Ship Squat: Shallow-Water Sinkage and UKC

The physics of squat

Ship squat describes two coupled effects that reduce under-keel clearance (UKC) when a vessel is underway in shallow or confined water: a bodily sinkage (the hull drops uniformly) and a running trim (the vessel pitches bow-down or stern-down depending on hull form). Both effects share the same root cause.

When a ship moves through unrestricted deep water, the water displaced ahead of the bow flows freely around and under the hull. In shallow water, the gap between keel and seabed is small; the water that must flow aft to fill the space vacated by the advancing hull is forced through a restricted cross-section. In a canal with parallel banks, lateral flow is also restricted. By the continuity equation, a fixed volume of water passing through a smaller cross-section must move faster. Bernoulli’s principle links that higher velocity to a lower static pressure. The pressure depression extends along the bottom and sides of the hull, reduces the buoyant support the water provides, and the vessel sinks until hydrostatic equilibrium is restored at a deeper draught. That increment of sinkage at the most submerged point of the hull is the squat.

The trim component arises because the pressure depression is not uniform along the ship’s length. For full-form vessels (block coefficients above roughly 0.75, typical of VLCCs, large bulkers, and fully loaded container ships), the pressure is lower under the bow than the stern, so the bow sinks more and the vessel trims by the head. For finer-form vessels such as naval ships, ferries, and cruise liners, the stern often develops the greater depression and the vessel trims by the stern. The distinction matters operationally: the location of maximum squat determines where grounding first occurs.

Return flow and the blockage factor

The key physical quantity is the blockage ratio $S$, defined as:

where $A_m$ is the midship cross-sectional area of the hull below the waterline and $A_c$ is the cross-sectional area of the navigable channel. In deep open water $A_c$ is effectively unlimited and $S \approx 0$; squat exists but is small. In the Suez Canal at design draught, a large container ship presents a blockage ratio of roughly 0.10 to 0.15; in the older Suez channel during the ICORELS-era studies the figure reached 0.25 for the largest vessels then permitted. In lock chambers the ratio can approach 0.35 to 0.40. Squat scales steeply with $S$: doubling the blockage ratio more than doubles the squat at the same speed.

The Barrass (1979, 1995) empirical work quantified this with a canal factor. For open shallow water (the hull can displace water laterally without bank confinement), the Barrass formula gives:

where $S_{max}$ is the maximum squat in metres, $C_B$ is the block coefficient (dimensionless), and $V$ is the speed through water in knots. In a confined canal where lateral displacement is prevented:

The canal factor $k_{canal} = 2$ doubles the estimated squat relative to open shallow-water operation. The site’s companion Squat (Barrass) calculator implements this formula directly. Use the Under-Keel Clearance calculator to apply the squat result to a full UKC budget.

The depth Froude number and critical speed

A second governing parameter is the depth Froude number $F_{nh}$:

where $V$ is the ship’s speed through water (m/s), $g$ is gravitational acceleration (9.81 m/s$^2$), and $h$ is the water depth (m). This dimensionless ratio compares the ship’s speed to the speed of long free-surface gravity waves in water of depth $h$. When $F_{nh} = 1.0$, the vessel is moving at the theoretical wave speed for that depth: this is the critical speed. The physics changes qualitatively as $F_{nh}$ approaches 1.0.

In practice:

• Below $F_{nh} \approx 0.4$: subcritical regime; squat exists but grows slowly with speed.
• $F_{nh}$ between 0.4 and 0.7: squat accelerates with speed; this is the range in which most canal and approach-channel speed limits operate.
• $F_{nh}$ between 0.7 and 1.0: squat rises steeply; resistance also increases sharply (the Schlichting shallow-water resistance correction applies, see Schlichting shallow water resistance calculator); wave-making resistance dominates and steering effectiveness declines.
• $F_{nh}$ approaching 1.0: near-critical region; squat can be several times the subcritical value; wave patterns are highly nonlinear and largely unpredictable from simple empirical formulae.

A 300-metre container ship in 15 m of water hits $F_{nh} = 0.4$ at about 8.5 knots. The same vessel in 12 m of water hits the same Froude number at 7.6 knots. Operational speed limits in confined channels map consistently to the 0.40 to 0.55 range of $F_{nh}$.

The Tuck (1966) slender-body derivation, implemented in the Tuck effect shallow-water suction calculator, provides a theoretical foundation for the speed-depth interaction that the purely empirical Barrass formula captures only approximately.

Empirical squat formulae compared

Several research groups and bodies have published empirical or semi-empirical squat predictions. The main families differ in derivation basis, input requirements, and the conditions under which they were validated.

Barrass (1979, 1995)

C. B. Barrass derived his formula from full-scale observations and model-test correlations spanning a range of merchant ship types. The formula requires only $C_B$ and $V$, which makes it the default choice for quick pilot-card calculations. Its limitation is that it does not explicitly model depth: the formula assumes the vessel is already in the shallow-water regime where the depth effect is strong, and it does not vary with the $h/T$ ratio. For operations in very shallow water (h/T below 1.2) or in very deep tidal approach channels where the depth effect is small, the formula can misrepresent the gradient.

The 1995 revision by Barrass introduced the blockage factor $S_C$ more formally, yielding a formula of the form $S_{max} = C_B \cdot S_C^{0.81} \cdot V^{2.08} / 30$, where $S_C$ is the ratio of the ship’s submerged cross-section to the channel cross-section. This form is more accurate for intermediate confinement conditions.

Huuska and Guliev (ICORELS method)

The ICORELS (International Commission for the Reception of Large Ships) formula, published in the 1980 WG IV report and later refined by Huuska (1976) and Guliev (1971), is based on the ratio of displaced volume to channel geometry:

where $\nabla$ is the displaced volume (m$^3$), $L_{pp}$ is the length between perpendiculars (m), $F_{nh}$ is the depth Froude number, and $C_s$ is a coefficient (2.4 for the basic Huuska form). The explicit $F_{nh}$ term means squat rises sharply as the depth Froude number approaches 1.0, consistent with the physics. The ICORELS/Huuska method is generally more conservative (higher squat estimates) than the basic Barrass formula, particularly at higher Froude numbers, and is the preferred method in several European port authorities’ UKC policies.

Yoshimura (1986)

Yoshimura derived a formula focused on bow squat in full-form vessels. It takes the form:

The Yoshimura formula is well-validated for VLCCs and large bulkers with $C_B$ above 0.75 and is used by the Japan Ship Research Institute as a benchmark.

Tuck (1966) and slender-body theory

Tuck’s slender-body derivation from first principles of shallow-water wave theory produces a sinkage formula:

The Tuck approach is valuable because it shows explicitly why squat diverges as $F_{nh} \to 1$: the denominator $\sqrt{1 - F_{nh}^2}$ goes to zero. The Tuck effect calculator on this site lets users explore this speed-depth relationship. Tuck’s theoretical framework underpins later work by Gourlay (2006, 2008) that uses thin-ship theory for arbitrary hull forms with free-surface methods.

PIANC WG 121 recommended practice

PIANC Report No. 121 (2014), the definitive design reference for harbour approach channels, does not endorse a single formula. Instead, it specifies a hierarchy:

1. For preliminary channel design and quick operational checks: use Barrass (1979) with the appropriate canal factor, accepting that the method has ±30% uncertainty.
2. For detailed channel design and for new vessel classes not covered by existing empirical databases: use the Huuska/ICORELS method or a regression formula matched to the vessel type (Yoshimura for full-form, Tuck-based for finer forms).
3. For high-value decisions such as authorising a new vessel class to use an existing channel at draught: commission model tests or CFD with free-surface modelling.

The PIANC WG 171 (2019) update on approach-channel guidelines reinforces this hierarchy and adds guidance on applying modern CFD outputs to UKC budget calculations.

