Ship Squatting Problem

A vessel with a displacement hull moving at even moderate speeds in shallow water will experience vertical sinkage, or ``squat,'' as a result of a pressure drop beneath its hull [4].

Squat Models

A number of empirical formulas have been devised to model the squatting problem:

Barrass [1]: S =1/30 · Cb · (As / [Ac - As] )2/3 · Vk2.08
Millward [3]: S =(L/100) · ([15 · Cb · (B/L) - 0.55] · Fnh2 ) / (1 - 0.9 · Fnh )
Norrbin [4]: S =(L/100) · ([100 / (L/h)] · [As / Ac] · Fnh2 ) /
(1 - [As / Ac] - [(h · W0) / Ac] · Fnh2 )
Tuck [5]: S =L · Cs · Fnh2 / (1 - Fnh2 )1/2

For all models, the ship clearance is equal to the channel depth minus the ship draft minus the ship squat:

Clearance: c = h - T - S

Look at some examples of the numeric and graphical output from the squat models.

Evaluate the squat models.
Plot (univariate) the squat models.
Plot (bivariate) the squat models.
Plot (trivariate) the squat models.

Nomenclature

Ac:cross-sectional area of channel (m2) As:immersed cross-sectional area of ship (m2)
B:ship beam (m) c:ship clearance, h-T-S (m)
Cb:ship block coefficient Cs:Tuck's ship form factor
Fnh:Froude number of depth, V/(gh)1/2 g:gravitational acceleration, 9.81 (m/sec2)
h:channel water depth (m) L:ship waterline length (m)
S:ship squat (m) T:ship draft (m)
V:ship speed (m/sec) Vk:ship speed (knots, i.e. nautical miles per hour)
Wo:channel waterline width (m)

References

  1. C. B. Barrass, ``The Phenomena of Ship Squat,'' International Shipbuilding Progress, 26:44-47, 1979.

  2. H. Blaauw and F. van der Knaap, ``Prediction of Squat of Ships Sailing in Restricted Water,'' 8th International Habour Congress, Antwerp, June 13-17, 1983, pages 81-93.

  3. A. Millward, ``A Preliminary Design Method for the Prediction of Squat in Shallow Water,'' Marine Technology, 27(1):10-19, January 1990.

  4. Nils H. Norrbin, ``The Effects of Flow Confinement and Asymmetry on a Ship in a Fairway Passage,'' Workshop on Ship Squat in Restricted Waters, Panel H-10 (Ship Controllability), Hydrodynamics Committee, SNAME, July 1996, pages 87-93.

  5. E. O. Tuck, ``Shallow Water Flows Past Slender Bodies,'' Journal of Fluid Mechanics, 26(1):81-95, 1966.

This service is a result of the project Formulation of a Model for Ship Transit Risk funded by the U.S. Department of Commerce, U.S. Army Corps of Engineers, and U.S Coast Guard (PIs: N. M. Patrikalakis, MIT, and H. L. Kite-Powell, WHOI).

URL: http://deslab.mit.edu/DesignLab/squat/home.html
Last modified: November 5, 1998