In our previous article we compared two and four Flettner rotors on the Ecoliner and found that doubling the devices does not double the savings. That comparison held one thing fixed: the route. Both configurations sailed the Great Circle at a constant 12 knots, which is the most common assumption in the industry.

It is also the assumption that costs the most. The shortest path is the cheapest for a ship that only burns fuel. For one that also harvests wind, shortest and cheapest are no longer the same, and the gap between them holds a large share of the business case.

This article explains how we compute a route, why the resolution of that calculation matters as much as the resolution of a Computational Fluid Dynamics (CFD) mesh, and what letting the route move is worth on the Ecoliner.

How Ships Are Routed Today

Weather routing is not new. R.W. James published the isochrone method, with time fronts plotted by hand, in 1957 . Zoppoli applied dynamic programming in 1972, computer implementations followed from the late 1970s, and Hagiwara and Spaans adapted the isochrone method to sail-assisted motor vessels in the 1980s. Today’s solvers also include calculus of variations, graph search such as Dijkstra and A*, evolutionary and heuristic optimisers, and increasingly machine learning (Zis et al., 2020). Graph search is widely used because it returns the optimum over the discretised space, at a computational cost that rises steeply with resolution.

On a conventional motor ship the gains are modest: the International Maritime Organization (IMO) GreenVoyage2050 portal puts the saving potential of weather routing at 0.5 to 5%, depending on ship size, type, and trade. A wind-assisted ship changes the problem. Once part of the propulsion comes from the wind, consumption depends on heading as well as on distance, and the cheapest path can sit a long way from the shortest.

The standards have only begun to address this. The International Towing Tank Conference (ITTC) guideline of 2024 admits route and speed optimization only at Level IV, the highest of its five assessment levels, which it recommends for ships that use extensive weather routing. And MEPC.1/Circ.896 (IMO, 2021), the IMO guidance on crediting wind propulsion, never mentions weather routing; it uses a global wind matrix independent of any voyage.

How We Compute a Route

Our routing tool builds a graph over the ocean: a mesh of nodes on the WGS84 ellipsoid between origin and destination, evenly spaced in distance, with land masked out. Wind and waves come from ERA5, the reanalysis of the European Centre for Medium-Range Weather Forecasts: an hourly reconstruction of atmosphere and sea since 1979, built from past observations rather than forecasts, which makes any study based on it a hindcast. With a time dimension added, every node carries the conditions the ship would have met on arrival, not a seasonal average.

Power consumption polars from our Performance Prediction Program (PPP), with and without devices, weight each edge by the energy needed to cross it, and a Dijkstra search returns the route of minimum total energy. Added resistance in waves enters through SNNM, a semi-empirical method (Liu and Papanikolaou, Ocean Engineering, 2020) the ITTC guideline accepts, and it matters: waves shift the propeller operating point, so rotor thrust relieves more brake power than in calm water. Because energy trades against time, the search is constrained to set arrival times relative to the Great Circle, which is what makes the result something a shipowner can price.

Resolution Matters, Just as It Does in CFD

A routing calculation is a discretisation, and like any discretisation it can be too coarse to trust. In our experience, whether the route is imposed on the Great Circle or free to move, a coarser mesh consistently reports lower consumption, which is to say higher savings.

The cause is the optimizer itself, which minimises consumption with whatever the model gives it, errors included. On a coarse mesh a segment can run for hundreds of miles at one heading, and if its conditions are favourable the ship is credited with them for the whole leg. Refining splits that leg into sub-segments matched to the wind they actually meet, and the time and heading the ship can hold in favourable conditions shrink. Cell shape matters too: cells longer along the track than across it allow finer heading choices and gentler, more realistic course changes. With the same number of cells this costs nothing extra but narrows the corridor the route can explore, and keeping the same width of ocean takes more cells and a much higher computational cost.

The direction is familiar: our low and high fidelity aerodynamic models showed savings falling as fidelity rose. Sun et al. (Journal of Marine Science and Engineering, 2022) also note that grid resolution affects the resulting path, and the ITTC guideline warns that «desktop studies using weather hindcast data may give too optimistic results compared to real-life routing situations». Mesh resolution is one way that optimism enters, and one the modeller controls.

What It Is Worth on the Ecoliner

The North Atlantic results from the previous article are the starting point. They are annual averages over departures throughout 2023, for Plymouth to New York and back on the Great Circle at a constant 12 knots, with high fidelity polars including wave resistance:

To isolate what route optimization itself is worth, the second case from our RINA Wind Propulsion 2024 paper (Bujeda et al., 2024) takes a single Saint Nazaire to Kourou passage, departing on 4 December 2023, and fixes the travel time of a Great Circle crossing at 12 knots, which is 12.51 days. The solver then looks for a better path within that time: heading and speed are free, the arrival time is not.

With calm water polars, optimising the route is worth 0.54 percentage points on this departure, close enough to nothing that it would not justify the analysis. With waves included, the same optimizer on the same voyage finds 8.97 points. The optimizer did not improve; the model did. A model carrying sea state can see that it is often worth accelerating to avoid a head sea even when the apparent wind angle worsens, and a calm water model cannot value that decision.

a) NazKou GC vs Optimal Route in CW

b) NazKou GC vs Optimal Route with Wave Resistance

Figure 3. Great Circle compared with the optimised routes obtained using wave-penalised and calm water polars, departure of 4 December 2023. (Image adapted from internal work)

a) NazKou Optimal route conditions in CW  b) NazKou Optimal route conditions with Wave Penalty

Figure 4. NazKou Optimal route conditions comparison using Wave Penalty and CW Polars (Image adapted from internal work)

The effect carries through to the investment case. For the Plymouth to New York round trip with the x2FR configuration, we repeated the 2023 annual average with the route optimised, keeping the 18.46 day round trip of the Great Circle at 12 knots:

These figures assume:

• LNG carrier of 8,210 tons capacity, Great Circle round trip of 5,317.32 nm over 18.46 days
• Fuel at 700$/ton and 300 operational days
• Total installed cost of 1,400,000$ for the x2FR configuration, including tilting mechanisms
• No carbon taxes, which makes the payback figures conservative

These are rough estimates, and costs should be reviewed against a manufacturer’s pricelist. Route optimization covered the x2FR configuration only. On these assumptions, letting the route move, with the same arrival time as the Great Circle, more than doubles the predicted power savings, from 8.10 to 18.04%, and cuts payback from 8.46 to 3.8 years.

Conclusion

The route is not a boundary condition, it is a design variable. On this vessel, optimising the path of the x2FR configuration cut payback from 8.46 years to 3.8, while adding a second pair of rotors on the fixed Great Circle pushed it out to 12.11. The x4FR configuration was not run on optimised routes, so the comparison stops there, but the largest gain we measured came from how the ship sails, not from what it carries.

That value is only visible to a model that sees what the ship is sailing through. Omit waves and route optimization looks close to worthless; coarsen the routing mesh and it looks better than it is. Getting the number right means resolving the physics and the discretisation together.

For a shipowner, the question was never only which devices to install. It is also how the vessel will be operated once they are aboard.