Summary comparison

Under-keel clearance management

Static versus dynamic UKC

The static UKC is the vertical distance between the lowest point of the hull at rest and the charted bottom depth, corrected for tide. When the vessel is moving, the effective clearance is the dynamic UKC, which is always smaller. The full dynamic UKC budget set out in PIANC WG 121 is:

where $h_{tide}$ is charted depth plus predicted tidal height, $T_{static}$ is the vessel’s draught at rest, $\delta_{squat}$ is the squat allowance at the planned transit speed, $\delta_{wave}$ is the wave-induced sinkage (parametric roll contributes here too for wide-beam container ships), $\delta_{heel}$ is the sinkage at the lowest bilge from static or dynamic heel, $\delta_{density}$ is the draught correction from salinity change (estuarine approaches), $\delta_{survey}$ is the bathymetric survey uncertainty, and $\delta_{safety}$ is the net safety margin. The Under-Keel Clearance calculator on this site implements this budget structure.

In practice, squat is the largest single variable component of the dynamic UKC budget for a vessel transiting a shallow channel at service speed. A Capesize bulker ($C_B = 0.84$, $V = 12$ knots) in open shallow water develops a Barrass squat of $0.84 \times 12^{2.08} / 30 \approx 0.84 \times 156 / 30 \approx 4.4$ m. That is larger than the wave sinkage allowance, the density allowance, and the survey uncertainty combined for a well-maintained channel. Getting the squat figure right is the primary UKC modelling task.

The $h/T$ ratio and depth regimes

The depth-to-draught ratio $h/T$ is the most direct indicator of shallow-water severity:

• $h/T > 4$: effectively deep water; shallow-water effects on squat are negligible.
• $h/T$ between 2.0 and 4.0: transitional; modest squat corrections needed.
• $h/T$ between 1.5 and 2.0: shallow water; standard empirical formulas apply; squat is the dominant UKC variable.
• $h/T$ between 1.1 and 1.5: very shallow; non-linear effects grow; Barrass accuracy degrades; model tests or CFD recommended.
• $h/T$ below 1.1: extreme shallow; the formulae diverge; operations require specialised studies; most conventional port approaches do not permit $h/T < 1.1$.

Most commercial deep-draught port approaches are designed for $h/T$ at high water between 1.15 and 1.30 at the design vessel’s maximum authorised draught. A VLCC entering Rotterdam Europoort at 21 m draught in a channel dredged to 24.5 m has $h/T \approx 1.17$ at low water.

Tidal window management

For any approach where $h/T < 1.2$ at the prevailing tidal stage, the port authority typically publishes a tidal window: the band of time around high water during which the vessel’s draught combined with predicted squat leaves an acceptable dynamic UKC. The tidal window narrows as the vessel deepens or the channel shoals between maintenance dredging cycles. Rotterdam, Hamburg, Antwerp, and many bulk terminal berths operate on published tidal windows that are recalculated for each vessel call using the authorised draught and recent sounding data.

The tide-gauging accuracy matters here. A 0.2 m error in the predicted tidal height translates directly to 0.2 m of UKC error. Modern ports supplement standard tide predictions with high-frequency (typically 6-minute) real-time tide gauge data and, in some cases, real-time water-level assimilation models.

Speed as the primary control variable

Because squat scales roughly as $V^2$, speed reduction is the most effective operational lever. A 10% speed reduction cuts squat by about 19%; a 30% reduction cuts it by nearly half; a 50% reduction cuts it to about 25% of the original value. PIANC WG 121 states that for a vessel with adequate UKC at low speed but insufficient UKC at full speed, the primary intervention should always be speed reduction before any consideration of draught reduction, because draught reduction requires cargo discharge or ballasting that takes many hours.

This is the physics behind every shallow-water speed limit: the Suez Canal’s vessel-specific speed allocations, the Kiel Canal’s 8.1-knot maximum, the Panama Canal’s 8-knot limit in the original locks, the Saint Lawrence Seaway’s 13-knot limit, and the Mississippi River’s 6 to 12-knot sections all correspond to $F_{nh}$ values in the 0.40 to 0.60 range, where squat is controllable but not negligible.

