Ship Fuel Consumption
Fuel burn rises with the cube of speed for a ship.
Formula
Variables
Example
Cutting speed 20% saves roughly half the fuel (0.8³≈0.51).
How it works
This relation says that a ship’s required fuel rate grows very rapidly as speed increases: if speed doubles, the fuel burn rises by a factor of 8. The cubic dependence is an engineering approximation that comes from the fact that water resistance increases strongly with speed, and the engine must supply more power to overcome that drag. The constant c captures the hull shape, propeller efficiency, loading, and sea conditions, so different ships can have very different fuel use at the same speed.
When to use it
Use this for quick estimates of how changing cruising speed affects fuel consumption on the same vessel in similar conditions. It is especially useful in voyage planning, cost trade-offs, and comparing fuel savings from small speed reductions.
Worked example, step by step
A cargo ship has c = 0.18 and is sailing at v = 14 knots. Step 1: Write the formula: F = c v^3 Step 2: Substitute the values: F = 0.18 × 14^3 Step 3: Calculate the cube: 14^3 = 2744 Step 4: Multiply: F = 0.18 × 2744 = 493.92 Final answer: the fuel rate is about 494 units per hour (in whatever units match c).
Common mistakes to avoid
- Using speed squared instead of speed cubed
- Forgetting that c depends on the specific ship and conditions
- Comparing fuel rates at different loads or sea states without adjusting the constant
Did You Know?
'Slow steaming' exploits this cube law — shipping lines cut speed to slash fuel bills and emissions.
Share this formula
More in Marine & Nautical
View allHull Speed
IntermediateTheoretical top displacement speed in knots from waterline length in feet.
Speed in Knots
BasicOne knot is one nautical mile per hour.
Nautical Mile to Kilometres
BasicConvert nautical miles to kilometres.
Buoyant Force (Archimedes)
IntermediateUpward force equals the weight of displaced water.
Ship Displacement
IntermediateA floating ship displaces its own weight in water.
Draft from Displacement
AdvancedDepth of hull below waterline from displacement and waterplane area.