In the past two posts I outlined the approach we’ve taken in preparing for our BVI trip. With the big-ticket things out of the way, my attention has turned to our specific routing for our tour of the islands.
As I mentioned previously, the BVI are renowned as a sailing paradise–and one of the reasons is what they call “line of sight” sailing. I will admit that the (relative) ease of navigation in the islands is a bit of a disappointment to me as I truly love navigation. When we did our Lake Michigan sail, I spent a LOT of time planning and mapping our trip.
Since the chart work for a BVI trip is pretty straightforward, I found myself inventing a rabbit hole to chase down. This descent into madness started with me pondering this simple thought: If a catamaran can’t sail as close to the wind as a monohull, doesn’t that make travel longer?
Tacking and the Pythagorean Theorem
On a hypothetical boat that can sail up to 45 degrees from the wind, tacking straight into the wind is relatively easy to calculate. If you sketch it out, you’ll see that you’re sailing the two legs of a right triangle–instead of the straight line which forms the hypotenuse. Thanks to Pythagoras, we can compute that to sail to a destination one mile straight into the wind on this boat, we will travel 1.42 miles on our back-and-forth tacking course.
But our catamaran, according to published data, really can’t get much closer to the wind than 60 degrees. I’ll save you the math, but with a couple extra steps we can see that on such a boat, to reach that destination a mile upwind, we will sail a full 2 miles.
And this is where I went off the rails. I started trying to come up with a comprehensive model that would–given inputs of heading-to-destination, distance-to-destination, wind heading, and boat’s tacking ability–calculate the exact bearing to sail, and the distance you’d travel. A half a pad of graph paper later, I was really struggling to make sense of it. I’d work for an hour, then give up, then try again.
Tacking and the Law of Sines
Mind you, this is really not too useful, even if I can make work. It doesn’t vary that much. But I was determined. At long last, I brought it up to a work colleague who happens to have PhD in mathematics, who suggested I look at the “Law of Sines.” The hard part in my model was that for a boat that tacks anything other than an exact 45 degrees, the calculations of the distances had too many variables and I kept getting stuck.
The Law of Sines lets you solve any triangle if you know two angles and one side–which I did for each case. The best part of the story? Recognizing my math limitations, I bought one of those laminated “quick guides” to trigonometry. I used the first page extensively during my little quest. After hours–days–of fruitless hacking and quizzing my PhD friend, I finally got it. I then happened to open the quick guide, and, sure enough, this exact solution was on page two. But who wants to read instructions, right?
~Kent
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