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Coastal piloting with radians

Jan 1, 2003
From Ocean Navigator #90
May/June 1998
After three days in the fog, we had to get across the eastern portion of Penobscot Bay, Maine, in visibility that was expressed in a small number of boat lengths. As the feeble, late-afternoon sun sank toward the Camden Hills, we were bound for Mark Island Light, six foggy miles away at 080° true.

As we departed Fox Islands Thorofare, a buoy, straining on the end of its rode, showed the tide flooding at about 1.5 knots, setting nearly perpendicular to our course, from right to left. As usual, our boat speed in Restless was six knots (Restless always does six knots; it is a constant of the universe I have come to depend upon). I seized this opportunity to demonstrate to my father a little practice in fog-bound piloting. With the tide setting us perpendicularly, at a simple fraction of our speed, the sometimes bothersome vector relationships of accounting for a current were relatively straightforward.

"So, Dad," I yelled from the nav table, "the flood will set us north, at a rate approximately one-quarter of our speed. Counteracting this requires steering one-quarter to the south."

"One-quarter of what to the south?" my father asked.

One-quarter of a radian," I said. A radian is a measure of an angle not in degrees but in distance. A radian is the angle made by laying the radius of a circle on the circle's edge, or circumference. The early Greeks were astounded to discover that in a given circle the radius always takes up the same amount of circumference of the circle: they called this angle a radian, and it equals approximately 60°.

"Fine," my father said. "What's this got to do with getting home before dinner?"

Well, radians allow one to use boat speeds to measure angles. Restless's speed is the radius of the fictitious circle, and the tidal current is the portion of the circle we want to measure. The drift of the tidal current was 1.5 knots, perpendicular to our boat's velocity of six knots; the tide would push us north by 1.5/6 = 1/4 radian. If a radian is 60°, one-quarter of a radian is 60/4 = 15°. If we steered 080°, we would make good 065°. So, rather than steer 080° true, I asked my father (one shouldn't tell one's father and captain anything) to steer 095°.

My brother Jim took out his GPS. I took out my dividers and plotted my dead-reckoning positions and his GPS positions every six minutes for the hour it took to cross. As we left the Thorofare, we ran the rhumb line rather well; it was not until mid-channel that the GPS revealed that we were slipping south of the rhumb. No doubt the tidal current was weaker here; the combination of GPS and DR revealed a drift of one, rather than 1.5 knots. This is the beauty of using both the DR and the GPS: the latter provides information that updates the former, while the former provides the information needed to steer the best course. With the new information, I asked (didn't tell) my father to come to 090 in mid-channel, and then back to 095 as we neared Mark Island Light.

My last DR had us about 1/8 nm offshore of the light, in about 70 feet of water, when my uncle shouted, "Ahhhhhturn left, I mean port, I mean just go that way" as the light suddenly popped from the fog.

My father was at first skeptical that any of this DR nonsense was needed on a boat with a well-functioning GPS. I had a number of responses to him.

Our exercise of combining DR with GPS was, well, a great deal of fun. Jim was shouting down lats and longs; I was plotting the fixes and the DRs, recalculating our course; my uncle was on the bow as lookout; Dad was drivingand for an hour we had an extraordinarily well-navigated boat. Grand fun, indeed. But equally as important, we practiced some reasonably fundamental piloting skills in a setting where error was not likely to be dangerous. Sure, we didn't need to plot all those DRs, we didn't need to calculate a course to compensate for the set and drift every six minutesbut it was the right thing to do, the thing that the captain of any vessel plying those same waters a century ago might have done. After all, part of the joy of sailing is using what you're given to get where you're going.

It was also a fine time to demonstrate to us all how GPS can actually aid the traditional practice of DR and coastwise plotting. These same skills are helpful while racing, or in any situation in which saving time and distance is crucial.

Such as, I pointed out to my father, getting to dinner.