The cube law and where it breaks
For a displacement-type hull in the regular operating range, delivered power at the propeller follows roughly:
P_new = P_ref × (V_new / V_ref)^n
With n ≈ 3. Tankers and bulkers sit closer to n = 2.8; modern container ships with finer form can approach n = 3.3 in the wave-making regime. Auxiliary fuel doesn’t scale - hotel, reefer, and engine-room load stays approximately flat regardless of speed.
So for a voyage of fixed distance D:
Main-engine fuel = ME_rate(V_ref) × (V_new / V_ref)^n × (D / V_new) / 24
Aux fuel = AE_rate × (D / V_new) / 24
At low speeds the aux term dominates; at high speeds the ME term dominates. The crossover is where the derivative with respect to V flips sign - that’s the fuel-optimum speed for that voyage.
A worked example
Bulker on a 6,000 nm leg. Reference speed 15 kn, ME rate at 15 kn = 45 t/day, aux rate = 3 t/day, fuel VLSFO (Cf 3.114):
| Speed | Voyage hours | ME fuel (t) | Aux fuel (t) | Total | CO₂ (t) |
|---|---|---|---|---|---|
| 15 kn | 400 | 750 | 50 | 800 | 2,491 |
| 13 kn | 462 | 487 | 58 | 545 | 1,697 |
| 12 kn | 500 | 360 | 63 | 423 | 1,316 |
| 11 kn | 545 | 274 | 68 | 342 | 1,064 |
| 10 kn | 600 | 222 | 75 | 297 | 924 |
Dropping from 15 to 12 knots saves 47 % of voyage fuel and 47 % of voyage CO₂. Going further to 10 knots saves 63 %.
The CII arithmetic
CII (for cargo ships) is:
CII_attained = Σ F_j × Cf_j × 1e6 / (DWT × distance)
Distance is fixed by the trade lane. DWT is fixed by the ship. Fuel is the only variable. So CII scales linearly with annual fuel consumption, and the slow-steaming saving translates directly.
A bulk carrier at 82,000 DWT, 80,000 nm/year, VLSFO-only:
- Baseline at 15 kn ≈ 5,000 t fuel → CII ≈ 2.37 g/(dwt·nm) → D rating for most bulker size bands.
- 12 kn average ≈ 2,700 t → CII ≈ 1.28 g/(dwt·nm) → comfortably A/B rating.
Two knots changed two CII bands. There’s almost no other operational lever with the same leverage.
Where slow steaming doesn’t help
- Ballast legs or short fast legs where the ship isn’t time-constrained. Going slower still consumes aux fuel over more hours and doesn’t improve cargo-work-per-mile.
- Scheduled liner services - a container ship on a weekly rotation can’t just drop 20 % speed without missing berths. The solution is more ships on the loop, not slower ships.
- Ro-Pax routes with fixed timetables - passenger expectations and schedule integrity cap achievable reductions.
- Cold / tropical climate extremes - below a certain speed, hotel + reefer + HVAC load (on ro-ro vehicle carriers and cruise) dominates and the aux crossover happens quickly.
Just-in-time arrival is cheap speed reduction
If the ship sits at anchor for 12 hours waiting for a pilot, those 12 hours are effectively a free deceleration. Coordinating with the terminal to slow the last 500 nm and arrive exactly when berth is ready (a Just-In-Time arrival) saves the fuel cube-law difference with zero schedule impact.
IMO’s MEPC.323(74) invites port-ship cooperation on JIT. Ports increasingly run PortCDM-style information exchanges. The voluntary nature makes this hard to mandate but most operators see 5–10 % fleet-level savings once the practice is embedded.
Charter-party friction
Slow steaming for CII can conflict with the charterer’s commercial interests. The BIMCO 2022 CII Operations Clause addresses this: the charterer warrants that voyage instructions won’t push the ship below a C rating, subject to specified allowances for delays, tactical speed-ups, and safety instructions. Owners who ignore the clause end up absorbing corrective-plan costs even when the bad rating was caused by charter instructions.
Sidebars to negotiate:
- Warranted speed range (e.g. 11–13 kn at ≤ 85 % MCR).
- Maximum weekly / monthly MCR above a threshold.
- Penalty / bonus for CII outcomes relative to target.
- Fuel-saving share when owner optimises beyond warranty.
Other levers that stack
Slow steaming is big but not alone:
- Hull cleaning: 3–8 % fuel once fouling accumulates. Recovers quickly; fades over 6–12 months.
- Propeller polish: 1–3 % on top.
- Trim optimisation: 1–3 % per voyage on modern hulls.
- Weather routing: 3–5 % on trans-ocean legs.
- WHR (capital): 4–8 % main-engine fuel displaced.
Stacking gets you from 20 % fuel reduction to 35 % without touching speed - combine with a 2 knot slow-steam and you’re at 55–60 %, comfortably A-rated.
How to size the trade-off
Try our Slow Steaming calculator - enter reference speed and rate, the candidate slower speed, and see voyage fuel and CO₂ for each. The Speed–Power Cubic Fit calculator helps you calibrate the exponent n from your own sea-trial data. Then feed the resulting annual fuel into the CII Attained calculator to see the rating effect.