# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**A Distance Off Method**

**From:**Dan Hogan

**Date:**1995 Jun 22, 11:35 PDT

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.