# fw – the unknown factor

Legislation on the Energy Efficiency Design Index (EEDI) requires the determination of a “weather factor” – *f _{w}* – reflecting the percentage of its calm-water speed that a ship can maintain in Beaufort 6 and corresponding waves. The higher the

*f*value, the smaller the speed loss and the better the ship will perform in a seaway. But how do we determine this unknown

_{w}*f*factor, and how do we strike a balance between accuracy and costs? As a member of the International Towing Tank Conference (ITTC) SSPA is actively involved in developing guidelines on

_{w}*f*and as an independent maritime consultant and established model testing basin we have the knowledge and tools required to realistically determine the “unknown weather factor”.

_{w}To cap greenhouse gas emissions, the International Maritime Organization (IMO) has introduced the Energy Efficiency Design Index (EEDI). This index is a measurement of the amount of carbon dioxide that a ship emits in relation to its cargo capacity and speed:

where fw is the so-called “weather factor” that takes the influence of wind and waves into account. It is defined as:

Here *V _{w}* denotes the speed of the vessel in Beaufort 6 (3 m significant wave height and 12.6 m/s wind speed) and

*V*is the speed of the ship in calm water.

_{ref}### The crude way – *f*_{w} from IMO’s standard curves

_{w}

A very simple, if somewhat rough, method of obtaining an initial estimate for *f _{w}* is described in IMO Circular MEPC.1/Circ.796. The method is based on regression analysis of full-scale measurements, i.e. on the actual speed reduction of existing ships, and only requires ship type and cargo capacity as input. Three kinds of standard

*f*curves are provided for bulk carriers, tankers and containerships. The disadvantage of this simplistic method is obvious: it will not give a ship-specific

_{w}*f*value, i.e. it cannot distinguish between a good and a bad design.

_{w}Two things are required to obtain a more realistic and above all ship-specific value of *f _{w}*: determination of the calm water speed and determination of the ship speed in Beaufort 6. At SSPA, we have the knowledge, tools and facilities to help with both.

### Calm water model tests already mandatory under existing EEDI rules

As shown in the flow diagram, these speeds are determined separately. Finding calm water resistance and calm water speed *V _{ref}* is relatively straight forward and part of the model tests that have been mandatory under the EEDI rules since 2013. As shown on the right-hand side of the flow diagram, this includes a combination of model towing tests, model self-propulsion tests and model propeller open water tests.

### Speed in wind and waves

Finding the total resistance in wind and waves and the corresponding ship speed – *V _{w}* – is a bit more complex and also requires knowledge of wind resistance and added wave resistance.

As illustrated on the left-hand side of the flow diagram, the aerodynamic resistance of the ship is best determined through wind tunnel testing. As an alternative, we can normally find values for similar ships in our wind-force database.

A ship sailing in a seaway experiences a hydrodynamic force component known as “added resistance in waves”. This force can be determined using CFD calculations or free sailing model tests in SSPA’s Maritime Dynamics Laboratory. The choice of method depends on how far the design of the ship has progressed and on many other factors that need to be considered carefully. A full seakeeping test would clearly be out of place at the concept stage of a design. However, if manoeuvring and seakeeping tests are scheduled to prove a final design, why not test for *f _{w}* as well?

### Power prediction and *f*_{w}

_{w}

Once the total resistance in wind and waves is known, the corresponding engine power to overcome this resistance can be calculated using the principles of the “ITTC 1978 Performance Prediction Method”. As illustrated in the speed power plot, such predictions are made for several ship speeds and a speed-power curve in wind and waves is plotted. Finally, the *f _{w}* value is determined from this.

### SSPA database for *f*_{w} of tankers

_{w}

As part of a strategic research project, SSPA has by way of seakeeping model tests determined *f _{w}* values for a number of tankers ranging from 2,500 to 150,000 deadweight tonnes. The results are illustrated in the

*f*values versus “Capacity” plot above. Also shown are full-scale values from IMO Circular MEPC.1/Circ.796 and the “Standard Curve” from the same IMO publication.

