Posts Tagged “Alpha”

Of Laylines and Beats

A Google Earth track of the virtual boat attempting an 'Olympic' course.
A Google Earth track of the virtual boat attempting an "Olympic" course. The course is to go from the leeward mark upwind to the windward (or weather) mark, sail across to the gybe mark, gybe (obviously!) and sail down to the leeward mark. After that, sail up to the windward mark again and then straight downwind to the leeward mark.

On the left, you can see the track left by simulating the Beoga Beag navigation software. It’s a short, olympic course suitable for dinghies and smaller boats. For a dinghy race, the whole thing should take less than an hour so the legs are quite short.

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Polar Curves

Polar curve for a Figaro, courtesy of SailOnline.
Polar curve for a Figaro, courtesy of SailOnline.

Even before a boat is built, the designers can predict how fast it will go at various sail angles. Using this information, they can make modifications to the hull to suit the type of sailing. For example, if an around-the-world race looks like it will see a lot of downwind sailing, it’s possible to optimise the downwind performance, and run test simulations with the boat, before ever committing to fibreglass.

The standard mechanism for displaying this information is a polar curve. Because the boat should sail at the same speed on either tack, only one side is shown. Essentially, a polar curve allows the designer (and the boat owner) to predict the hull speed for a particular true wind angle and strength. In the example above (courtesy of SailOnline.org), you’ll notice that the boats fastest speed is at a true wind angle of about 120 degrees. In the case of a 30 knot breeze (the red line), the boat should get over nine knots through the water. At TWA’s of twenty degrees and less, the boat will stop, regardless of the wind speed.

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To tack, or not to tack, that is the question...

Looking at the upper-level navigation software introduces some particularly interesting questions. The low-level software will keep the boat on a TWA, or true wind angle. Technically, it’s an apparent wind angle, but that’s ok.

The upper level has to decide what is the best TWA. To do this, it has the current position of the boat and the position of the next waypoint. It also knows the current TWA and the compass heading. Without bogging down in the maths, it can compute the distance and bearing to the next waypoint using something called a Haversin algorithm. Given the current TWA and the heading, it can determine the wind direction. We can compute the VMG or “velocity made good” for each new heading possibility, based on the predicted Polar (more on that anon). So, we can see that a particular heading is the best course to get us as fast as possible to the next mark. All of this is standard stuff, and is used on sailboat race courses every day.

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