A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Accuracy/precision in plotting tools.
From: Joel Jacobs
Date: 2004 Mar 30, 19:12 -0500
From: Joel Jacobs
Date: 2004 Mar 30, 19:12 -0500
Herbert, I enjoyed reading your detailed explanation. Thank you for writing it, Joel Jacobs ----- Original Message ----- From: "Herbert Prinz"
To: Sent: Tuesday, March 30, 2004 3:49 PM Subject: Re: Accuracy/precision in plotting tools. > 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