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Container ship underkeel clearance

This article is an abridged version of a report describing a set of measurements on container ships entering and leaving Hong Kong harbour. They form part of a larger data set of full scale measurements gathered by CMST to develop UnderKeel Clearance (UKC) predictions for ships in shallow water.

In February 2005 20 full-scale trials was undertaken on 16 deep-draught container ships entering or leaving Hong Kong harbour. The transit was effectively in calm water, with only small, short period waves present. The trials procedure and general dynamic draught calculations were described in Gourlay & Klaka (2007). In the trials, measurements were made of the vertical elevation of three points on each ship, using real-time kinematic GPS receivers measuring at 1 second intervals. By comparing the dynamic readings to stationary readings taken at the berth, the change in vertical position of the ship when under way (relative to the static position) could be determined. Corrections were made for the changing tide height and geoid undulation.

Ship dimensions
Table 1: Ship dimensions

Figure 1 shows the concept of dynamic sinkage and dynamic trim, as measured during the trials. The ship sinks down relative to the still water level when under way, due to its forward movement and environmental effects. Neglecting heel for the moment, the dynamic sinkage is characterized by a dynamic sinkage sfwd at the forward perpendicular, and dynamic sinkage saft at the aft perpendicular. The midship sinkage is then (saft + sfwd)/2. The static trim is (Taft – Tfwd), while the dynamic trim is ( saft – sfwd).

static ship
Figure 1: Ship in static floating position (grey outline) and under way (black outline). Dashed line shows undisturbed water level. Ship in static floating position has static draught at forward perpendicular Tfwd, and static draught at aft perpendicular Taft. Ship under way has dynamic sinkage at forward perpendicular sfwd, and dynamic sinkage at aft perpendicular saft.
 By measuring the vertical position of three points on the ship, and assuming the ship to be rigid, the vertical elevation results were used to calculate midship sinkage, dynamic trim and dynamic heel. Dynamic heel is here defined as the change in heel angle relative to the static floating position.

In practice, dynamic sinkage has steady and unsteady components. A steady midship sinkage and dynamic trim occur due to constant forward speed in constant water depth (commonly called ‘squat’). A steady breeze or a steady rate of turn can produce a steady heel angle. However, many unsteady effects on dynamic sinkage occur over varying time scales. Wave action, ship acceleration, depth changes, rudder movement and wind gusts all produce ‘unsteady’ effects on dynamic sinkage, which can be difficult to separate from the ‘steady’ effects.

For this reason, we shall leave the ‘steady’ and ‘unsteady’ components of vertical movement together, and make the following definitions:

  1. ‘Midship sinkage’ is the total downward displacement of the ship’s midships on the centreline, relative to the static floating position, at any instant in time. This includes the short-period midship oscillations commonly called ‘heave’.
  2. ‘Dynamic trim’ is the ship’s total change in trim (positive stern-down), relative to the static floating position, at any instant in time. This includes the short-period oscillations commonly called ‘pitch’.
  3. ‘Dynamic heel’ is the ship’s total change in heel (positive to starboard), relative to the static floating position, at any instant in time. This includes the short-period oscillations commonly called ‘roll’.

With these definitions, the dynamic sinkage of any point on the ship, relative to the still water level, is completely described by its midship sinkage, dynamic trim and dynamic heel at that instant. Adding the dynamic sinkage at each point on the ship to its static draught at that point, the dynamic draught at each point on the ship can be found, as described in Gourlay & Klaka (2007). The point on the hull with the largest dynamic draught is the part of the hull that is closest to the seabed at that instant, if the seabed is locally flat and horizontal. Therefore the overall dynamic draught, which is the largest value over all of the hull extremities, governs the net under-keel clearance and hence grounding risk. If the seabed is rocky or irregular, the point on the hull most likely to ground may not be the point with the largest dynamic draught. However in this case a conservative underkeel clearance calculation should use the minimum water depth in the area, combined with the dynamic draught as described above.

