TO: The Microwave, Moon Net, Rover, and EME Groups. .............
FROM: Dick, K2RIW 2004/06/08. ..................
RE: New 12 Cipher Grid Locators: Choices, Characteristics, and Theory.

INTRODUCTION -- This is a 4 page LONG E-mail that discusses the characteristics of the currently-used Maidenhead Grid Locator system, and
the future plans for expanding it's positional resolution. The information should help readers who want to choose A METHOD of expanding the Locator
resolution; the popular choices seem to by either a 24 or a 25 letter system. I included some information on how the Locator system functions;
thus, a skilled programmer will be able to write source code that uses his favorite method of expanding the resolution. .................

6 VERSUS A POSSIBLE 12 CIPHERS -- The currently used 6 cipher Grid Locator (ie., my QTH is FN30HT) yields a positional resolution of 5 minutes
of Longitude by 2.5 minutes of Latitude; which is 2.5 nautical miles of Latitude. An increasing number of operators feel that more positional
resolution is required, in order to determine the distance and bearing between particular locations with greater accuracy. The Maidenhead Locator
is very adaptive. As more ciphers are added, the resolution increases proportionally. With up to 12 ciphers in the Locator, we will be able to
take full advantage of the better GPS receivers that are now available they have an accuracy of a few meters. .............

THE NEW STANDARD -- I believe that a higher resolution 10 or 12 cipher, Maidenhead Grid Locator STANDARD is about to be established. However,
there seems to be two ways to do this. The new standard should be one that is agreed upon by the Microwave, Millimeter Wave, Roving, and EME
communities -- the people who will be using it the most. I have an opinion, but I don't have a very strong feeling as to which is the best
standard. What follows are two points of view (the 24 letter standard, and the 25 letter standard), for your consideration. .................


(1) Today (2004/06/06) Ron, W2IOL expressed an opinion (it is repeated below) about a possible way of increasing the resolution of the Maidenhead
Grid Locator system beyond the usual 6 ciphers. Ron's technique of using 25 letters (A through Y) instead of 24 letters (A through X) for ciphers 9
and 10 seems logical, because the divisor of 25 seems to make the math "nicer", meaning more manageable. By the 25 letter approach Ron's "full"
12 cipher Locator is FN20PS77GU58; by the 24 letter approach it is FN20PS77GU30. .............

(2) However, I favor the 24 letter system (A through X) for the following 2 reasons:
(A) It uses the same system that has been agreed upon for ciphers 5 and 6 (A through X).
(B) The "nicer" math is something that only occurs within our computer programs, and we will rarely see the "benefit", unless we are forced to
calculate a Grid Square by hand. .............

TWO OR THREE LETTERING SCHEMES? -- The two competing methods of establishing the higher resolution came about because there already is a
dual lettering scheme within the current de facto standard; meaning that ciphers 1 and 2 use the 18 letters (A through R), and ciphers 5 and 6 use
the 24 letters (A through X). I believe this came about because the Maidenhead designer's decided to make the Major Spherical "Rectangles" 20
degrees of Longitude by 10 degrees of Latitude. The 10 numbers of ciphers 3 and 4 (0 through 9 each) then divide the Major "Rectangles" into Minor
Rectangles of 2 by 1 degrees. To continue the scheme by using the 24 letters (A through X each) for ciphers 5 and 6 causes the next smaller
rectangles to equal 120/24 = 5 minutes of Longitude, by 60/24 = 2.5 minutes of Latitude. ...............

WHY NOT 26 LETTERS? -- In the original scheme, the Maidenhead designer's could have used all 26 letters (A through Z) for ciphers 5 and 6; but, that
would have made each of the finer rectangles 120/26 = 4.61538461538... by 60/26 = 2.30769230769... minutes of Longitude and Latitude. These are
non-terminating decimal numbers (repeating decimals). The designer's must have realized that the first user's of the Maidenhead Locator System would
be calculating their Grid Locator by hand; the repeating decimals would have been confusing and unpleasant. ...............

25 AND 24 LETTERS -- Had the designer's used 25 letters (A through Y) for ciphers 5 and 6, the finer rectangles would have been 120/25 = 4.8, by
60/25 = 2.4 minutes of Longitude and Latitude. They probably felt that this, too, was an unpleasant divisor. Thus, they decided on 24 letters (A
through X), and the smaller rectangles became 5.0 by 2.5 minutes of Longitude and Latitude. .................

