Talk:Mercator projection/Archive 2

Archive 1

Archive 2

Aspect ratio of unity

I have come to find that this means a 1:1 aspect ratio. However, searching "aspect ratio of unity" didn't provide any answers (this Wikipedia article being the first hit) and so I had to go through the calculations myself to verify this. Is this really a commonly used/understood phrase in English or should it be changed to "a 1:1 aspect ratio" or something similar? — Preceding unsigned comment added by TheOnlyRealEditor (talk • contribs) 14:56, 6 July 2020 (UTC)

"Unity" is another word for "one"; "an aspect ratio of unity" just means "an aspect ratio of one" or "an aspect ratio that is one". I understood it well enough, but if it's confusing to some, I don't see any reason not to rephrase it. Justin Kunimune (talk) 15:02, 6 July 2020 (UTC)

mathematicians and physicists use the word "unity" to mean "1". It's so common a useage that I wouldn't even notice it, but you may be right that non-mathematicians aren't familiar with this. I'd say go ahead and change it if you think it's confusing. Geoffrey.landis (talk) 13:01, 17 August 2020 (UTC)

Width vs height being important, shouldn’t those aspect ratios be, for example, 1:1? And in this case, just make it “square”, I’d say. Strebe (talk) 17:47, 17 August 2020 (UTC)

Constant bearing

If we're going to state "A course of constant bearing... is used in marine navigation because ships can sail in a constant compass direction for long stretches, reducing the difficult, error-prone course corrections that otherwise would be needed frequently when sailing other kinds of courses" I would say this needs a citation (or more than one). Mariners don't travel long distances on a constant compass heading because this isn't efficient and mariners did indeed know the Earth was round (or at least they all did by Mercator's time)(*).

But mariners did travel SHORT distances on a constant compass heading, and the remarkable thing about Mercator (and no other projection) is that LOCALLY, every spot is accurate in shape and correctly oriented north/south. Globally, it may be wrong and distorted, but in any given place, every piece is right and undistorted.

I moved this statement out of the lede (it is in the "properties" section).

(*in any case, back in Mercator's time, winds and currents determined the route a ship would choose). Geoffrey.landis (talk) 13:01, 17 August 2020 (UTC)

Moving the matter of rhumbs out of the lede contradicts the raison d’être of the projection and thereby does a serious disservice to the article. To Mercator, and to the generations of navigators who used it, it was all about the straight rhumbs. I don’t think Geoffrey.landis's observations here fairly characterize the practical considerations, either. I don’t want to argue over the definitions of “short” and “long” distances, but, in fact, mariners did sail “long distances” (many hundreds of nautical miles) along rhumbs. It was much too hard to frequently compute what the new course ought to be while also tacking and beating and keeping track of distance via dead reckoning. Sailors were not mathematicians. They needed failsafe ways of working under difficult conditions. Maneuvering to keep a constant bearing was plenty enough to deal with. As observed by Mercator, paraphrasing, “You will not arrive by the shortest route, but you will surely arrive”. The surely arrive was everything; ships were frequently lost and grounded because they could not figure out the right course to take because they didn’t know where they were. In order to sail a course other than a rhumb, you would have to know exactly where you are at all times. That was practically never true. Sailing a rhumb, on the other hand, meant that all you had to know or do was keep a constant course as long as you knew where you were when you started, where you intended to be when you stopped, and you had a map that correctly mapped those two coordinates. It’s also false that sailors were at the mercy of winds and currents. That was only true if there was no wind, which was a seasonal problem in the tropics but rarely any other time or place. Ships routinely sailed nearly upwind. While Mercator’s concept of rhumbs was ahead of sailing technology in his time, by the 18th century, its use was constant and celebrated. Strebe (talk) 16:50, 17 August 2020 (UTC)

It sounds like this could use a citation either way. I'm not sure where to look for one, though. I feel like Flattening the Earth might say something about it, but my copy is in storage right now (I assume someone else here has access to it and can check). Justin Kunimune (talk) 17:11, 17 August 2020 (UTC)

No end of sources about sailing specifics are available, but this is more an editorial judgment: Do rhumbs belong in the lede or not? For an introduction to the complexities of sailing, see, for example, [1]. Excerpting,

These sin(α) sin(β) sin(γ) values can be used to determine the initial course when departing and the final course when arriving for a ship sailing a great circle course, but does not tell the sailor what his course should be at any other time on the journey. Thus this sailing is more of academic interest, rather than of practical use, and is absent in many manuscripts.

