Interaction of seagoing ship / tidal fairway: ship-generated loading

The change in draught- and speed-related ship-induced loading on the shipping routes entails a definition of the characteristic parameters (e.g. ship wave system, displacement current) and requires knowledge of the functional relationships (e.g. ship speed and vessel width, shipping channel conditions, passing clearance). Picture 1 shows a diagram of the ship wave system among others.

Since the start of the new century, a large number of analytical and empirical methods have been developed for calculating the interaction of ship and waterway. Initial calculations with hydrodynamic-numerical models reveal deviations compared to the results of hydraulic scale models, so that these numerical models cannot yet be viewed as a confirmed scientific aid for determining upgrading-related changes to ship-induced loading in shipping channels. At the moment, it is only possible to make confirmed quantitative predictions of ship-induced loadings in inhomogeneous waterways by means of hydraulic model tests in a scientifically confirmed model scale (state-of-the-art engineering and science).

In recent years, the BAW Hamburg office has looked at the issue of the interaction between seagoing ship and tidal fairways both with studies on hydraulic models and with field study measurements. More information can be found under BAWiki.

Definition of the characteristic parameters:

When a ship moves through the water, wave systems of differing periods are generated at the bow, stern and alongside the ship as a result of the displacement current and the changes in pressure and water level. The ship wave and current system when passing through channels e.g. in an estuary in the sub-critical speed range (ship speed less than the wave propagation velocity) is characterized by the following:

  • the bow swell (sB) directly at the body of the ship,
  • the water level depression (zA) to the side of the ship,
  • the stern wave (HP) as part of the long-period primary wave system,
  • the secondary waves (HS) superimposed on the primary wave system,
  • the simultaneously occurring return current (vR).

The changes in water level in shipping channels of restricted depth and width, as the wave pattern seen by a viewer on the bank, are shown as a side view in superelevation.

Functional relationships:

The magnitudes of the water level fluctuations and currents generated by moving ships are a function of:

  • the ship speed vS and the passing clearance L
  • the ship's dimensions (length l, width b, draught t, submerged main section AS)
  • total resistance of the ship (ship's shape) in the canal RT,K
  • the shipping channel conditions (water level B and bed width BS, water depth h, transverse profile and shape A, bank shape and embankment slope 1 : m)
  • current conditions in the waterway
  • other influences such as curvature, propulsion type, water density

The key parameters for ship-induced loading on shipping channels have transpired to be:

  • the ship speed (vS)
  • the passing clearance (L) from the bank which determines the hydraulically relevant partial cross-section (AT),
  • and the ratio of total water depth to submerged depth (h/t), with AT the partial cross-section ratio AT / 0,5 AS.

In simplified terms, the physical processes involved when a ship passes through inhomogeneous waterways (or is not travelling in the middle) are explained by the fact that the ship divides the waterway into two partial sections AT1 and AT2, where half the displacement volume is conveyed past the ship in each case. The different partial cross section ratio AT1 / 0,5 AS and AT2 / 0,5 AS results in quantitatively unequal ship-induced loading at the corresponding sections of the bank.

Analytical and empirical methods:

While the water level depression zA is calculated primarily by analytical derivations (see also Krey, 1913; Constantine, 1960; Bowmeester et al, 1977; Führböter; 1982), the computing methods for determining wave height can also be derived empirically using model studies and/or field study measurements (see also Römisch, 1969). While some empirical methods take account of the short-period secondary waves, it is not known in detail what function the described parameters have as they are generated by the differing distribution of pressure at the body of the ship depending on ship speed and particularly on the ship's shape.

The following relationships are determined in simplified from professional literature for the sub-critical speed range in which commercial shipping travels for economic reasons (about vS <0,9·[g·d]0,5):

  • water level depression and wave height
  • zA prop. vS k whereby 2 < k <3,5
  • zA prop. nk whereby -1,5 < k < -1
  • return current velocity
  • vR prop. vS
  • vR prop. n-1

Picture 3 shows the range of possible calculation results for the marginal conditions of a measured cross section on the Lower Elbe compared to measured values from hydraulic model of the BAW office in Hamburg.

