Abstract
Polar navigation requires more powerful ships with increased hull strengthening capable of overcoming the additional resistance presented by sea ice and able to withstand the impacts of the many ice formations that might appear. The increase in capability of a ship to overcome the resistance whilst moving through ice infested waters, plus the extra weight of its structure due to the higher strengthening, requires greater power. Consequently, the added requirements needed by ice-going vessels entail higher emissions of pollutants into the atmosphere, greater initial investment for shipbuilding and huge operational costs. Hull strengthening of ice class vessels is defined by a proper Classification Society in their rules, which tend towards conservative equations. This work describes a methodology to obtain lighter hull structures of polar vessels using an impact model of a ship against an ice floe, based on energy methods, and focussed on early stages of design. The hull structure of the bow region of an ice class ship is designed according to the Finnish-Swedish Ice Class Rules (FSICR) and both results of the weight of the ship’s bow calculated through direct calculation and current regulations are compared. Finally, some conclusions related with weight reduction are shown.
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Abbreviations
- \(A\) :
-
Contact area [m2]
- \(a\) :
-
Length of a rectangular-plate panel [m]
- \(B\) :
-
Breadth [m]
- \(b\) :
-
Width of a rectangular-plate panel [m]
- \({b}_{\mathrm{b}}\) :
-
Constant width of the beam in contact with the foundation [m]
- \(C\) :
-
Geometry factor for the collision [-]
- \(D\) :
-
Depth [m]
- \(d\) :
-
Ice floe edge’s deflection [m]
- \({d}_{2}\) :
-
Ice floe width [m]
- \({E}_{\mathrm{ice}}\) :
-
Young’s modulus of the ice [Pa]
- \(e\) :
-
Width of a rectangular-load footprint, parallel to \(b\) [m]
- \(F\) :
-
Contact force [MN]
- \({F}_{\mathrm{max}}\) :
-
Maximum contact force [MN]
- \(f\) :
-
Length of a rectangular-load footprint, parallel to \(a\) [m]
- \(g\) :
-
Gravity acceleration [m s−2]
- \(H\) :
-
Height of the load patch [m]
- \({H}_{1}\) :
-
Load height for a rectangular uniformly partially distributed load [m]
- \({H}_{2}\) :
-
Load height for a triangular partially distributed varying load [m]
- \({h}_{\mathrm{f}}\) :
-
Width of the profile’s flange [mm]
- \({h}_{\mathrm{w}}\) :
-
Height of the profile’s web [mm]
- \({h}_{2}\) :
-
Ice floe thickness [m]
- \(I\) :
-
Moment of inertia of the beam cross section (rectangle) [m4]
- \(k\) :
-
Modulus of the foundation [kg m−1 s−2]
- \(L\) :
-
Frame span [m]
- \({L}_{\mathrm{BOW}}\) :
-
Length of the bow region [m]
- \({L}_{\mathrm{b}}\) :
-
Length of the beam approached to the ice floe [m]
- \({L}_{\mathrm{pp}}\) :
-
Length between perpendiculars [m]
- \({L}_{2}\) :
-
Ice floe length [m]
- \({L}_{3}\) :
-
Application point of the ice load [m]
- \({L}_{4}\) :
-
Initial point of the ice load [m]
- \({M}_{\mathrm{avg}}\) :
-
Maximum bending moment on an averaged frame between fixed at both ends and hinged [N m]
- \({M}_{\mathrm{max}}\) :
-
Maximum bending moment on a simply supported or hinged frame [N m]
- \({M}_{\mathrm{max}1}\) :
-
Maximum bending moment on a frame with rectangular uniformly partially distributed load [N m]
- \({M}_{\mathrm{max}2}\) :
-
Maximum bending moment on a frame with triangular partially distributed varying load [N m]
- \({M}_{\mathrm{max}}{^{\prime}}\) :
-
Maximum bending moment on a frame fixed at both ends [N m] supported [N m]
- \({M}_{1\mathrm{red}}\) :
-
Reduced mass of the ship [kg]
- \({M}_{2\mathrm{red}}\) :
-
Reduced mass of the ice floe [kg]
- \(n\) :
-
Pressure–area exponent [–]
- \({\mathrm{OD}}_{\mathrm{Par}}\) :
-
Optimal designs in the Pareto front [–]
- \(P\) :
-
Ice load [MPa]
- \({P}_{0}\) :
-
