A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Accuracy/precision in plotting tools.
From: Herbert Prinz
Date: 2004 Mar 30, 15:49 -0500
From: Herbert Prinz
Date: 2004 Mar 30, 15:49 -0500
Jim Thompson raises a questions that is very pertinent to a list mainly concerned with the _history_ of navigation. Plotting, a short lived and rather cumbersome sight reduction technique of the last century, has not received sufficient attention here, despite the fact that a few aficionados still practice it. Some even go as far as to teach it as the only method of position line navigation, often mistakenly identifying it with the latter. As it is the case with the art of splicing braided line, the attraction of plotting, too, is not so much in its utility as in the joy obtained from the skillful handling of the tools of bygone eras. Its popularity is connected with the admiration (and the envy) we have for those those old salts who swung their dividers in 12 foot waves without killing some crew or at least poking their eyes. However, there is this unnamed hero who, after having confirmed by plotting that his position was in the navigable zone of a hurricane, poked his throat with the dividers and was consequently lost at sea without a trace. (I may have more details on this story on the day after tomorrow.) > 1. What are the accuracy and precision that I can expect from a charting > tool like a reasonably well made Portland triangle from a reputable company? > > 2. Are compass roses on small scale Mercator charts not perfect circles? Dear Jim, Ad 2. (First things first) You are probably thinking of the fact that a perfect circle in the real world becomes an egg when projected on a Mercator chart. However, this does not come into play here. A compass rose shows angles, that's all. Whether it is a piece of cardboard in a compass or a stylized diagram in a chart, its shape can be square, octagonal, circular, whatever. It does not matter. What counts is that the graduation is correct. On the other hand, I can see no reason why one would want to draw a compass rose on a chart in any other shape than perfectly circular. In the real world, we measure azimuths by dividing the horizon into 360 equal parts, called degrees. Therefore, on a real world compass the graduation of the rose must be uniform all around. The Mercator projection is orthomorphic (conformal), meaning that it preserves angles at close distances. We know that it does not do this over long distances. Hence the difference between orthodrome and loxodrome. But the distortion of azimuth angles (i.e. the angle between loxodrome and orthodrome) varies with position and distance. So, there is no way to draw a distorted compass rose on a Mercator chart that would show correct great circle azimuths anywhere. Instead, one works with loxodromes, accepting that these are, in fact, bent curves in reality. Therefore, if you find compass roses on mercator charts that are not evenly graduated, we must assume that this is due to the quality of the paper, which may have stretched with changing humidity more in one dimension than in the other. The same reasoning holds for universal plotting sheets. You mentioned using practice sheets. I would assume that the high price of the ones sold by the government is partly due to the good quality of the paper on which they are printed. Maybe this is only wishful thinking. Check the graduation with dividers. But if you use a compass, use the same section of the compass for the different quadrants of the rose, and then vice versa. This will tell you immediately whether the rose or the compass is the culprit of any divergence. Ad 1. To put the question about the practical error in perspective, let us consider the _theoretical_ error that we are committing by using a plotting sheet. Remember that the scale of a Mercator projection changes with latitude. At lat 40 deg, cos(40deg) = .766 At lat 41 deg, cos(41deg) = .755 The difference is 1.5%, meaning that the difference in scale between these two particular latitudes changes by 1.5 percent per degree. The higher the latitude, the worse this gradual change. Now, on your plotting sheet, draw a horizontal baseline of 100 mm from the center towards east. This corresponds to some 96 nm, or thereabouts, on a DMAAC VPOSX001 (3 inch per deg lat). If you wanted to represent that same distance at lat 41 within the same plot, you would still use the same 100 mm, wouldn't you? Draw a 100 mm long parallel of latitude at 41 deg, from the center longitude to the east. But the correct length of a line representing the same distance would be 101.5 mm. Draw that, too. Connecting both end points to the center, compare the angles on the rose. What's the difference? Half a degree? Something to consider before you invest in a set of plotting tools made of platinum-iridium alloy. Best regards Herbert Prinz