NavList:

Bob Bossert,

Thank you for those references. They certainly confirm that this "lore" is old! :) The first source you provided, from "International Textbook Company" is not high on my list of reliable expertise. That does not mean they're wrong (any more than it meant that Wikipedia articles were likely to be wrong back in 2010, when that was a common assumption), but it does mean that we need to verify their claims.

You originally said that polyconic charts were helpful because Lake Michigan and Lake Huron are north-south aligned, and this made a polyconic chart desirable. That hypothesis is relatively easy to knock down: the contemporaneous Corps of Engineers charts of Lake Ontario are also on a polyconic projection (you can tell by the coordinate ranges in the corners of the chart --if not otherwise labeled). And Lake Ontario is obviously an east-west aligned lake. Got that? Regardless of the orientation of the dominant "axis" of the lake, the common charts of the Great Lakes were all drawn on a polyconic projection, at least through the middle of the 20th century.

Consider the more general issue. Is the claim about the properties of the projection reasonably correct in the first place? Is a polyconic projection better for displaying true bearings? On a local scale, up to a couple of hundred miles, absolutely not. Both the Mercator projection and the polyconic projection as well as a great many other projections (including the very simple plane longitude scaling --see PS) are all locally conformal. This simply means that local shapes are preserved in all relative proportions (squares are still squares when mapped), and also, as a corollary, local relative bearings are preserved. There is no advantage in the case of visual bearings. In your earlier post, you had written: "Bearings on Polyconic charts for North South aligned bodies are more like what you'd see on the water versus Mercator [my emphasis]". And that isn't true. The area covered by the chart is too small for any of this to matter.

Over great distances, at least longer than a few hundred miles and especially over thousands of miles, the rules change. If you look at a Mercator chart and draw a straight line from New York to Paris, you'll end up aiming east when the true direction is northeast (true in the sense of shortest and therefore "great circle"). On the other hand, meridians of longitude are always straight on a Mercator projection, so north-south tracks over great distances correspond closely to great circles by bearing. Meanwhile, a Lambert projection does a much better job with great circles over larger distances in any direction. It does not perfectly map great circles to straight lines, but it does quite well and this is true over distances on the order of a couple of thousand miles. This range is roughly five times better than the range for acceptable great circle tracks on a Mercator projection. But note that this is strictly matter or "practical" quality. It was good enough for aviation in the first few decades of long-distance flying, but it wasn't perfect.

Directly contradicting the claim, it's east-west bearings that display the biggest problems on a Mercator chart. That's why trans-Atlantic cases comparing a Mercator rhumbline with a true great circle are so popular for their educational value. A track from New York City to southern France (Cannes, to be specific), for example, is about 6400 km great circle distance, and that's significantly curved on a Mercator projection (if you draw a straight line on a Mercator chart, that bearing would be "bad"). If instead, we compare something closer to north-south --for example New York City to La Paz, Bolivia, also about 6400 km great circle distance-- the great circle path is nearly straight on a Mercator projection, and the straight line bearing on a Mercator chart is "good".

Back to Lake Michigan. It's a body of water that is long north to south and narrow east to west. On clear days with unusual refraction, one can see lights and landmarks at ranges of 25 miles or, rarely, even twice that. Any locally conformal projection can manage bearings at such ranges, and even if we consider abstract bearings down the full length of the lake, the very fact that the lake runs north-south guarantees that a Mercator projection would work well in this case. And the simple fact is that there is no impact with distances so short. Almost any projection that is close to locally conformal will yield excellent results.

Frank Reed

PS: Easiest way to draw a locally conformal chart: Collect a list of lat, lon pairs that should appear on your chart. Select a central point, call it lat0, lon0. For every lat, lon point, calculate dy = (lat - lat0) and dx = (lon - lon0)×cos(lat0). Note that this is exactly what one does on a universal plotting sheet. In that case, the cos(lat) factor is applied by scaling from the curves usually found near the bottom of the UPS. Those curves are no more and no less than values of cos(lat). A chart drawn this way is locally conformal and will serve almost any purpose --for navigation or other common mapping needs-- for distances up to a few hundred miles.