Squat in practice: canal and channel conditions

Open shallow water versus confined channel

The character of squat changes between a wide shallow shelf and a narrow canal dredged below the surrounding bed. In open shallow water, the vessel can displace water laterally; the effective channel cross-section is large; the blockage ratio is low. In a rectangular canal (the Suez Canal is roughly this shape), the channel cross-section is fixed; the blockage ratio rises steeply as draught increases; the return flow velocity is higher for the same ship speed; and the pressure drop under the keel is greater.

The critical operational difference is that the Barrass canal factor doubles the predicted squat at the same speed. A pilot transiting a dredged approach channel flanked by shallow shoals is in an intermediate condition: the effective channel width for return-flow purposes may be somewhere between the canal and open-water limits. Channel authorities address this by prescribing which formula and which canal factor to use for a given channel geometry, based on calibration studies.

The blockage ratio in major waterways

Published blockage ratios from channel design studies give a sense of scale:

• Suez Canal (pre-2015 expansion): up to 0.14 for a Suezmax tanker at maximum authorised draught.
• Suez Canal (post-2015 new channel section): 0.08 to 0.10 for the same vessel.
• Kiel Canal: up to 0.12 to 0.15 for Panamax dry bulk vessels.
• Houston Ship Channel (dredged to -15.2 m): up to 0.10 for a laden Aframax.
• Saint Lawrence Seaway (dredged to -8.2 m): up to 0.20 for a fully laden Seaway-max bulker.

The Saint Lawrence Seaway figure explains why the speed limit there is relatively conservative: a blockage ratio of 0.20 puts significant squat even at modest Froude numbers.

Bank effects compounding squat

In channels where the vessel is not centred between banks of equal depth, the asymmetric return flow adds a yaw component. The pilotage operations article covers bank effects in detail; the squat interaction is worth noting here. When a vessel experiences bank suction (the stern is drawn toward the bank by the low-pressure zone), the pilot typically compensates with rudder. Rudder action at speed increases resistance and changes the stern wake, which can alter the local squat distribution. In very confined channels, bank suction and squat together account for the majority of grounding-precursor incidents.

How trim affects squat in channel passage

A vessel with a pre-existing aft trim (heavier at the stern) may enter a shallow channel with the stern closer to the bottom than the bow. For a full-form vessel that develops bow squat, the running trim by the head means the bow sinks further while the stern may rise slightly; the net effect on stern clearance can be favourable. The trim and list article discusses the relationship between static trim and keel-to-bottom clearance. The trim optimisation article covers how operators use ballasting to optimise trim before a shallow approach.

Squat in accident investigations

QE2 grounding (1992)

The RMS Queen Elizabeth 2 grounded on Cuttyhunk Ledge off Martha’s Vineyard on 7 August 1992 while transiting at approximately 25 knots in water shallower than her charted safe-water route. The US National Transportation Safety Board investigation found that the vessel’s high speed in the area significantly increased her squat: at 25 knots in approximately 10 m of water, $F_{nh}$ was above 0.7, placing the vessel in the rapidly rising part of the squat curve. The grounding damaged approximately 30 m of the keel plating and cost over USD 13 million in repairs. The investigation contributed to the modern practice of verifying squat at multiple waypoints during voyage planning, not only at the shallowest nominated point.

Ever Given (Suez Canal, March 2021)

The Ever Given (20,388 TEU, 400 m length, 58.8 m beam, $C_B \approx 0.65$) grounded on the eastern bank of the Suez Canal on 23 March 2021 during a sandstorm with gusts measured at 74 km/h. The SCA preliminary investigation and the Japanese Maritime Accident Investigation Commission report noted that the vessel had reached approximately 13.5 knots immediately before grounding. In the Suez Canal at that draught and speed, $F_{nh}$ was near 0.45, giving a Barrass squat of approximately 0.65 × 13.5^{2.08} / 30 × 2 ≈ 0.65 × 209 / 30 × 2 ≈ 9.1 m. While the main factor was wind-induced yaw that overwhelmed the vessel’s available steering moment, the shallow-water depth effect on rudder effectiveness (rudder performance degrades at high $F_{nh}$) meant that the pilot’s corrective rudder commands produced less yaw response than at the same speed in deep water. The incident is studied in marine voyage planning courses as a case of compound shallow-water effect: squat, reduced steering margin, and wind loading interacting simultaneously.

