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»For every complex problem, there is an answer that is clear, simple, and wrong.« This quote from H.L. Mencken could also describe commonly used hydrodynamic models for hull performance monitoring.
Most hull performance monitoring systems use model test reports to normalize draft, i.e. converting results for arbitrary draft to a[ds_preview] benchmark condition. In model test reports, typically only two speed-power curves are available (ballast and design condition) and these cover only the top third of the speed range. For lower speeds, simple extrapolations are employed. By necessity, trim is not considered at all in this approach. Some advocate the use of finer draft-trim-speed-power interpolation, Hansen (2011), Bertram (2014). In this approach, many combinations of trim, draft and speed are investigated, covering the whole operational range of the ship. The required hydrodynamic knowledge base can be taken from trim optimization systems, such as the ECO Assistant of DNV GL.

The experts investigated the difference between the simplified approach based on model test reports and the advanced approach based on a dense CFD matrix. The hydrodynamic knowledge base of the software for the test ship was approximated by a 6-order polynomial expression for the required power as function of trim , draft T and speed V. The polynomial had a correlation coefficient of R2 = 0.9997, indicating a very good fit.

For the same speed range and draft-trim conditions as in the model tests, CFD and model test prediction coincide very well. Higher deviations occurred only for ballast draft and low speeds. This can be qualitatively explained by the different approaches: Model tests follow a form factor approach, namely ITTC ’78, where the form factor is assumed to be speed independent. Several investigations have shown that this is not (quite) true, especially when there is large wave breaking and flow separation (ballast condition). The full-scale CFD simulations capture these effects, the model tests don’t.

Fig. 1 shows the change in power with increase in draft for various speeds on even keel. The top right corner shows a range of speeds that are almost straight lines. In this region (speeds above 21.5kn and drafts above 12m), linear interpolation between model test results is OK. However, for lower speeds or lower drafts, relations are obviously nonlinear and the simplistic approach of many performance monitoring systems is no longer applicable. For different trim values, the linearity starts at different speed/draft values.

For one vessel, the difference between power predicted from model tests and from the dense CFD matrix for a long-term in-service recording was evaluated. Data sets were 15 minutes averages from monitoring. The mean difference between model-test approach and CFD approach was 9.8% (Fig. 2). Some particularly large differences occur for intermediate draft (probably due to surface-piercing bulbous bow) and very low draft. Differences are also particularly large for low speeds (Fig. 3), probably due to extrapolation errors in the simple approach. In summary, large differences appear for off-design conditions that appear often in operational practice.


Dr. Volker Bertram, Dr. Andreas Krapp, Björn Walther