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

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Re: The Sun does not stop for anyone
From: David Pike
Date: 2016 Dec 27, 10:27 -0800

Frank you wrote: “You absolutely do not need a Mercator chart to plot your intercepts and lines of position.”

I don’t think anyone said a chartlet had to be Normal Mercator projection. There are plenty of other projections which are, as you say, conformal and would fit the bill. I chose the Normal Mercator simply because I’m most familiar with it. Call it a nostalgia trip if you like. It would be perfectly OK me to use ordinary graph paper, so long as I marked it in nautical miles N/S and E/W. If I wanted my chartlet marked only with minutes of latitude N/S and minutes of longitude E/W it needs a bit more thought. What I definitely can’t do at 53N is use one graph paper division for both a minute of latitude and a minute of longitude. I could always move house to 60N, and then I could use two divisions for a minute of latitude and one division for a minute of longitude, but that’s an expensive way of solving the problem.

I think the important points to remember are these:

The properties of an ideal map are:
Constant scale
Shapes correct
Areas equal
Great circles are straight lines
Rhumb lines are straight lines

Angles are correct, but in my opinion this requires a bit more explanation over what is meant by correct. For me it means readily measurable with a protractor. For this to happen, there must be a measured 90 degrees at each meridian/parallel intersection (although the protractor is allowed to swivel across the chart as in the case of the Lamberts Conformal Chart), and for this to happen the scale must expand at the same rate in any direction. This is what I understand to be meant by conformal. I.e. the chart conforms to this particular requirement.

Unfortunately, it’s impossible to have all features at the same time, so all projections have to be a compromise. The Normal Mercator chart has angles correct and shapes are correct over small areas. It could be argued at the top of Greenland is considerably morphed compared to the south if you look at the whole country at once, but that’s because it’s so far from the great circle of tangency. Away from the great circle of tangency, the chart is not constant scale or equal area, which means equatorial countries lose out by looking much smaller than their more northerly or southerly cousins. It’s also important to remember that there’s more than one kind of Mercator projection. The Normal Mercator is projected onto a cylinder whose great circle of tangency is the Equator, but you can also use a meridian as the great circle of tangency, the Transverse Mercator. A long thin country running approximately N/S like UK or Italy might benefit from this. As far as I remember, the OS GB maps are based on a Transverse Mercator projection. You can even have an Oblique Mercator projection where the great circle of tangency can be the great circle from almost any point to any other. E.g. if an airline or air force flew regularly between two places neither N/S or E/W of each other, e.g. UK to Cyprus, it might be worthwhile producing an Oblique Mercator between the two points, because this would retain as many of the six properties of the ideal chart as possible for this particular route. The strangest chart I ever saw was to go with a roller map that enabled raw hyperbolic Decca values to be fed directly onto an XY plotter. I don’t think that chart qualified for any features of the ideal chart (unless you wanted to fly by Decca).
http://www.jproc.ca/hyperbolic/decca_rx_ind_961_1b.jpg

DaveP

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