NavList:

Joe Plazak, you wrote:
"VFR Terminal Area Chart (VTA)   Transverse Mercator Projection"

The "Transverse Mercator" often comes up in discussions of the significance of the (standard, global) Mercator projection.

Let's get this out of the way. They're not the same thing. They're based on the same math, absolutely, but the rotation by 90°, generates enormous differences. That "rotation" I'm referring to is a fundamental aspect of the definition of the "Transverse Mercator" (TM) projection. In this projection, some arbitrary meridian of longitude is treated as the "equator" and pseudo-latitude and pseudo-longitude coordinates are introduced relative to that central meridian. Note that the pseudo-latitude coordinate increases east-west from that central meridian. In the most popular implementation of Transverse Mercator, known as UTM, these coordinates are delivered in meters so that the relationship to angular coordinates on the globe is suitably hidden (suitable to the precision "surveying" function of these maps).

Critical to navigation implications, since the TM projection is rotated 90°, the classic, famous property of the Mercator projection, namely that lines of constant bearing (rhumblines) are simple straight lines on the map, is defenestrated --thrown right out the window! Hence the Transverse Mercator's relevance to navigation is marginal, at best. Also note that the TM projection is never used for global maps, radically different from the classic Mercator (see PS).

The examples you gave of recently updated "VFR Terminal Area Charts" in Canada that appear to use the Transverse Mercator projection present a a couple of interesting puzzles, worthy of the mathematical skills of some of the more mathematically inclined NavList members.

They say that these charts are TM projected, but can you tell?! Can we prove by realistic measurement on the charts that they have that projection?? These specific charts cover relatively small areas, roughly 80 nautical miles north-south and 100 nautical miles east-west (in southern Canadian latitudes... not far from 45°N). The scale of the charts is listed as 1:250,000 which implies a chart width of about two and a half feet. That sounds about right for a printed aviation chart. Could you measure this chart and demonstrate that it is definitely plotted as a TM projection? Is the difference greater than the thinnest visible stroke of ink on the chart? Would some other projection (or many) also fit the chart as plotted? If instead we plotted very simple x,y coordinates with x=dLon/cos(Lat₀) and y=dLat where dLon and dLat are relative to the center of the chart at (Lat₀, Lon₀), would there be any measurable, practical difference? Are these really Transverse Mercator charts in any provable way, or is that just the name on the box? In addition, would anyone ever measure anything in the real world on a chart like this? If not, then we may want to ask next, what is the point of declaring a specific projection in the first place?

Frank Reed

PS: I should add... before someone grumbles about it... that, yes, yes, you can find examples of (nearly) global maps using the TM projection online, but you will only find these as abstract illustrations of maps that can exist in principle which have no function in the real world. For example, you can find such semi-global maps in articles about the TM projection's properties, like on Wikipedia. But never in the real world. It would be daft to publish a global TM map, and most implementations of the TM projection, like UTM, are limited to very narrow bands around certain arbitrarily chosen meridians (in the case of the UTM grids, which was the only significant practical application of the TM projection, these arbitrary meridians were chosen in the late 1940s by the US Army and related agencies). These UTM grids are like gores on a globe --long narrow north-south strips running from pole to pole.