Experimental and numerical probe into the effects of adding one and two steps to a mono-hull planing vessel on its performance in calm water

Document Type : Article


Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran


In the current study, two different vessels with a single step and two steps are experimentally and numerically studied. The considered speeds are 8 and 9 m/s, equivalent to beam Froude numbers of 3.44 and 3.86. The experimentally measured parameters include bow rise-up, trim, and vessel’s resistance. On the other hand, numerical simulations of fluid flow around the vessel at 10 m/s and 12 m/s speeds are conducted using STAR-CCM+ software. Two-phase flow is analyzed using finite volume method and volume of fluid technique. Moving mesh approach through the Overset technique is applied for discretization of the domain. Based on the experimental results, it is observed that addition of the transverse step enhances the vessel’s stability and reduces its trim. It is also concluded that the resistance of a single stepped high-speed vessel reduces, compared to a vessel of without step. Meanwhile, numerical studies indicate that as the second step moves away from the transom, the resistance increases, and trim decreases. It is also concluded that both single-step and two-step models are stable at speeds up to 12 m/s.


[1] Von Karman, T. H. “The impact on seaplane floats during landing”, National Advisory Committee on Aeronautics, Washington, DC. (1929)
[2] Martin, M. “Theoretical prediction of proposing instability of high-speed planing boats”. David W. Taylor Naval Ship Research and Development Center. Report, No. 76-0068, (1976).
[3] Zarnick, EE. “A non-linear mathematical model of motions of a planing boat in regular waves”. David Taylor Naval Ship Research and Development Center., report no. DTNSRDC-78/032, (1978).
[4] Sebastiani, L., Bruzzone, D., Gualeni, P. “A practical method for the prediction of planing craft motions in regular and irregular waves”. In: Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering. Estoril, Portugal. (2008).
[5] Ghadimi, P. Dashtimanesh, A. Djeddi, S R. Faghfoor Maghrebi, Y. “Development of a mathematical model for simultaneous heave, pitch and roll motions of planing vessel in regular waves”, International Journal of Scientific World, 1 (2), pp. 44-56. (2008).
[6] Ghadimi, P. Tavakoli, S. Dashtimanesh, A. Pirooz, A. “Developing a Computer program for detailed study of planing hull’s spray based on morabito’s approach”. Journal of Marine Science and Application, 13 (4), pp. 402-4015. (2008).
[7] Ghadimi, P. Tavakoli, S. Feizi Chekab, M. A, Dashtimanesh, A.” Introducing a particular mathematical model for predicting the resistance and performance of prismatic planing hulls in calm water by means of total pressure distribution”. Journal of Naval Architecture and Marine Engineering, 12 (2), pp.73-94. (2015).
[8] Ghadimi, P. Tavakoli, S. Dashtimanesh, A. “An analytical procedure for time domain simulation of roll motion of the warped planing hulls. Proceedings of the Institution of Mechanical Engineers”, Part M: Journal of Engineering for the Maritime Environment, Published Online: DOI: 10.1177/1475090215613536. (2015).
[9] Tavakoli, S. Ghadimi, P. Dashtimanesh, A. Sahoo PK “Determination of Hydrodynamic Coefficients Related to Roll Motion of High-Speed Planing Hulls, Proceedings of the 13th International Conference on Fast Sea Transportation, DC, USA. (2015).
[10] Haase, H. Soproni, JP. Abdel-Maksoud, M. “Numerical analysis of a planing boat in head waves using a 2D+T method”. Journal of Ship Technology Research. 62 (3), pp.131-139. (2015).
[11] Ghadimi, P. Tavakoli, S. Dashtimanesh, A. Zamanian, R “Steady performance prediction of a heeled planing boat in calm water using asymmetric 2d+t model”. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, Published Online, 1-24. DOI: 10.1177/1475090216638680. (2016).
[12] Ghadimi, P. Tavakoli, S, Dashtimanesh A, calm water performance of hard-chine vessels in semi-planing and planing regimes. POLISH MARITIME RESEARCH 4 (92) 2016 Vol. 23; pp. 23-45.
[13] Kazemi, H. Salari M “Effects of Loading Conditions on Hydrodynamics of a Hard-Chine Planing Vessel Using CFD and a Dynamic Model”. International Journal of Maritime Technology. 7, pp. 11-18. (2017).
