Scale effects on the wave-making resistance of ships sailing in shallow water

Qingsong Zeng*, Robert Hekkenberg, Cornel Thill, Hans Hopman

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)
61 Downloads (Pure)


The conventional extrapolation of ship resistance from model tests to full scale presumes that the coefficient of wave-making resistance (Cw) depends on the Froude number only. This leads to the assumption that Cw of a ship is identical to Cw of its scaled model. However, this assumption is challenged in shallow water due to viscous effects, which are represented by the Reynolds number (Re). In this study, different scales (different Re) of the Wigley hull and the KCS hull are used to investigate the scale effects on Cw numerically. After verification and validation, systematic computations are performed for both ships and their scaled models in various shallow-water conditions. Based on the results, significantly larger values of Cw are found for the KCS at model scale in very shallow water, suggesting that the conventional extrapolation has to be reconsidered. Additionally, this study reveals the relationship between the changes in frictional resistance coefficient (Cf) and the changes in Cw caused by shallow water, which benefits the prediction of shallow water effects on Cw. Finally, use of a larger ship model, where the Re is also higher, is recommended for resistance tests in shallow water to reduce scale effects on Cw.

Original languageEnglish
Article number107654
Number of pages11
JournalOcean Engineering
Publication statusPublished - 2020


  • Resistance extrapolation
  • Scale effect
  • Shallow water
  • Wave-making resistance


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