Fuel and CO₂ impact of reducing voyage speed, accounting for the cube-law main-engine behaviour and the constant auxiliary baseline.
Formula
$$ F_\text{slow} = \left(\text{ME}\text{ref} \cdot \left(\frac{V\text{slow}}{V_\text{ref}}\right)^n + \text{AE}\right) \cdot \frac{D / V_\text{slow}}{24} $$
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $F_\text{slow}$ | Voyage fuel at slow-steaming speed | t | result |
| $\text{ME}_\text{ref}$ | Main-engine daily fuel rate at reference speed | t / day | voyage log |
| $V_\text{ref}$ | Reference speed | kn | ship / design |
| $V_\text{slow}$ | Slow-steaming speed | kn | operator choice |
| $n$ | Speed exponent (≈ 3) | - | Rayleigh cube law |
| $\text{AE}$ | Auxiliary + boiler daily fuel rate (speed-independent) | t / day | voyage log |
| $D$ | Voyage distance | nm | voyage plan |
The $\text{AE}$ term rises linearly with trip hours and eventually cancels the main-engine saving - the optimum usually sits between 50 % and 70 % of design speed.
Sources
- MAN Energy Solutions - Propulsion Trends.
- IMO MEPC.364(79) - Cf conversion factors.