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
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $P_\text{new}$ | Projected delivered power at target speed | kW | result |
| $P_\text{ref}$ | Delivered power at reference speed | kW | sea-trial / model test |
| $V_\text{ref}$ | Reference speed | kn | sea-trial / design |
| $V_\text{new}$ | Target speed | kn | operator 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.