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Speed–Power Cubic Fit

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Projects delivered power at any speed from a reference point using the Rayleigh cube law with an adjustable exponent.

Formula

$$ P_\text{new} = P_\text{ref} \cdot \left(\frac{V_\text{new}}{V_\text{ref}}\right)^n $$

Symbol legend

SymbolMeaningUnitSource
$P_\text{new}$Projected delivered power at target speedkWresult
$P_\text{ref}$Delivered power at reference speedkWsea-trial / model test
$V_\text{ref}$Reference speedknsea-trial / design
$V_\text{new}$Target speedknoperator choice
$n$Speed exponent - cube law $n = 3$, tankers 2.8–3.0, container ships 3.1–3.3-empirical fit

Only main-engine fuel scales with this law; auxiliary loads stay roughly flat. Use this to size slow-steaming savings before multiplying by voyage hours.

Sources

  • MAN Energy Solutions - Basic Principles of Ship Propulsion.
  • Holtrop & Mennen (1982) - ship resistance regressions.