What precision is needed when plotting positions on a chart? Mariners have lived with the “inaccuracy” of celestial navigation, so one might argue that “four miles is close enough.” This is probably true on a passage far from land when a daily fix is done to maintain the DR. But when close to land something better is required for finding those magic, out-of-the-way spots, that hidden pass, or for confidence that you are safely navigating among reef-strewn waters in little or no visibility. Navigating with confidence can avoid turning a pleasure voyage into a nightmare of frustration and worry, not to mention lessening the potential for disaster.

With the advent of GPS, formerly undreamed of accuracy in position is now continuously available to the mariner. Selective availability degrades GPS performance for the civilian user, but differential GPS provides even better accuracy. However, charts we’ve relied on for so long are sometimes grossly inaccurate in positions as shown by the GPS. I’ve experienced differences in latitude and longitude of up to one mile on the most current charts in areas such as the Solomon Islands. This has made navigation tricky in areas where reefs and look-alike islets abound with narrow passages between them, and “eyeball navigation” is required due to the lack of navigational aids.

A comprehensive treatment of the inaccuracy of old chart surveys was presented in an article by Nigel Calder (“The roots of chart accuracy,” Issue No. 87). Calder writes, “Apart from the fact that the astronomically derived starting points are often seriously in error (sometimes by milesaccording to the British Admiralty, the worst discrepancy, which is in the South Pacific, is seven miles), there are frequent surveying errors on these older charts (imprecisely measured angles between features or poorly calculated distances, etc.).” So, even when the datum used for a particular chart is entered in the GPS, there is no guarantee that the positions will match. The “offset” of these positions is still a function of the accuracy available to the surveyors when the chart information was collected and subsequently used in compiling the chart.

The average voyaging sailor is still faced with either old charts, charts without correction data, or charts that are known to have some correction for satellite-derived positions but just don’t always seem to work out properly. Ironic, when you think about itthe new technology has brought us problems along with solutions.

Interestingly, my first GPS (still my primary one) was purchased in 1992 and cost $1,200. It has a feature that doesn’t exist on its “latest and greatest” $200 backup (three months old), which has plenty of bells and whistles such as a tracking display. The feature of the (now discontinued) Micrologic Explorer GPS that serves me so well is its ability to determine the offset for any particular chart and apply that offset until you tell it otherwise. Conversely, if you know the offset by comparing a GPS reading with a known position on a chart, you can insert it, and the displayed positions will now match the chart that is in use. It will continue to apply these offsets until they are cancelled. Each time the unit is turned on, a warning is displayed to remind you that offsets are being used. So getting the GPS in sync with the chart you are using is a first step in avoiding the pitfalls from differing positions.

Even without a GPS that inputs offsets automatically, once you know the offsets in latitude and longitude, it’s a matter of carefully adding or subtracting the offsets before plotting a position. And note that I say “carefully.” As you know from the exercise of correcting a compass using TVMDC, it is easy to make mistakes between the need to add or subtract. A sketch often helps keep you straight.

An important thing to remember, though, is that the precision you obtain in plotting the latitude and longitude of your known position on the chart determines how accurately the “offsets” are calculated, either manually or automatically. Also, it would be nice to take advantage of the three-decimal-place accuracy of GPS (recognizing that selective availability makes that third decimal place suspect).

Scales and divisions The precision you obtain in plotting will certainly be a function of the scale of the chart and the latitude and longitude divisions printed on that chart. But chartmakers haven’t done us many favors in that regard. A random sampling of charts shows the minutes of latitude and longitude are divided in several ways depending on the scale of the chart. Most charts I’ve encountered use tenths of a minute, in which each smallest division equals six seconds (0.1-minute spacing). At least these are in decimal format so that eye interpolation is the easiest. But estimating the space between divisions by eye can still take a lot of practice to come anywhere near a state of accuracy that takes advantage of the GPS precision. Other charts, however, use divisions of five, 10, or 15 seconds of a minute. Plotting in a “decimal” format on these charts is a frustrating exercise of conversion; it’s time consuming and leads to mistakes.

The accuracy triangle is a graphical technique I have developed that allows at least one more decimal point of accuracy in eye interpolation and simultaneously provides a “decimal scale” for those charts still using divisions in seconds of a minute. Once constructed on a chart, it remains for future use. With this technique, plotting a GPS position of, say, 2° 12.852′, can be done with confidence, to at least 2°12.85′. With normal eyeball interpolation the best you would expect is 2° 12.8′.

The technique uses the principal of proportionality of sides of a triangle. I construct and use an accuracy triangle on both the latitude and longitude sides of a chart in the following fashion.Constructing the accuracy triangle

Choose any one-minute division on the latitude or the longitude scale of the chart. (Though in practice both are constructed, I will use the latitude scale only in this example.) I call this “one-minute division” the scale line. Draw a line at any convenient angle. A line 90° to the scale line works fine, especially if you use the intersection of a printed latitude line with the latitude scale, in which case the line is already drawn for you (see Figure 1). Measure a distance of 10 units along this line, which I call the division line. (I find that 10 centimeters is convenient, allowing any distance to be read quite accurately to 0.5 mm on a small metric ruler, equal to 0.005 minutes of latitude or longitude. With practice, this can be reduced by half to 0.0025 minutes). Now draw a line from the end of the 10 units (centimeters in my case) at the intersection point with the division line to the other end of the scale line (the one-minute division on the latitude scale), completing the accuracy triangle. I call this newly constructed line the baseline.

Assume you have used a set of dividers to measure the latitude of some position above the 22° north latitude line. Place the dividers on the scale line (see Figure 2) and mark this point. Using the parallel rulers, construct a line parallel to the baseline to intersect the division line. (In practice, the line isn’t drawn, only the intersecting point on the division line is determined.) I now use the metric ruler to determine the distance along the division line to be 6.45 millimeters, which equates on this chart to 0.645 minutes of latitude. The desired north latitude is therefore 22° 0.645′. Even with the latitude scale divided into tenths (as in this example) the expanded scale of the division line, with the metric ruler, is easier and more accurate to read.