Theoretical predictions

The theoretical method used to compare against the measured midship sinkage and dynamic trim results is the Tuck (1966) method, modified slightly to cater to ships with transom sterns, as in Gourlay (2008). This method was developed for constant ship speed, in open water of constant depth. However for slowly-varying ship speed and/or water depth, the theory can be used as a quasi-steady theory, by applying the ship speed and water depth at any instant through the transit. Full unsteady versions of the same method do exist (see e.g. Plotkin 1976, Gourlay 2003), but are limited to simple depth profiles and hull shapes. The required inputs for the theoretical predictions were.

  • Ship hull offsets
  • Ship speed through water
  • Water depth profile


Measured and predicted midship sinkage for an example transit, together with measured speed over ground and calculated water depth, are shown in Figure 2. The measured sinkage is unfiltered. As discussed in Gourlay & Klaka (2007), the RMS error in absolute midship sinkage is around 0.05m, mostly due to uncertainty in the static reading. The short-period random GPS error is around 0.01 to 0.02m. Oscillation amplitudes are typically around 0.02 to 0.03m.The measured results show the effect of speed and water depth on midship sinkage. Given that the transit involves significant speed changes and depth changes, the overall performance of the theoretical method is quite good.

predicted sinkage
Figure 2: Measured and predicted midship sinkage (positive downward). Corresponding water depth at midships and speed over ground also shown.

Measured and predicted dynamic trim for the three example transits are shown in Figure 3. Short-period random GPS error are around 0.015 to 0.03m, and absolute RMS error around 0.07m. The measured dynamic trim is positive (stern-down). If we study the dynamic trim plots, we notice that some large changes in dynamic trim occur in regions of near-constant speed and water depth. Detailed analysis of the trials data showed that the cause of these changes is the ship’s rate of turn.

dynamic trim
Figure 3: Measured and predicted dynamic trim (positive stern-down). Corresponding water depth at midships and speed over ground also shown.


The Tuck method predicts midship sinkage with reasonable accuracy for moderate speed and depth changes, but unsteady effects are also important when speed or depth changes are abrupt. The prediction of dynamic trim was more approximate, due to the sensitivity of the theory (and the actual flow) to the longitudinal hull volume distribution. Nevertheless, the general dependence of dynamic trim on speed and water depth was confirmed by the measurements. Like midship sinkage, unsteady effects on dynamic trim were seen to be important when speed or depth changes were abrupt. The large rate of turn experienced by the ships during this transit gave an opportunity to study dynamic heel, which is an important component of dynamic draught for container ships. Heel angles in the order of 1o to 2o were measured, and the heel angles were reasonably well predicted by the quasi-steady turning and wind formulae.

The turning manoeuvres also allowed identification of an important dynamic draught effect, namely the increased stern-down trim with rate of turn. Since the stern is the point on the hull which normally comes closest to the seabed, this increase in stern-down trim translates into a decrease in under-keel clearance, and should be allowed for accordingly.


We acknowledge the support of the Hong Kong Marine Department in providing funding and assistance with this research, as well as A.P. Moller-Maersk for providing access to the ships for the measurements, and their corresponding basic hull data. The co-operation of the Hong Kong Pilots’ Association in arranging and performing transits is also greatly appreciated.


  • Gourlay, T.P. & Klaka, K., Full-scale measurements of containership sinkage, trim and roll, Australian Naval Architect, Volume 11, No. 2, pp 30-36, 2007.
  • Gourlay, T.P., Ship squat in water of varying depth, International Journal of Maritime Engineering, Volume 145, Part A1, pp 1-12, 2003.
  • Plotkin, A. The flow due to a slender ship moving over a wavy wall in shallow water. Journal of Engineering Mathematics, Volume 10, No. 3, pp 207-218, 1976.
  • Tuck, E.O. Shallow water flows past slender bodies. Journal of Fluid Mechanics, Volume 26, pp 81-95, 1966.