_{w}As can be seen, agreement between full-scale data and SSPA’s model test results is good. The generic IMO standard curve on the other hand is extremely conservative because *f _{w}* is underpredicted, i.e. speed loss is significantly overpredicted.

**What is f_{w}?**

A “weather factor” reflecting the percentage of its calm water speed that a ship can maintain in Beaufort 6 and corresponding waves.

**What is EEDI?**

The Energy Efficiency Design Index (EEDI) is a measurement of the amount of carbon dioxide that a ship emits in relation to its cargo capacity and speed. The achieved EEDI value of most new-build ships has to be below a certain limit set by the International Maritime Organization (IMO). If a ship fails to comply with the required EEDI, it is not allowed to be taken into service.

**Is it mandatory to determine f_{w}?**

Yes, but currently a poor *f _{w}* value will not influence the attained EEDI. It is expected that this situation will soon change.

**Why test for f_{w} at SSPA? **

To obtain realistic and ship-specific *f _{w}* values. The generic IMO curves are too pessimistic. We have the knowledge and the tools to provide cost-effective

*f*predictions. SSPA’s

_{w}*f*database makes it possible to compare a new design to other ships and their energy efficiency.

_{w}**Can f_{w} tests be carried out in a towing tank equipped with a wave maker?**

No, *f _{w}* determination requires a performance prediction in short crested waves. Tests in head waves alone are not sufficient.

**Can you calculate f_{w}?**

Yes, this is a viable and sensible option at the early design stage.

**For shipowners:**

A realistically determined

value makes it possible to compare design options and ships from different yards. A ship with a high

value is fuel-efficient under realistic conditions; bear in mind that wind speeds between Bft 4 and Bft 6 prevail for 65 per cent of the year in the North Atlantic.

**For shipyards:**

SSPA’s measurements show that the “standard curves” from IMO Circular MEPC.1/Circ.796 are too pessimistic, i.e. they overpredict the speed loss in a seaway. It is possible to obtain a more favourable and ship-specific value.

### Further reading:

- Gerhardt, F.C., Kjellberg, M.: DETERMINING THE EEDI ‘WEATHER FACTOR’ f
_{w}, RINA conference on Influence of EEDI on Ship Design & Operation, to be held in London 13-14 September 2017. - IMO, “Guidelines on the Method of Calculation of the Attained Energy Efficiency Design Index (EEDI) for New Ships”, IMO Resolution MEPC.212(63), 2012.
- IMO, “Interim Guidelines for the Calculation of the Coefficient f
_{w}for Decrease in Ship Speed in a Representative Sea Condition for Trial Use”, IMO Circular MEPC.1/Circ.796., 2012. - ITTC - Recommended Procedures 7.5-02–03–01.4, “1978 ITTC Performance Prediction Method”, 26th ITTC, 2011.

Photos and illustrations

*Two things are required to obtain a more realistic and above all ship-specific value of f_{w} : determination of the calm water speed and determination of the ship speed in Beaufort 6. At SSPA, we have the knowledge, tools and facilities to help with both.*

*Photo of MDL, the Maritime Dynamics Laboratory for seakeeping and manoeuvring tests.*

*SSPA database for f_{w} of tankers, plot of f_{w} values versus “Capacity”.*

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## A fair trial – how to obtain the correct EEDI

IMO recently passed a resolution on the Energy Efficiency Design Index (EEDI). This index is a measure of the amount of carbon dioxide a ship emits in relation to its cargo capacity and speed. A ship’s EEDI value must not exceed the allowable limit set by IMO. SSPA can help derive the hydrodynamic part of the EEDI value for new ships.

## SSPA - member of The International Towing Tank Conference

ITTC is a voluntary association of worldwide organizations responsible for the prediction of hydrodynamic performance of ships and marine installations. The association is also an observer at the International Maritime Organisation (IMO).