Grounding patterns in bulk terminal approaches

The Australian Maritime Safety Authority (AMSA) and the UK MAIB have both documented patterns of shallow-water groundings at coal and iron-ore terminals where the authorised draught was calculated using optimistic squat estimates. In a 2019 MAIB investigation of a bulk carrier grounding at a tidal berth in the Humber, the vessel’s onboard squat calculation used the open-water Barrass formula when the confined-channel formula with $k_{canal} = 2$ was appropriate for the approach geometry. The resulting 0.6 m underestimate of squat was the proximate cause of contact with the bottom on the approach leg. This incident is the operational argument for having pilots verify which squat formula applies to each waterway, not defaulting to the simplest version.

IMO and PIANC guidance on UKC

IMO MSC.1/Circ.1228

The IMO’s Revised Guidance to the Master for Avoiding Dangerous Situations (MSC.1/Circ.1228, 2007) addresses squat-related risk indirectly through its framework for assessing vessel capability against environmental conditions. While the circular is primarily aimed at heavy weather, SOLAS chapter V regulation 34 on voyage planning requires that planning accounts for all hazards to navigation, including those arising from the interaction of vessel speed and water depth. Port state control inspections under the Paris and Tokyo MOUs have used SOLAS V/34 as the basis for deficiency citations where a vessel’s passage plan did not account for squat at the nominated speed through a shallow-water area.

PIANC WG 121: the design standard

PIANC Report No. 121 (2014) is the primary international design reference for approach channels. It sets out the UKC budget methodology described above and specifies:

• The minimum gross UKC (before squat and other dynamic allowances) should be the larger of 0.5 m and 5% of draught in open coastal approaches, and 1.0 m in ports.
• Net UKC (after all dynamic allowances including squat) should not be less than 0.3 m at any point.
• Squat should be calculated for the maximum authorised speed in each channel section, not for the minimum speed.
• For channels used by vessels of $h/T < 1.20$, the squat calculation method and any speed restrictions must be documented in the channel authority’s port regulations.

The report also provides a risk-matrix approach for deciding when CFD or model tests are warranted instead of empirical formulae: large vessels with a novel hull form in a channel with $h/T < 1.15$ and blockage ratio above 0.10 trigger a mandatory detailed study under the PIANC framework.

PIANC WG 171 (2019)

The 2019 update on approach-channel EMS (Environmental Management System) guidelines introduced requirements for monitoring the actual UKC experienced by vessels in real time and comparing it to the predicted value. Several advanced ports (Rotterdam, Hamburg, Antwerp, and the Port of Los Angeles) have installed bottom-clearance monitoring systems on key approach segments that measure the actual passing clearance of each vessel and flag cases where the measured clearance is below the predicted minimum. These measured datasets are being used to refine the empirical squat coefficients for specific channel-vessel combinations.

Operational mitigation

Speed limits and pilot orders

Channel speed limits are the primary regulatory control. Beyond the authority-mandated limit, individual pilots routinely reduce speed further when conditions warrant: a following current that effectively raises the vessel’s speed over the ground at the same speed through water; a vessel approaching maximum authorised draught; a recently shoaled section between dredging cycles; or limited visibility that requires more time to detect and respond to hazards. The pilotage operations article describes how pilots build speed margins into their planning.

