Posts Tagged “Polars”

The Marvel of 3D Printing...

The prototype wind direction indicator.
The prototype wind direction indicator. The shaft is (deliberately) too long, and you can see the pair of low torque potentiometers at the bottom of the shaft. The housing was made using a 3D printer. Unfortunately, the PLA material is quite reflective, so it doesn't show up particularly well in this image.

So, while debating the different merits (or otherwise) of various mounting solutions, someone suggested using a 3D printer to actually print the housing for the masthead wind direction indicator. The more I thought about that plan, the better I liked it. As it happens, 091 Labs in Galway have a working 3D printer, from the Mendel90 family. What’s more, they are trying to get a 3D printing service off the ground! I wasn’t customer number one, but I was probably pretty close.

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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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The Software...

The FreeBSD Daemon, ready to take on Neptune and his cohorts.
The FreeBSD Daemon, ready to take on Neptune and his cohorts.

I’ve been asked recently, about the software platforms used on board Beoga Beag. This seems as good a time as any, to talk about the various layers. As mentioned previously, the lower layer is a custom board, running an ATmega8 Atmel processor. The software (Igor and Otto) is custom-written in C for the boat.

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Five Degrees of Wrong.

So, as I mentioned, the virtual boat was too eager to tack. If you’re dead downwind of the mark, and you set off on a starboard tack, within a metre of being on the left-hand side of the course, the other tack is favoured.

I added code that essentially stated “unless the other tack is at least five degrees better than the existing one, ignore it.” So, if I’m at 44 degrees TWA and the other tack is better by a degree (-43 say), stay where you are. This works quite nicely. If you look at the plotted course, it shows the boat sailing nice upwind legs, to the waypoint. As Henry would say, “it’s sailing up the ladder.”

Without that little extra piece of code, it would tack repeatedly, attempting to sail directly upwind by constantly tacking. A strategy that’s doomed to fail because tacking slows the boat down, and isn’t something you should do too often.

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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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The Timetable.

The official start to “hurricane season” is June 1st, this year. The traditional end to the season is the end of November, but the hurricanes seem to wane out by early to mid-November. A back-of-the-envelope calculation says that it’ll take up to sixty days to get from Start to Finish. That’s a worst-case estimation, but useful nonetheless. If we are to launch before the start of the season, we’d need Beoga Beag sailing to the start line by April 1st at the latest. Let’s face it, that’s not going to happen. We don’t have the pilot boat designed yet, we have extensive testing to do on the pilot boat, we need to then build the main boat, and start to fit her out. No way are we going to make that date.

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