Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Study on Squat of Ships in Restricted Waterway
Yizhou Ren, Cailian Wang, Weiyi Zhang, Xiaoliang DouMarine Design & Research Institute of China
Shanghai, China(Barrass, 2012). Grounding of passenger liner Queen Elisabeth II is oneof the most striking cases, which produced repair bill of 13 million dollars,
plus an estimation for lost passenger booking of 50 million dollars(Pasquay, 2001).

ABSTRACTWith the development of ship sizes, available space for ships to navigate
in restricted waterway gradually decreases. Therefore it is vital to givean accurate prediction of squat in restricted waterway for the sake ofsafety. Objective of this paper is to present method to apply appropriate
formulae to specific channels and ships for prediction of squat. In thisstudy, popular formulae for squat prediction are compared and validated
to measured data of several model tests with similar feature of target
condition. Formulae for further investigation are selected based oncomparison results. Then these formulae are applied to object channel
with three typical sizes of ships. Moreover, maximum speed in restrictedwaterway due to effect of squat is predicted and analyzed. The result
demonstrates that larger ships tend to occur more significant squat inrestricted waterway and consequently should sail with more limited
draught considering safety. It is recommended to validate applicabilityof formulae for object condition with similar tests before application tospecific cases.

There is no doubt that ships may also encounter sinkage and trim
similarly when sailing in deep or open waterway, meanwhile squat in
restricted waterway is usually more prominent. Moreover, in deep or
open water sinkage and trim is less likely to bring about major
consequences, while in restricted waterway squat is more possible to leadto negative phenomenon including grounding and manoeuvrability
issues due to insufficient under keel clearance (UKC). As Cockroft(1984) summarized, approximately 90% of all marine accidents occur in
restricted waterway. Therefore it makes contribution to navigation safety
to perform accurate prediction of squat in restricted waterway withshallow water depth as well as narrow width and accordingly reserveadequate UKC.
There is a large volume of published studies investigating methods topredict ship squat including analytical methods, experimental
investigation, empirical formulae and numerical simulation. As classicalresearch method with long history, analytical methods have beendeveloped making use of assumption inherent in potential flow theory
such as slender body theory (Tuck, 1966). Tuck’s method wasestablished originally for unrestricted channel and extended to canals(Tuck, 1967) and dredged channels (Beck, Newman and Tuck, 1975).
Naghdi and Rubin (1984) solved the problem of the squat of a "twodimensional" ship using a nonlinear steady-state solution of thedifferential equations of the theory of a directed fluid sheet. Gourlay(1999) raised a method for computing steady nonlinear hydraulic flow
past a ship in a channel. Lataire, Vantorre and Delefsortrie (2012) built
mathematical model for prediction of squat in restricted and unrestricted
rectangular fairways. Experimental investigations are naturally moreaccurate to predict squat. Uliczka and Kondziella (2006) investigatedsquat of large container ships in extremely shallow water through model
tests and compared the result with field measurement. Zeraatgar, Akbari

KEY WORDS: squat; restricted waterway; under keel clearance;
empirical formulae; shallow water.
INTRODUCTION
With the upgrading of the ship fleet, recent years have witnessed
increasing trend of dimensions of ships. Meanwhile port or waterway
authorities are usually unable to expand the waterway dimensions withthe synchronous pace. Therefore, available space for ships to navigate in
restricted waterway have gradually decreased. The restricted room
underneath and alongside ships has noticeable influence on the increaseof the ship draught and consequent reduction of distance between theship bottom and the sea or river bed when moving forward. Thisphenomenon is known as ‘ship squat’ (Constantine, 1960).
Squat is a strong risk factor for grounding that potentially results insevere damage to the ship and in extreme cases may give rise to complete
loss of ships as well as channels and ports. It is never excessive concern
because more than 40 ships have suffered grounding in recent years

Vakilabadi and Yousefnejad (2011) carried out a series of model tests
to determine the squat for vessels with the Series-60 hull forms in3777