Speed Optimization Tool for Marine Voyages
The Speed Optimization Tool helps ship operators, engineers, and chartering teams
determine the optimal vessel speed that minimizes overall voyage cost.
It balances fuel consumption against time-related costs using
a physics-based power model and realistic operational inputs.
This makes it suitable for slow steaming analysis, charter party planning,
and operational efficiency studies.
What the tool calculates
For each candidate speed within the selected range, the calculator evaluates:
- Voyage time from distance and speed
- Main engine power using a scaling law (P ∝ Vⁿ)
- Total power demand including sea margin and auxiliary load
- Fuel consumption using SFOC
- Fuel cost from fuel price
- Time cost from daily operational or charter cost
- Total cost = fuel cost + time cost
The result is a full cost–speed curve, from which the tool identifies both the
cost-optimal speed and the fuel-optimal speed.
Underlying model & assumptions
Power–speed relationship:
P(V) = Pref × (V / Vref)ⁿ
Total power:
(Main engine power × (1 + sea margin)) + auxiliary load
Fuel consumption:
Fuel (t) = Energy (kWh) × SFOC (g/kWh) / 1,000,000
The exponent n typically lies between 2.7 and 3.5 for displacement vessels,
with n ≈ 3 commonly used as a first approximation. You may adjust it to reflect
hull form, loading condition, or empirical trial data.
Cost-optimal vs fuel-optimal speed
This tool deliberately distinguishes between two important operational speeds:
-
Fuel-optimal speed:
The speed that minimizes total fuel consumption, usually the lowest practical speed.
-
Cost-optimal speed:
The speed that minimizes total cost, where higher fuel burn may be justified
by reduced voyage duration and lower time-based costs.
In tramp and time-charter operations, the cost-optimal speed is often more relevant than the fuel-optimal one.
In liner or emission-constrained operations, fuel-optimal or emission-optimal speeds may take priority.
How to use the Speed Optimization Tool
- Enter the voyage distance and economic parameters (fuel price, time cost, currency).
- Define the reference speed and power, SFOC, sea margin, and auxiliary load.
- Select a realistic speed range and step size.
- Run the optimization to generate the cost curve and optimal speeds.
- Export the result as PNG or PDF for reporting or comparison.
Typical use cases
Operational planning
- Slow steaming studies
- Fuel vs schedule trade-off analysis
- Weather margin sensitivity checks
- Auxiliary load impact assessment
Commercial & chartering
- Time charter vs bunker price scenarios
- Voyage cost minimization
- Laycan and schedule feasibility
- Speed clauses evaluation
Limitations & good practice
- This is a steady-state model; acceleration, currents, and heavy weather effects are not explicitly modeled.
- Results depend strongly on SFOC and time cost—use realistic values.
- Use consistent assumptions when comparing multiple voyages or vessels.
- For regulatory work, combine this tool with emissions and efficiency indicators such as EEOI or CII.
Related calculators
The Speed Optimization Tool is most powerful when used together with the following calculators: