Why does fuel consumption scale with the cube of speed?

The power a hull needs to overcome wave-making and frictional resistance rises roughly with the cube of speed at displacement velocities. Since fuel burn tracks engine power, daily consumption follows the same cube relationship near the design speed.

Why is the slowest speed not always cheapest?

Slowing down cuts fuel sharply but lengthens the voyage, so you pay more days of charter hire. The optimum balances falling fuel cost against rising hire cost, which is why a mid-range speed usually wins.

What is slow steaming?

Slow steaming means deliberately running below design speed to save fuel when bunker prices are high or hire is cheap. This calculator quantifies the trade-off so you can decide whether it actually lowers total cost on a given voyage.

How accurate is the cube-law model?

It is a good approximation within a few knots of the reference speed where the consumption curve is smooth. Far from that point, or in heavy weather and with hull fouling, real curves diverge, so treat the result as a planning estimate.

Does the tool send my voyage data anywhere?

No. Every calculation runs entirely in your browser. Nothing about your vessel, route, or commercial terms is transmitted or stored on a server.

Vessel Speed-Fuel Optimisation Calculator

Choosing a vessel’s speed is a commercial decision, not just a nautical one. Going faster burns dramatically more fuel; going slower racks up more days of charter hire. This calculator sweeps a range of speeds and finds the one that minimises the total voyage cost for your distance, bunker price, and hire rate.

How it works

Bunker consumption is modelled with the classic cube law, where consumption at speed V relates to a known reference point:

consumption(V) = ref_consumption × (V / ref_speed)^3      tonnes/day
voyage_days    = distance / (V × 24)
fuel_tonnes    = consumption(V) × voyage_days
fuel_cost      = fuel_tonnes × bunker_price
hire_cost      = voyage_days × daily_hire
total_cost     = fuel_cost + hire_cost

The tool evaluates total_cost at every speed in half-knot steps across your range and reports the minimum. Because fuel rises with the cube of speed while days fall only linearly, the cost curve is U-shaped and has a clear minimum.

Worked example

A handysize vessel burns 45 t/day at a reference speed of 14 knots over a 5,000 nm voyage. With bunkers at USD 620/t and hire at USD 18,000/day, dropping from 16 knots to around 12 knots can save tens of thousands of dollars because the fuel saving outweighs the extra charter days — until the hire cost of the longer voyage starts to dominate again at the very low end.

Notes

Use the vessel’s actual sea-trial or noon-report consumption for the reference point, and add margins for weather, currents, and hull fouling before committing to an operational speed. The cube law is most reliable near the design speed.