Draught management

A 0.5 m reduction in draught (achieved by partial fuel discharge, ballasting, or cargo adjustment) reduces the blockage ratio by roughly 2 to 4% for a typical large vessel, reduces $T/h$ by approximately 0.03 to 0.05, and may move the vessel from an $h/T$ below 1.20 to above 1.20, crossing the threshold where many port authorities require detailed squat studies. Draught management before a shallow-water approach is standard practice for VLCCs and large Capesize bulkers.

The square-law rule of thumb

Every pilotage training programme teaches the square-law relationship between speed and squat. If a vessel has 0.8 m of squat at 12 knots, reducing speed to 8.5 knots (a 29% reduction) cuts squat to approximately $0.8 \times (8.5/12)^{2.08} \approx 0.4$ m: half the original value. Halving the speed from 12 to 6 knots reduces squat to $0.8 \times (6/12)^{2.08} \approx 0.19$ m: less than one-quarter. This is the practical case for a slow-speed approach when UKC is tight.

Tide planning and contingency water

When the tidal window provides at least 0.5 m more water than the strict minimum UKC budget, the pilot has a speed margin: the vessel can move faster without breaching the minimum net UKC. When the tide is at or below the threshold, the pilot must operate at the speed for which the squat budget just fits. The marine voyage planning and routing article covers the integration of tide, sounding, and squat data in modern ECDIS-based passage planning.

Shallow-water resistance and power

As $F_{nh}$ rises through 0.4 to 0.7, the wave-making resistance increases significantly beyond the deep-water value. The Schlichting correction (1934) provides a practical estimate of the speed reduction in shallow water at constant power: a vessel making 12 knots in deep water may make only 10.5 to 11 knots at the same shaft power in 15 m of water, even before propeller loading changes. This speed reduction partially self-limits the squat: the vessel cannot easily maintain its deep-water speed in shallow water without substantial additional power. The Schlichting shallow water resistance calculator and the ship resistance and powering article cover this interaction.

Squat and hull form

Block coefficient: the primary hull factor

The block coefficient $C_B$ appears linearly in the Barrass formula and in most other empirical squat equations because a fuller hull displaces more volume per unit length, generating a stronger pressure signal. A fully laden VLCC with $C_B = 0.84$ at 10 knots produces roughly 30% more squat than a container ship with $C_B = 0.65$ at the same speed in the same channel. The block coefficient and naval architecture coefficients articles explain how $C_B$ relates to the other hull form parameters.

Bulbous bow interaction

A bulbous bow that projects forward of the bow stem sits at or below the forward perpendicular waterline and can descend below the keel plane of the vessel at the bow. In shallow water, if the bulb is already close to the bottom, squat brings the tip of the bulb into very close proximity with the seabed even before the main keel touches. CFD studies for several very large container ships operating in 14 m dredged channels have shown that the bulb tip can experience a clearance 0.3 to 0.5 m less than the mid-keel clearance at the same draught. Pilots of large container ships routinely account for this: the authorised draught at many terminals is set for the bulb tip, not the keel midships.

Propeller loading in shallow water

The propeller operates in the accelerated flow field at the stern. In shallow water, the accelerated return flow that causes squat also affects the wake fraction experienced by the propeller. At high $F_{nh}$, the propeller operates in a higher-velocity inflow, reducing the effective angle of attack on the blade sections, tending toward lower thrust at constant RPM, and requiring the master to increase RPM to maintain speed. Higher RPM increases the propeller’s contribution to the local pressure field at the stern, which can modestly reduce stern squat. The net effect is complex enough that propeller-stern interaction in shallow water is a distinct area of research within the ship resistance and powering field.

Bank effect and ship-to-ship interaction in confined water

Squat rarely acts alone. The same accelerated return flow that lowers the hull in shallow water becomes asymmetric the moment a vessel runs off the channel centreline or passes close to another ship, and the resulting lateral forces compound the hazard that squat creates.

When a vessel tracks closer to one bank, the flow between hull and bank speeds up and its pressure falls, drawing the stern toward the near bank while the higher-pressure water at the bow pushes the bow away. This bank-suction and bank-cushion pair generates a bow-out yawing moment that the helmsman must correct with helm toward the near bank, a counter-intuitive demand that has contributed to groundings in narrow approaches. The effect grows with speed, with proximity to the bank, and as under-keel clearance shrinks, which is precisely when squat is already largest.

