Power of the Arrow

To introduce our November 2006 issue, CW editor John Burnham gives a quick lesson on vectors and their usefulness for navigating in current.

First there were little boats, drawn with a ruler and cut out to race across the living-room floor. Sloops, yawls, schooners, and ketches with such names as America, American Eagle, and Barlovento. Drawing the boats was fun, and I made whole fleets of boats, small and large, then spent many happy days racing them around courses, moving them one to six boat lengths at a time, depending on the roll of the die.

Drawing triangular sails didn't lead me to a career as an artist, but it was a natural introduction to geometry and one of the reasons I preferred the subject to other math courses. Not only was there the drawing part, but this kind of math could also be seen, so it was easier to understand.

By the time I first noticed something called a vector, I was an English major in college, dipping my toe into an introduction to naval architecture. Vectors sure looked like lines, but they were much more powerful; now, at the tip of my pencil, I could draw something I couldn't see, such as the lift and drag forces on sails, keels, and rudders.

My Webster's says a vector is "a quantity that has magnitude and direction and that is commonly represented by a directed line segment whose length represents the magnitude and whose orientation in space represents the direction." In plain terms, it's a line with an arrow on one end, and its length, depending on the scale you use, represents the speed or force you're expressing.

In two fundamental ways, vectors provide sailors with visual explanations of how our sailboats are moving and the forces acting on them: first, how the wind in our sails changes when a boat begins to move; and second, how a boat's motion through water is affected when the water itself is moving (due to tidal, river, or other current). The first helps us predict whether we may have to reef when, for example, we reach our next waypoint and turn upwind. The second is even more useful: It helps us plan how to sail a direct course over the bottom when navigating in current.

This month's Hands-On Sailor section features two stories on piloting in current, starting with "A Compass (Still) Saves the Day" by Joseph Huberman. Aboard their 43-footer on a foggy day while approaching the Cape Cod Canal, the Hubermans learn a valuable lesson about which instruments to navigate by when in strong current. In "Practice Up for Fog and Current" by Jeremy McGeary, a CW contributing editor, you'll find a solution to the Hubermans' challenging scenario, and you'll learn a couple of ways to plot your course across a current. If you look closely at Jeremy's first diagram, which teaches you how to draw out your course on the chart to allow for the current, you'll see vectors representing the speed and direction of the current and the boat. The author doesn't scare anyone by calling them vectors, but you'll recognize them from the arrows at one end.

You don't really need to worry about the underlying math as you do your coastal piloting, just as you may not need to refer to your paper charts often, since electronic charts can now give you so much detail. (See "Comparing Today's Smart Charts.") Normally, your eyes can handle the rest, orienting you to all that's around your boat-rocks and islands, wind and current, buoys and lighthouses, and, of course, other boats.

But what happens when you must deal with the limited visibility caused by fog, rain, or darkness? That's a good time to be ready to pick up a pencil, a pair of dividers, and parallel rules and lay down a course on the chart that allows for current and a safe margin of error. Keep in mind that you don't have to be an artist to draw a straight line. Nor a mathematician to put an arrow on the end of it.