[14] Faruk S.O, Kemal K.O, Cakici F, Gokce K, Hydrodynamic assessment of planing hulls using overset grids, Applied Ocean Research 65 (2017) 35–46.
[16] Ghassemi H, Kohansal A, Hydrodynamic Analysis of Non-Planing and Planing Hulls by BEM, Scientia Iranica B (2010) 17(1), 41-52.
[17] Ghadimi P, Sajedi S.M, and Tavakoli S, Experimental study of the wedge effects on the performance of a hard-chine planing craft in calm water, Scientia Iranica B (2019) 26(3), 1316-1334.
[18] Sajedi, SM. Ghadimi, P. Sheikholeslami, M. Ghassemi, MA “Experimental and numerical analyses of wedge effects on the rooster tail and porpoising phenomenon of a high-speed planing craft in calm water”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233 (13). pp. 4637-4652. (2019).
[19] Savitsky, D. Gore, J. L. “Re-evaluation of the planing hull form”, Journal of Hydronautics, 14, (2), pp.34–47. (1980).
[20] Faltinsen, O. M “Hydrodynamics of High-Speed Marine Vehicles”, Cambridge University Press, Cambridge University Press, New York, New York. (2005).
[21] Savitsky, D. Morabito M. “Surface wave contours associated with the forebody wake of stepped planing hulls”, Marine Technology, 47, (1), pp.1–16. (2010).
[22] Danielson, J. Stromquist, J, “Conceptual design of super yacht tender”, Marine System Center for Naval Architecture, KTH University. (2012).
[23] Clement, EP “A configuration for a stepped planing boat having minimum drag”. This publication is available on the web site of the International Hydrofoil Society: www. foils. org. (2006).
[24] Dong, W. Guo, R “Study on the mechanism of resistance reduction to the stepped planing craft by air injection”. Journal of Ship Mechanics, 6(6). (2002).
[25] Dong, W. Guo R “Experimental investigation on the resistance reduction of stepped planing craft by formation of air cavity”. Journal of Hydrodynamics, 17(4). (2002).
[26] Clement, EP. Koelbel, JO “Progress during the past century toward the development of efficient, load-carrying, stepped planing boats”. Proceedings of the Fifth Biennial Power Boat Symposium, SE Sect. SNAME. (1993).
[27] Savitsky D, “Hydrodynamic Design of Planing Hulls”, Marine Technology, 1(1), (1964).
[28] Svahn D “Performance prediction of hulls with transverse steps”. MSc Thesis, KTH, Stockholm. (2009)
[29] Kaidy, R “Advance topics in stepped hull design”. International Boat Builders Exhibition and Conference, Session 302. (2013).
[30] Najafi, A. Nowruzi, H. Karami, M. Javanmardi, H “Experimental investigation of the wetted surfaces of stepped planing hulls”. doi.org/10.1016/j.oceaneng.2019.106164. (2019).
[31] Sajedi, S M. Ghadimi. P. Ghadimi, A. Sheikholeslami, M “Experimental appraisal of hydrodynamic performance and motion of a single-stepped high-speed vessel in calm water and regular waves”. doi.org/10.1177%2F0954406220968126. (2020)
[32] Sajedi S M, Ghadimi P “Experimental investigation of the effect of a step and wedge on the performance of a high-speed craft in calm water and statistical analysis of its seakeeping in irregular waves”. doi.org/10.1063/5.0018993. (2020).
[33] Sajedi S M, Ghadimi P, Sheikholeslamid M, Ghassemi MA “Experimental study of hydrodynamic performance of a Monohull Planing vessel equipped by combined transverse step and transom wedge in comparison with a model of no appendage”, Sciential Iranica, Transcriptions B: Mechanical Engineering, Ref. No: SCI-2007-4680. (2020).
[34] Amin Najafi, Hashem Nowruzi, Javad Ameri, Hydrodynamic assessment of stepped planing hulls using experiments, Ocean Engineering, Volume 217, 1 December 2020, 107939, https://doi.org/10.1016/j.oceaneng.2020.107939.
[35] Amin Najafi, Hashem Nowruzi, Javad Ameri, Mohammad Karami, An experimental study of the wetted surfaces of two- stepped planing hulls, Ocean Engineering, Volume 222, 15 February 2021, 108589. https://doi.org/10.1016/j.oceaneng.2021.108589.
