NavList:

Frank wrote:

Yes, that's all right on the money! Standard small plotting charts, sometimes known as "Universal Plotting Sheets" are conformal but not Mercator. Also the sections in Bowditch and other resources that describe how to construct Mercator charts are not providing instructions for constructing simple plotting charts.

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"Universal Plotting Sheets" are pre-printed forms published by the Defense Mapping Agency as VP-OS, stock number VPOSX001. They are a convenient form to use when drafting a "small area plotting sheet" on the Mercator projection. This form is not necessary since a small area plotting sheet can be drawn on any piece of blank paper requiring only three lines, horizontal-parrallel of latitude; vertical-meridian; angled-for determination of longitudes. No other lines are necessary but some may chose to draw in additional parallels and meridians.

Frank, it appears that you didn't see my prior messages. Bowditch, Ho 9; Dutton's Navigation and Piloting;  Air Navigation, HO 216; Air Navigation, U.S. Air Force Manual 51-40,  do not give instructions to make a "Universal Plotting Sheet" they all say that they are giving instructions for constructing "small area plotting sheets" that incorporate the Mercator projection. 

I posted this before:

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From: Gary LaPook

Date: 2016 Dec 27, 00:14 -0800

Frank wrote:

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" What you have described here is the Bowditch directions for making a homemadeMercator

chart of a region of the world covering some several degrees --not a standard plotting chart!

That's what meridional parts are required for."

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But that is not what is written in Bowditch. What is written is :

"324. Small area plotting sheets.-A Mercator plotting sheet can be constructed by the method

explained in article 307. For a relatiely small area a good approximation can be more quickly

constructed by the navigator by either of two alternative methods based upon a graphical solution

of the secant of the latitude, which approximates the expansion." Bowditch, HO 9, 1962 ed. The

exact same wording is found in the 1977 ed.  (Article 307 explains the use of table 5, Meridional

parts.)

"224. Small area plotting sheets. A Mercator plotting sheet for a relatively small area can easily

be constructed by the navigator. Two alternative methods based upon a graphical solution of the

secant of the latitude the approximate degree of expansion are explained below." Air Navigation,

HO 216, 1967.

As I said in my previous post, "a good approximation of what," obviously a Mercator chart. 

"317 Plotting sheets are designed for use by the navigator at sea where no large scale charts are

available. They are basically Mercator charts showing only the graticle of meridians and parallels

with a compass rose, without any other chart data." Dutton, 12th ed., 1969

What Frank has objected to is naming these small area plotting sheets, constructed using the

graphical method, as MERCATOR plotting sheets because they are not constructed using

Mercator's method of Meridional parts. Apparently the graphical methods approximate

Mercator's method well enough that the U.S. Navy Hydrographic Office believes that it is

appropriate to give them that name. Dutton, the standard navigation textbook used at the U.S.

Naval Academy, also agrees with this naming convention.

As I said before Frank, I believe you may be being overly pedantic on this naming issue. You

appear to be the only one who has a problem with it. And, again, as I said before, a Mercator

chart constructed using the standard table 5 of Bowditch of Meridional parts only approximates a

true Mercator chart. 

So, here is a test. What say I construct two small area plotting sheets covering 34 to 35 degrees of

latitude, one using the graphical method and one using Meridional Parts. Frank would have to

admit that the second one is truly a Mercator chart. Now, could you tell which chart was which,

which one was constructed with the graphical method and which one was made with Meridional

Parts? If you could not tell them apart then you must admit that both were Mercator charts,

including the one made graphically.

So, how would we test them, what characteristic would tell them apart?

Well, the expansion of Meridional parts, and charts constructed with them, show an uneven

latitude scale, constantly expanding the spacing of one minute latitude lines as you move away

from the equator so the chart that has a constantly explanding latitude scale would be the

Mercator chart and the other one would be the imposter. 

Looking now at table 5. The Meridional parts for latitude 34-00 is 2158.5 and for 34-01, 2159.7 a

difference of 1.2. Looking at the top of the plotting sheet, 34-59 is 2229.7 and for 35-00, 2230.9,

again a difference of 1.2. This means that the spacing of the parallels one minute above 34

degrees and one minute below 35 degrees have exactly the same spacing. In fact, all the lines up

to 34-25 will be spaced 1.2 and all the lines from 34-55 to 35-00 will also be spaced 1.2 units

apart, the same as at the bottom of the plotting sheet. In fact, 56 out of the 60 spaces will be

drawn 1.2 units apart and 4 will be drawn 1.3 units apart intersperced randomly, but will not be

expanding continuously towards the top of the plotting sheet. 

The standard universal plotting sheets have the one degree parallels of latitude three inches apart

making a scale of 20 minutes of latitude per inch so the one minute lines are spaced 0.05 inches

apart. Doing the same computations for a chart constructed with Meridional parts, keeping the

same three inch spacing for degrees of latitude, makes the spacing of 1.2 units equal 0.04972

inches, just 0.00028 inches different from the standard universal plotting sheet constructed with

the graphical method. Do you think you could spot a spacing difference of about three

ten-thousanths of an inch? (3/10,000 inch) 

So if I constructed these two plotting sheets Frank would not be able to tell which was which

using normal plotting tools, he would need a micrometer and a microscope to do it, so, I submit,

that a plotting sheet constructed using the graphical method IS a Mercator chart. 

And U.S. Air Force Manual 51-40, "Flight Navigation" (1951) gives a method to construct a MERCATOR chart using the inverse of the other graphical methods. This method allows you to cover a greater range of latitude in that it keeps the meridians equally spaced and varies the parallels just like other Mercator charts that cover a greater latitude range. see attached.

The Air Force thinks it's a Mercator chart, the U.S. Navy Hydographic Office thinks it's a Mercator chart, Dutton thinks it's a Mercator chart and so do I. 

gl