works the UKC over a shoal: water over the patch minus ship in the water, where the ship in the water is the deepest draft plus squat. This page is where the squat figure comes from. Static UKC is depth plus tide minus draft; dynamic UKC takes the squat off it.
  • Squat is not the only allowance. Heel in a turn, a swell, the chart's own accuracy and silting each take their share, and the company's minimum UKC sits on top of all of them. Squat is the one you can change from the bridge.
  • The speed at which squat alone eats the whole static clearance is a useful number to have in your head before entering a channel: on the illustrative ship below it is about 14 kn.

Worked example

Illustrative example — the ship and the channel are not a real ship and not from the exam bank; the formulas are Barrass's, the numbers are ours.

Block coefficient Cb of the laden ship0.85
Speed through the water in the channel10 kn
Reduced speed to compare6 kn
Ship's breadth b42 m
Static mean draft T12.5 m
Channel width B (for a channel with sloping banks, the mean width, so that B × H is the real cross-section)200 m
Water depth H in the channel15 m
  1. Open water: 0.85 × 10² ÷ 100 = 0.85 mThe quick open-water line: the lower end of what to expect.
  2. Confined channel: 0.85 × 10² ÷ 50 = 1.7 mThe quick confined line: twice the open-water figure, the upper end.
  3. This channel: S = (42 × 12.5) ÷ (200 × 15) = 0.175; H/T = 15 ÷ 12.5 = 1.2, inside the fitted rangeHow much of the channel's section the ship fills; and a check that the general formula applies here.
  4. General formula at 10 kn: 0.85 × 0.175^0.81 × 10^2.08 ÷ 20 = 1.25 mThe general formula places this channel between the two quick lines.
  5. At 6 kn: 0.85 × 0.175^0.81 × 6^2.08 ÷ 20 = 0.43 m, about 0.35 of the squat at 10 knSlowing down gives most of the clearance back, because speed is squared.
  6. Dynamic UKC: (15 − 12.5) − 1.25 = 1.25 m at 10 kn; 2.5 − 0.43 = 2.07 m at 6 knWhat is really left under the keel while she moves, before the other allowances.

Answer1.25 m

Common mistakes

Using the open-water line, 0.85 m, in a channel.

With the banks close the water under her has nowhere else to go. The general formula gives 1.25 m here, the confined line 1.7 m. The open-water figure leaves 0.4 m of sinkage out of the UKC sum.

Working the squat with the speed over the ground.

Squat follows the water flowing past the hull. Stemming a 2 kn current at 8 kn over the ground, she squats as a ship doing 10 kn.

Treating the formula as the ship's own squat.

It is an estimate for a ship alone in steady water, fitted to a range of hulls. The ship's own squat tables and the pilot card, where they exist, come first; the formula is the check.

Note for mariners These are estimates for a ship alone in steady water; a bank, another ship, a swell or a turn each adds its own sinkage; the ship's squat tables, the pilot card and the company's UKC policy outrank the formula.

Sources C. B. Barrass, Ship Squat and Interaction (2009) and Barrass & Derrett, Ship Stability for Masters and Mates (squat chapter); PIANC Report 121 (2014), Harbour Approach Channels Design Guidelines; IMO Res. A.893(21), Guidelines for voyage planning