Resistance and Economic Speed of Ships and Tows in Inland Waterways
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147, Issue 6
Abstract
The resistance of commercial vessels in inland waterways is an essential and widely investigated problem. Depending on vessel and channel shape and size, many empirical equations were developed in the past to determine the resistance of vessels. In order to obtain an accurate relationship to predict the total resistance of inland vessels for variable channel and vessel dimensions, numerous model resistance tests with motor ships, push tows, and barge convoys were evaluated. If the speed of the vessel is limited to a defined economic speed, which is usually not exceeded in inland waterways, it is shown that the resistance from model tests of both ships and tows can be determined well by a resistance equation, which is based on a formula derived by van de Kaa for canals. A satisfactory agreement of the calculation results can be demonstrated for motor ships with measurements in field tests. It turns out that the adopted resistance equation of van de Kaa provides good results for inland vessels in a wide range of inland waterway dimensions.
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Data Availability Statement
Some or all data, models, or code used during the study appear in publications and published or unpublished reports of the two institutions indicated in the acknowledgments. Data and reports of the Development Centre for Ship Technology and Transport Systems (DST) should be directly requested at the DST in Duisburg. Unpublished reports by the former FAS in Berlin are available from the author on request.
Acknowledgments
The author would like to express his special thanks to the Development Centre for Ship Technology and Transport Systems in Duisburg (DST), the former Duisburg Model Basin (VBD). The extensive and systematic ship resistance tests in the towing tank and the well-documented test results in reports and publications of the DST made a tremendous contribution to this study. Many thanks also to my esteemed colleague at the BAW Karlsruhe and the former FAS Berlin, Dr. Manfred Fuehrer. The model tests performed and supervised by him and the analysis of the test results in FAS reports made a large contribution to the evaluations of the resistance of ships and tows in the case of strongly restricted channels.
Notation
The following symbols are used in this paper:
- AC
- undisturbed wetted channel cross section without vessel (m2);
- AM
- submerged midship cross-sectional area (m2);
- AW
- channel cross section reduced by vessel and drawdown (m2);
- B
- total beam (m);
- BC
- channel width (m);
- BWL
- beam on the waterline (m);
- CB
- block coefficient;
- CF
- hull frictional coefficient in deep water;
- CF,B
- shallow water frictional coefficient for the ship bottom;
- CGlobal
- global resistance coefficient;
- CP, CP0, CP1, CP2
- pressure (form) resistance coefficient;
- CShallow
- shallow water resistance coefficient;
- Fr
- channel Froude number;
- Frh
- depth Froude number;
- FrL
- length Froude number;
- FrRh
- Froude number in terms of the hydraulic radius;
- g
- gravitational acceleration (m/s2);
- h
- water depth (m);
- hm
- average water depth (m);
- index 1
- cross-sectional quantities with the vessel;
- L
- total length of vessel or barges (m);
- L/∇1/3
- length-displacement ratio (slenderness);
- LWL
- length on the waterline (m);
- m
- blockage ratio;
- PC
- undisturbed wetted channel perimeter (m);
- PM
- wetted midship perimeter (m);
- R2
- coefficient of determination;
- RF
- frictional resistance of the full-size vessel (N);
- RFM
- frictional resistance of the model vessel (N);
- Rh
- hydraulic radius (m);
- RT
- total resistance of the full-size vessel (N);
- RTM
- total resistance of the model vessel (N);
- S
- wetted area of the hull (m2);
- S/∇2/3
- wetted area coefficient;
- SB
- ship bottom area (m2);
- SL
- submerged lateral area of the ship (m2);
- T
- draft of ship or barges (m);
- V
- vessel speed relative to the water (m/s);
- Vcr
- (Schijfs) subcritical speed (m/s);
- Vec
- limiting economic speed (m/s);
- Vn
- nautically permissible speed (m/s);
- VR
- average return velocity (m/s);
- Vscr
- super-critical speed (m/s);
- W
- water level width of the channel (m);
- Z
- average water level drawdown (m);
- α
- correction factor for irregularity of the return flow field;
- ΔCF
- additional surface roughness coefficient;
- ∇
- volumetric displacement (m3);
- λ
- model scale;
- ν
- kinematic viscosity (m2/s); and
- ρ
- water density (kg/m3).
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Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147 • Issue 6 • November 2021
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© 2021 American Society of Civil Engineers.
History
Received: Dec 3, 2020
Accepted: Jun 18, 2021
Published online: Aug 9, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 9, 2022
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