This page explains how weather data was sourced for each waypoint of the route and how this data was combined with a ship speed and direction to find the apparent wind speed and direction to the Flettner rotor.

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Sourcing wind data was a crucial part of the project as the effectiveness of the Flettner Rotor would ultimately be determined by the wind resource available. Having planned and mapped the route the project would consider, the next step was sourcing reliable weather data. Initial plans to use yearly-averaged weather data were scrapped with the realisation that this would not adequately represent weather data on a single trip across the North Atlantic. Instead, real-time weather data from the European Centre for Medium Range Weather Forecasting (ECMWF) was used to calculate the potential savings. ECMWF is a trusted source for weather data worldwide, with many reputable partners and members such as the UK Met Office, and is used in many published papers with a similar focus on Flettner Rotors. Weather data for each point on the route was downloaded from the online database which requires python script to access and download an NC file, and then can be read using free-to-download software Panoply.

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Data was downloaded twice daily, as is standard for data-sets from the “ERA-Interim” database (on of the many databases available from ECMWF), which includes the relevant wind data. As a simple forecast download, the time step was set to 3 hours, this number must be more than 0 to obtain only forecast parameters, where a step of 0 gives more in depth analysis data, a step of 3 was chosen out of the available 3, 6, 9, and 12 options. The geographical location to be covered in the data was set using longitude and latitude co-ordinates in the format North/West/South/East. The understanding of the python script was gained through the use of the numerous help pages available on the ECMWF website (ECMWF, 2018). The Python script for the February weather data is shown below, along with the georeferenced plot of U component wind velocity on 01/02/18 at 03:00am.

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Georeferenced plot of U component of wind velocity on 01/02/18 at 03:00am as presented by Panoply Software

 

Once downloaded and accessed via Panoply software, the data was arranged in a table using Microsoft Excel. Using the following equations the true wind speeds and direction, along with the boat’s speed and direction can provide the apparent wind speed and direction in relation to the boat, to be later used in thrust calculations.

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u_t and v_t are the longitudinal and latitudinal components of wind speed as downloaded from the ECMWF database, respectively. Using the course direction of the ship (α_b) and the average cruising speed of 13.3 knots (or 6.84 m/s), the boat speed can be split into longitudinal and latitudinal components (u_b and v_b) to be subtracted from the components of true wind speed and to obtain the apparent wind speed (which is relative to the ship).

 

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The angle of apparent wind can be given as:

 

 

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Where α_a refers to the apparent wind angle (0° being North), not including the orientation of the ship. Since Excel is being used, it should be noted that the ATAN formula on excel which functions as tan^-1 only yields results in the first and fourth quadrants, effectively only giving angles between -90° to 90°.

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To combat this the results were adjusted using the following system for each dataset:

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• Both u_a  and v_a values positive: no angle conditioning required

• Only negative v_a value:  +180°

• Only negative  u_a value:  +360°

• Both  u_a and v_a values negative:  +180° 

 

The apparent wind angle can be used to find the angle of attack relative to the boat, α.
 

With longitudinal and latitudinal apparent wind speeds u_a and v_a respectively,  the apparent wind speed can be expressed in a magnitude U.

 

 

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This is the form which can be used in subsequent calculations, with the magnitude of apparent wind speed, U, and the angle of attack relative to the boat, α.

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Although the angle of attack is crucial to the power generation, it is understood that an angle of 20° and -20° will have the same power generation because the rotor rotation can be reversed. However, the coefficient of thrust, presented in the background theory section, does not give these desired results.

 

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Therefore, the angles of attack for each data set are presented by an angle between 0° and 180° to give the desired results from this equation.

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References

ECMWF, 2018. Copernicus Knowledge Base. [Online]
Available at: https://confluence.ecmwf.int/display/CKB/Copernicus+Knowledge+Base
[Accessed 10 March 2019].