[36] De Marco, A. Mancini, S. Miranda, S. Scognamiglio, R.Vitiello, L” Experimental and numerical hydrodynamic analysis of a stepped planing hull”. Applied Ocean Research, 64: pp 135-154. (2007).
[37] Najafi, A. Nowruzi, H “On hydrodynamic analysis of stepped planing crafts”. Journal of Ocean Engineering and Science. 4, pp. 238–251. (2019).
[38] Doustdar, M, Kazemi, H “Effects of fixed and dynamic mesh methods on simulation of stepped planing craft”. Journal of Ocean Engineering and Science. 4: 33–48. (2019).
[39] Sajedi, SM. Ghadimi, P “Experimental and Numerical Investigation of Stepped Planing Hulls in Finding an Optimized Step Location and Analysis of Its Porpoising Phenomenon”, Mathematical Problems in Engineering. (2020)
[15] Judgea C, Mousaviraad M, Sternc F, Leed E, Fullertond A, Geiserd J, Schleicherd C, Merrilld C, Weild C, Morind J, Jiangd M, Ikedae C “Experiments and CFD of a high-speed Deep-V planing hull”–Part I: Calm water. doi.org/10.1016/j.apor.2020.102060. (2020)
[40] Afriantoni A, Romadhoni R, and Santoso B “Study on the Stability of High Speed Craft with Step Hull Angle Variations”, in The 8th International and National Seminar on is heries and Marine Science. (2020)
[41] Taunton, DJ. Hudson, DA, Shenoi RA “Characteristics of a series of high-speed hard chine planing hulls” part 1: performance in calm water. International Journal of Small Craft Technology. 152: B55–B75. (2010)
[42] Taunton DJ, Hudson DA, Shenoi RA “Characteristics of a Series of high-speed hard chine planing hulls” part 2: performance in waves. International Journal of Small Craft Technology, 153, B1-B22. (2011)
[43] Vitiello L, Miranda S, Balsamo F, Bove A, Caldarella S “Stepped hulls: model experimental tests and sea trial data”. Proceedings of the 17th International Conference on Ships and Shipping Research, Athena, Greek. (2012).
[44] Lee E, Pavkov M, Mccue-Weil W “The Systematic variation of step configuration and displacement for a double-step planing craft”. Journal of Ship Production and Design. 30(2): 89–97. (2014)
[45] Nourghassemi H, Ghassemi H, Taghva H “Numerical Hydrodynamic Results of the Two Stepped Planing Hull”. American Journal of Mechanical Engineering. 6(3), pp. 93-97. (2018)
[46] Ghadimi P, Panahi S “Numerical investigation of hydrodynamic forces acting on the non-stepped and double-stepped planing hulls during yawed steady motion”. Journal of engineering and maritime environment. DOI: 10.1177/1475090217751549. (2018).
[47] Esfandiari, A, Tavakoli S, Dashtimanesh A “Comparison between the Dynamic Behavior of the Non-stepped and Double-stepped Planing Hulls in Rough Water”: A Numerical Study. Journal of Ship Production and Design. (2019)
[48] Zou J, Lu S, Jiang Y, Sun H, Li Z “Experimental and Numerical Research on the Influence of Stern Flap Mounting Angle on Double-Stepped Planing Hull Hydrodynamic Performance”. Journal of Marine Science and Engineering. (2019).
[49] Sajedi, SM. Ghadimi, P “Experimental investigation of the effect of two steps on the performance and longitudinal stability of a mono-hull high-speed craft”, Cogent Engineering 7 (1), 1790980. (2019).
[50] Ma W, H, Zou J, Yang H “Test research on the resistance performance of high-speed trimaran planing hull”, Polish Maritime Research 4(80) 20, pp. 45-5. (2013).
[51] Kazemi, H., Doustdar, M.M., Najafi, A. et al. Hydrodynamic Performance Prediction of Stepped Planing Craft Using CFD and ANNs. J. Marine. Sci. Appl. (2021). https://doi.org/10.1007/s11804-020-00182-y.
[52] ITTC Recommended Procedures and Guidelines, 24th ITTC 7.5-03 02-03, (2011).