In order to predict ship-induced loading in inhomogeneous shipping channels, wave propagation processes such as refraction and shoaling play a major role in the generation of waves and currents in addition to the interaction of ship and waterway, so that these physical processes have to be included in the calculation (without parameter configuration).

The traditional empirical and analytical models only offer what it is in quantitative terms a highly inadequate estimation of ship-induced loading from large sea-going vessels on the large inhomogeneous shipping channels and particularly in tidal areas. Consequently, these methods cannot be used for theoretical determination of future loading.

Computational calculations of ship hydrodynamics

Hydrodynamic numerical methods – History

In the early 1990s, it was possible using the available computer hardware and processed forms of the BOUSSINESQ equations (Nwogu 1993)1 to simulate phenomena such as ship waves in water of limited depth and width including the wave propagation processes of refraction, shoaling, diffraction and reflection as well as current refraction, squat and trim – initially for sub-critical travel. Initial comprehensive calculations using the WAKE2D program of the National Research Council of Canada – Canadian Hydraulic Center (NRC-CHC 1997)2 were carried out on behalf of the BAW office in Hamburg during studies on the Lower Elbe. The computed results using WAKE2D revealed, among other things, a tendency to drastically overestimate the short-period waves compared to the values measured on the hydraulic model.

Other theoretical numerical methods for the current flowing around ships, such as FANKAN (Fluid-Automaten-Netz für Kanäle für völlige Schiffe; Pagel and Führer 1989)3 had not been developed in such a way as to permit adequately precise discretisation of the hydrodynamically optimised form of seagoing ships (bulbous bow) and therefore distorted the dynamic loading on shipping channels.

Initial trial calculations with another model called SHALLOWTANK (Chen 1998)4 (Chen and Uliczka 1999)5 showed qualitatively – and, to a certain extent, also quantitatively – good correspondence with the measured results obtained during trials with the hydraulic model in the Hamburg office of BAW-DH. The SHALLOWTANK computing method has also already been used to calculate ship-induced loading for trans-critical and super-critical ship speeds (Chen 1997)6. Following further necessary verification calculations and after submission of a validation document, it was considered conceivable at the time to use this program to look at issues of ship-induced loading in inhomogeneous waterways.

Although numerical processing (e.g. with WAKE2D or SHALLOWTANK) constituted state-of-the-art research in the late 1990s, it was not deemed a scientifically undisputed aid for dealing with the task of the interaction of seagoing ship and tidal fairways.

At the time, it was only possible to make confirmed quantitative predictions of ship-induced loadings in inhomogeneous waterways by means of hydraulic model tests in a scientifically confirmed model scale (state-of-the-art engineering and science) – and to an extent this is still true today.


1 Nwogu,O.,Alternative form of Boussinesq equation for nearshore wave propagation, J. of Waterway, Port, Coastel and Ocean Engineering, Vol. 119, No. 6, ASCE, USA, 1993

2 NRC-CHC, Numerical Model Study of Ship-Induced Waves und Currents in the Elbe Estuary, Controlled Technical Report, HYD.CTR-093 (unveröffentlicht), Ottawa, Canada, 1997

3 Pagel, W und Führer, M., Umströmungs- und Widerstandsverhalten völliger Schiffe bei Kanalfahrt. Ergebnisse einer diskreten Modellierung und ihrer experimentellen Verifizierung, Mitteilungen der Forschungsanstalt für Schiffahrt, Wasser- und Grundbau, Schriftenreihe Heft 3, Berlin, 1989

4 Chen.X.-N., Schiffswellenbildung über einer querveränderlichen Topographie, Abstracts - 19. Duisburger Kolloquium Schiffstechnik/ Meerestechnik, Das Schiff für überkritische Fahrt, Duisburg, 1998

5 Chen,X.-N. und Uliczka,K., On Ships in Natural Waterways, Proceedings of Int. Conf. on Coastal Ships and Inland Waterways, The Royal Institution of Naval Architects, Feb. 1999, London 1999

6 Chen,X.-N., Theoretische Grundlagen der Wellenwiderstandseliminierung bei überkritischer Fahrt, besonders durch den Einsatz gekrümmter Katamarane, Proceedings - 18. Duisburger Kolloquium Schiffstechnik/Meerestechnik, Das Schiff in begrenzten Gewässern, Duisburg, 1997

Hydraulic Modelling