## Wind, Tide and Boat Speed

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They are the 3 things you need to work out how long it will take to get from point A to point B in a boat.

Getting the first two is quite easy, all you need is your own personal meteorologist and some help from the Proudman Oceanographic Laboratories in Liverpool, the first one can build you a forecast using the wonderful ‘SiSoft Weather Maker’ the second a library from which you can query tidal speed and direction at specific coordinates.  The third thing isn’t quite so simple…

I have mentioned polars previously but I wanted to expand on that and explain what they are and how I use them in more detail.

When a sailor talks about ‘polars’ they are refering to the graph which describes the behaviour of their boat.  It is refered to as a polar because the type of graph used to show this information is a polar diagram.

On a normal graph a position in graph space is defined by using a set of Cartesian coordinates [x,y] on vertical and horizontal axes.  On a polar diagram a position in space is defined using polar coordinates [Θ,r] on an angluar axis and a radial axis, with the option of a vertical axis [z].

In our case:

 Θ = True Wind Angle (TWA) r = Boat Speed (BS) z = Velocity Made Good (VMG)

The TWA is the angle of the wind relative to the boat, BS is the speed of the boat through the water, VMG is the component of the boat speed that is in the direction of the destination.

Skandia Cowes Week has around 38 classes which range from very small to very large, for which we need a polar to describe each class.  So as to reduce the amount of work we had to do we only collected 3 polars.  One which represents a displacement hull, one a sportsboat (or planeing) hull as well as one for multihulls and all of them with an IRC handicap rating of 1.0.  Using this we can then scale the polar values to the equivalent rating for each class in the fleet.  This is easy for the large classes as the IRC rating is easily obtained, for the day boats this is less so.  We in fact use another common handicapping method, the Plymouth Yardstick, and becuase there is a one design boat which has both a known PY and IRC rating we can workout the scale factor for the small boats in the fleet.

With this background it becomes easier to see what the curves represent, each is fitted through 5 points, representing a different angle of sail, beating, close reaching, beam reaching, dead reaching and running respectively.  The 5 curves then represent a True Wind Speed (TWS), in this case, 6kts, 10kts, 14kts, 18kts and 25kts.  The horizontal lines are the point at which VMG becomes important, they represent the situation where your destination is either directly into the wind, or directly with the wind, because you physically can’t sail directly into the wind, you sail at an angle to it and tack every so often, so as to counteract the perpendicular distance you travel from your target.  So if your destination is 5° from the wind, we assume you are beating and therefore your boat speed will be that at your closest angle to the wind which could be 30°.  Drawing a line from your beating angle to the vertical axis gives us the VMG, which will become important later.

Lastly, if the wind speed lies between two defined curves, we take the upper and lower bound and linearly interpolate between the values, with all of this data it is possible to work out VMG and boatspeed for a given wind angle and wind speed for any boat in the fleet.

To get your boat speed you need to know the angle you are sailing to the wind, so you need to know your ‘Course To Steer’ (CTS) which is the heading you follow so that when tides are accounted for you’ll end up at your destination.  Unfortunately to work out the CTS you need to know your boat speed, and so as you can see we have a dilemma.

We get around this by looping over the function to calculate your CTS until the change in CTS is within a defined threshold, with the initial boat speed obtained by using an angle to the wind equal to the bearing of your destination.

Once you have the CTS and the corresponding boat speed for that CTS you can work out how long it will take to get to your destination. This is all well and good if the distance to that destination is quite short, but sometimes you will be working out the ETA for a destination that is several tens of miles away, and both the wind and tide will change from the values you originally used as you progress spatially and temporally to your destination.

To overcome this issue we can do one of 2 things; divide the trip into a defined number of segments and calculate the ETA for each segment, which still has the disadvantage of becoming more inaccurate over longer distances, or repeatedly calculate the distance traveled in a defined time interval, using new wind and tide data, until the distance between your current position and your destination is within a defined threshold.

The second method has the added advantage of allowing for the scenario where given the wind, tide and boat speed, the actual direction traveled is back to your start point.  When this occurs an assumption that one is kedged can be made, so the algorithm will add a time increment until either the wind picks up enough that you can continue against the foul tide, or the tidal stream changes to become more favorable.

And that is how you get predicted finish times that are accurate to ±5 seconds over 4 hours.