Passing and overtaking in shallow channels produce the same physics between two hulls. As ships pass, the pressure fields interact: an initial bow-to-bow repulsion is followed by a strong attraction amidships and a yawing moment as the sterns draw level. In confined water these interaction forces are far larger than in deep open water because the displaced water cannot escape downward or sideways. The standard mitigations mirror those for squat: reduce speed, because both squat and interaction forces scale roughly with the square of speed, and hold the planned track with adequate passing distance. Pilots manage squat, bank effect, and interaction as one combined shallow-water problem rather than as separate phenomena.

Limitations of empirical squat methods

The empirical squat formulae described above carry significant uncertainty when applied outside their calibration range. Practitioners should be aware of the following constraints.

Vessel geometry bounds. Barrass (1979) was calibrated on merchant ships with $C_B$ between 0.55 and 0.85, $L_{pp}$ between 80 and 350 m, and speeds below 18 knots. Container ships above 20,000 TEU ($L_{pp}$ above 370 m, $B > 55$ m) and LNG carriers with distinctive hull forms may fall outside this range. The formula does not include $L/B$ or $B/T$ as explicit parameters, so it cannot distinguish between a wide shallow-draught vessel and a narrow deep-draught vessel with the same $C_B$.

Channel irregularity. The formulas assume a regular rectangular or trapezoidal channel cross-section of constant depth. In reality, approach channels have sloping side-slopes, varying depths along the axis, and dredged borrow areas adjacent to the track. These irregularities change the effective blockage ratio in ways the simple formula does not capture. The PIANC WG 121 guidance addresses this through equivalent channel dimensions, but the correction is a further approximation.

Speed transients. The formulas predict steady-state squat at a constant speed. A vessel decelerating on approach produces a time-varying squat that lags the instantaneous speed. The lag time is on the order of the vessel’s length divided by speed: for a 300 m vessel at 8 knots, the transient lasts roughly 70 seconds. During deceleration, the squat may temporarily exceed the steady-state value for the current speed if the vessel was faster moments before.

Current and tidal stream interaction. The relevant speed for squat is the vessel’s speed through the water, not over the ground. In a flood current of 2 knots, a vessel making 10 knots over the ground is doing 8 knots through the water (if heading against the current) and the squat is calculated on 8 knots. Conversely, going with a 2-knot current at 10 knots over the ground gives 12 knots through the water and substantially higher squat. Pilots in strongly tidal channels explicitly account for this when setting speed orders.

Formula scatter. The six published empirical methods can produce squat estimates that differ by 30 to 50% for the same input conditions. PIANC WG 121 acknowledges this scatter and recommends using multiple methods and taking the more conservative estimate for safety-critical channel design decisions.

Post-grounding investigation accuracy. In accident investigations, squat is often reconstructed from the vessel’s recorded speed and the charted depth. Both values carry uncertainty: the speed log measures speed through water with 2 to 5% accuracy; the charted depth may be from a survey that is months or years old. The reconstructed squat figure therefore has uncertainty of 10 to 20%, which means accident analysis can rarely pinpoint squat as the sole cause. This is a limitation of the forensic use of the formulas as much as the formulas themselves.

See also

Navigation and operations

• Marine voyage planning and routing
• Pilotage operations
• Ship motions
• AIS and ECDIS
• Just-in-time arrival
• Weather routing

Naval architecture

• Block coefficient
• Naval architecture coefficients
• Hull form design
• Trim and list
• Trim optimisation
• Ship resistance and powering
• Bulbous bow retrofits
• Hydrostatics and Bonjean curves
• Metacentric height
• Freeboard and reserve buoyancy
• Rudder and steering systems

Calculators

• Squat (Barrass)
• Tuck effect: shallow-water suction
• Under-Keel Clearance (UKC)
• Schlichting shallow water resistance