Nominal, peak or average ice pressure [MPa]
- \(s\) :
-
Frame spacing [m]
- \(T\) :
-
Draught [m]
- \({T}_{1\mathrm{red}}\) :
-
Reduced kinetic energy of the ship [J]
- \({T}_{2\mathrm{red}}\) :
-
Reduced kinetic energy of the ice floe [J]
- \(\mathrm{TOW}\) :
-
Total weight of the bow region of a vessel design [t]
- \({\mathrm{TW}}_{\mathrm{b profiles}}\) :
-
Total weight of the bulb flat profiles [t]
- \({\mathrm{TW}}_{\mathrm{L profiles}}\) :
-
Total weight of the angle profiles [t]
- \({\mathrm{TW}}_{\mathrm{plate}}\) :
-
Total weight of the shell plate [t]
- \({\mathrm{TW}}_{\mathrm{stringers}}\) :
-
Total weight of the ice stringers [t]
- \({\mathrm{TW}}_{\mathrm{T profiles}}\) :
-
Total weight of the custom-built T profiles [t]
- \({t}_{\mathrm{f}}\) :
-
Thickness of the profile’s flange [mm]
- \({t}_{\mathrm{s}}\) :
-
Thickness of the shell plate [mm]
- \({t}_{\mathrm{w}}\) :
-
Thickness of the profile’s web [mm]
- \(U\) :
-
Energy for crushing of the ice floe [J]
- \(V\) :
-
Energy for bending of the ice floe [J]
- \({v}_{\mathrm{ice}}\) :
-
Ice floe velocity [m s−1]
- \({v}_{1}\) :
-
Ship velocity [m s−1]
- \(W\) :
-
Width of the load patch [m]
- \({w}_{1}\) :
-
Width of the load patch smaller than \(s\) [m]
- \({w}_{2}\) :
-
Width of the load patch equal to \(s\) [m]
- \({w}_{3}\) :
-
Width of the load patch bigger than \(s\) [m]
- \({x}_{b}\) :
-
Displacement due to bending of the ice floe [m]
- \({x}_{\mathrm{cr}}\) :
-
Displacement due to crushing of the ice floe [m]
- \({x}_{1}\) :
-
Movement of the ice floe produced by the displacement of the ship [m]
- \({x}_{2}\) :
-
Displacement due to the translation of the ice floe [m]
- \(Z\) :
-
Section modulus [m3]
- \(\alpha\) :
-
Waterline angle [°]
- \(\beta\) :
-
Frame angle [°]
- \(\beta {^{\prime}}\) :
-
Normal frame angle [°]
- \(\gamma\) :
-
Sheer angle [°]
- \(\Delta\) :
-
Displacement [t]
- \(\delta\) :
-
Ice-edge opening angle [°]
- \(\lambda\) :
-
Characteristic of the system [m−1]
- \({\rho }_{\mathrm{ice}}\) :
-
Ice density [kg m−3]
- \({\sigma }_{\mathrm{ris}}\) :
-
Required yield stress [MPa]
- \(\varphi\) :
-
Buttock angle [°]
- \(\psi\) :
-
Flare angle [°]
- FSICR:
-
Finish-Swedish Ice Class Rules
- IACS:
-
International Association of Classification Societies
- IMO:
-
International Maritime Organization
- LIWL:
-
Lower Ice waterline
- M/S:
-
Motor ship
- MOO:
-
Multi-objective optimization
- PC:
-
Polar class
- RMRS:
-
Russian Maritime Register of Shipping
- STA:
-
Swedish Transport Agency
- TRAFI:
-
Finish Transport Safety Agency
- UIWL:
-
Upper ice waterline
- WARC:
-
Wärtsilä Arctic Research Centre
- WMO:
-
World Meteorological Organization
- (b):
-
Bulb flat profile
- (T):
-
Custom-built T profile
- (L):
-
Angle profile
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Acknowledgements
Thanks to Simón Carrillo-Segura, for his help and contributions to the research project.
Funding
No funding was received for conducting this study. However, the research has received funding for dissemination from the Ministry of Science and Innovation, State Research Agency, and the European Regional Development Fund under Grants RTI2018-094744-A-C22 (NICESHIP).
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Samuel Ruiz-Capel, Kaj Riska and José Enrique Gutiérrez-Romero. The first draft of the manuscript was written by Samuel Ruiz-Capel and all authors commented and reviewed previous versions of the manuscript. All authors read and approved the final manuscript.
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Ruiz-Capel, S., Riska, K. & Gutiérrez-Romero, J.E. A methodology for designing light hull structure of ice class vessels. J. Ocean Eng. Mar. Energy 9, 341–357 (2023). https://doi.org/10.1007/s40722-022-00271-w
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DOI: https://doi.org/10.1007/s40722-022-00271-w