…Mid-latitude or middle latitude sailing was often used to convert a departure into a difference in longitude. Since the ship is not sailing at a constant latitude, the average of the initial and final latitude for the course was defined as the mid-latitude. The departure was divided by the cosine of the mid-latitude to provide an estimate of the difference in longitude. This technique is reasonably accurate for short distances, particularly near the equator where the meridians do not converge quickly as one travels North or South. For distance greater than a few hundred miles or when sailing in northern or southern waters, this method is not sufficiently accurate, and the student was advised to use the technique of Mercator Sailing…

The paper then elaborates on “Mercator Sailing”, the point of which was to estimate distances accurately provided that you sail on a rhumb. Notice that this is the recommended technique for “more than a few hundred miles”. In other words, it was common to sail long distances along rhumbs. It was far more important to get to your destination than to get get there faster but risk getting lost. Strebe (talk) 18:10, 17 August 2020 (UTC)

Ah; I wouldn't have considered a few hundred miles as "long distance" on a global scale. That's short enough that there is negligible deviation from a great circle (unless you're nearly at the pole); it doesn't matter whether you take a constant bearing or a great circle.

But, the discussion here is good, some of it should go into the article, and a citation or three would be good. The material is mostly already there, but since Strebe calls marine navigation the raison d’être of the projection, it could be helpful to label it such. I suggest adding a subheading under "uses" titled "Marine Navigation" Geoffrey.landis (talk) 23:18, 17 August 2020 (UTC)

OK, done: I added a section "Marine navigation" under "Uses" that basically states what was discussed here. Check it and rewrite as needed (and, add a citation if you can. Is there a source for that quote paraphrased above?

-- The "uses" section also had a lot of text devoted to critics of the projection. That seemed out of place, so I moved it to a more appropriate heading. Geoffrey.landis (talk) 23:55, 17 August 2020 (UTC)

Image not showing poles

That is really bad, because you cannot really see the properties of the Mercator-projection on a incomplete map. — Preceding unsigned comment added by Chricho (talk • contribs) 22:53, 12 April 2011 (UTC)

Probably you are kidding, but did you care to read the first paragraph? Alvesgaspar (talk) 23:06, 12 April 2011 (UTC)

No, I am not kidding, I know about Mercator projection (it is trivial). E.g. there should be a much bigger gap between Greenland and the pole. Look at the image below, that one is showing the poles, it is much better. --Chricho ∀ (talk) 11:45, 17 August 2011 (UTC)

The Mercator projection does not show the poles as their distance from the equator is infinite. In the image below the largest latitude shown is 85º. -- Alvesgaspar (talk) 12:21, 17 August 2011 (UTC)

Oh sorry, you are right, I confused it and talked nonsense. However, the image should show a bit more to make it obvious. --Chricho ∀ (talk) 12:36, 17 August 2011 (UTC)

I think I get it now. Chricho, apparently, wanted 2 patches which would go like this:

!85-90 degree area cannot be shown!

*map itself goes here*

!85-90 S area cannot be shown!

Uchyotka (talk) 10:40, 21 August 2020 (UTC)

Article needs to explain difference between Mercator and central cylindrical projections

Almost every source I've seen on the internet about map projections confuses the Mercator and central cylindrical projections. We would be doing the world a huge favor by concisely and clearly explaining the differences in this article. Perhaps it could be a paragraph or subsection under the Properties section. Nosferattus (talk) 03:01, 18 August 2022 (UTC)

@Justinkunimune: I think you might be the best candidate for this heroic task! Nosferattus (talk) 03:03, 18 August 2022 (UTC)

Lol sure, I can do that. I added a note to the bottom of Properties as you suggested; what do you think? It could also go in the Mathematics section, but that section is pretty long and structured so I didn't see a good spot for it. Justin Kunimune (talk) 11:34, 18 August 2022 (UTC)

That’s a good observation. Strebe (talk) 05:29, 18 August 2022 (UTC)

y(φ) "must" be antisymmetric

A note at the bottom of the page says, "The function y(φ) is not completely arbitrary: it must be monotonic increasing and antisymmetric (y(−φ) = −y(φ), so that y(0)=0): it is normally continuous with a continuous first derivative."

Why must it be antisymmetric? I see no reason why it must be so. 31.52.108.53 (talk) 20:56, 21 November 2022 (UTC)

That’s just the conventional definition of cylindric projection. Strebe (talk) 04:08, 22 November 2022 (UTC)