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The following courtesy of
	 The Navigation Foundation  (Tel. 301-622-8448)
	 P.O. Box 1126, Rockville MD 20850
	 The Navigator's Newsletter, Issue Twenty-three, Winter 1988-89

Dan Hogan
     dhhogan@earthlink.net	
	dhhogan@delphi.com

*******************************
A Simplified Technique for Costal Piloting
by Edward J. Nesbitt

	This artricle offers a simple way to solve the frequent problem of
determining how far offshore one is during coastwise sailing, or what is the
distance to a lighthouse or buoy being passed.

	Take two compass bearings in degrees on the point selected. The first
should be when it's forward of the beam and the second when it's abaft the
beam. Also record the times when each was taken and then determine the rate
at which the degrees changed per minute by dividing the difference in
bearings in degrees by the number of minutes between the readings.

	You can find the answer "how far away you are," in nautical miles, by
simply dividing that number into the speed of your boat (over the bottom) in
knots.

	I've used this procedure for over five years but have never met anyone who
knew of it before. I worked it out on an airplane flight after wondering how
far away a particular mountain peak was and reasoning that there must be
some way to compute it based on how fast the angle to it through the plane's
window was changing. I'd thought of this before on a sailboat but didn't
have the time to doodle about it.

	There is a slight error (about 10 percent) due to this simplification which
one could correct by reducing the the distance in the answer by 10 percent,
and he'd be "bang on." But who knows a boats speed that accurately anyway?

	This method has two advantages over the procedure usually employed: it does
not depend upon the boat maintaining a steady course (which no small boat
does) and you don't have to make your readings when the point in question is
at a precise angle to your course. You can start and end when you think of
it, although to keep the error to 10 percent, it's best to be within 10 to
30 degrees of the abeam on both readings. But even if one reading was 40
degrees from abeam and the other 10 degrees, the error (still high) would
only be 18 percent and a conscientious navigator could compensate for it if
he wanted.

	A compass bearing is easily taken by a hand held compass, or by one on an
RDF, or taken from the binnacle. Even if there is an error in the compass,
it will be the same on both readings since they are only 30 to 60 degrees
apart. The boat can deliberately change course by 10 to 20 degrees between
readings with neglible effect on the accuracy of the answer.

	To the scientifically curious who might be wondering how this simplified
procedure works, it is due to the fortuitous coincidence that the rate of
change of the trigonometric function of both the sign and the tangent, in
units per degree, when the degree is small, is .0175 (2 pi divided by 360),
and that by 24 degrees, which is in the expected range of angles before and
aft of the beam used in this procedure, the tangent rate of change is only
.0185 which is only about 10 percent greater than 1/60. The procedure uses
boat speed in nautical miles per hour, and the degree change minute. The
sixty minutes in each hour exactly cancels this out, at least with the 10
percent that he answer is high. This procedure is therefore not a discovery
but rather a simple observation. Just remember: divide the boat's speed by
the degree change per minute.

   

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