HOW MANY MAIDENHEAD CIPHERS? -- When the 24 letter system (A through X) is used on ciphers 9 and 10, the associated rectangle has the dimensions of
30/24 = 1.25, by 15/24 = 0.625 seconds of arc; that's a Latitude resolution of 63 feet. When the final numbers (0 through 9) are used for ciphers 11
and 12, the associated rectangle has the dimensions of 0.125 by 0.0625 seconds of arc; that's a Latitude resolution of 6.3 feet. .............

7.5 MINUTE MAPS VERSUS 10 or 12 CIPHERS -- The U.S. Geologic Survey states that objects on the 7.5 minute series of Survey Maps have a one
sigma accuracy of better than 40 feet; this equals a delta Latitude of 0.4 seconds. A good GPS receiver produces about the same accuracy. Therefore,
there is not much benefit in going beyond a Maidenhead Locator of 12 ciphers. Many operators may feel that 10 ciphers (a Latitude resolution of
63 feet) is adequate for their high accuracy purposes. ...................

MAIDENHEAD ADVANTAGES -- It is interesting to note that 12 ciphers of the Maidenhead Locator system produces approximately the same location
accuracy as 14 or 15 digits of Longitude and Latitude; depending on whether the Longitude number is below or above 100 degrees (2 digits or 3). Thus,
the Maidenhead system is more compact and unambiguous; there is no confusion as to whether the Location is in the degrees minutes and
fractional-minute format, as opposed to the degrees minutes and seconds format. ..............

THE HUMAN FACTOR -- The Maidenhead Locator System has another hidden advantage -- human accuracy. Because the Locator consists of Letters (L)
and Numbers (N) in a LLNNLLNN... format, it is quite easy to receive and write down the location, without transposing the bits of information. By
comparison, when an operator receives and writes 13 or 14 consecutive digits, it is quite easy to write the digits incorrectly, or in the wrong
order (transposed). The telephone company recognized this human characteristic a long time ago; that's why your telephone number used to be
ANdrew 5-1234, instead of 265-1234. .............

MAIDENHEAD THEORY ...............

What follows is 6 paragraphs that explain how the Maidenhead Locator System works. ............

MAIDENHEAD THEORY -- The Maidenhead Grid System first divides the World into spherical "rectangles" of 20 degrees of Longitude by 10 degrees of
Latitude. Starting with the International Date line and proceeding East (from -180 degrees West longitude, to +180 degrees East longitude), the 18
possible (each 20 degrees wide) Longitude rectangles are labeled with the letters A through R, respectively. The 18 possible (each 10 degrees high)
Latitude rectangles (from -90 degrees [South Pole] to +90 degrees [North Pole] ) are labeled with the letters A through R, respectively. Therefore,
the first two letters of a Grid Locator go from a possible address of AA through RR. The Longitude cipher always precedes the Latitude cipher, in
the whole Maidenhead System of pairs of Letters (L) and pairs of Numbers (N), in the form of -- LLNNLLNN... .................

THE FIRST RESOLUTION STEP -- Next, each one of the 20 by 10 degree rectangles is broken up into 100 sub-squares (10 sub-squares wide by 10
sub-squares high) yielding sub-squares that are 2 degrees wide by 1 degree high. The lower left sub-square is labeled 00, the upper right sub-square
is labeled 99. So far, the total 2 degree by 1 degree Grid Locator could consist of all possible addresses from AA00 through RR99. .........

THE 2nd RESOLUTION STEP (NORMAL 6 CIPHER GRIDS) -- Next each of the 2 degree by 1 degree sub-squares are divided into sub-sub-squares that are 24
squares wide by 24 squares high, and these are labeled AA through XX, with AA being the lower left corner, and XX being the upper right corner. Each
of the sub-sub-squares has dimensions of 1/12 degree (5 minutes) in Longitude by 1/24 degree (2.5 minutes) in Latitude. So far, all the
possible 5 minute by 2.5 minute accuracy Grid Locators (addresses) could go from AA00AA through RR99XX. ...............

THE 3rd RESOLUTION STEP (EXTENDED RESOLUTION) -- What I added carries out the same system for 6 more ciphers (3 more resolution steps). The next
two number ciphers divide the sub-sub-squares into boxes that are 10 boxes by 10 boxes, labeled 00 (lower left corner box) through 99 (upper right
corner box). These sub-sub-sub-square boxes have dimensions of 0.5 minutes (30 seconds) of Longitude, by 0.25 minutes (15 seconds) of Latitude.

THE 4th RESOLUTION STEP -- My next step divides those boxes into 24 boxes wide, by 24 boxes high. These boxes have the dimensions of 30/24 (or
1.25) seconds in Longitude, by 15/24 (or 0.625) seconds in Latitude, and are labeled AA through XX. ..............

THE 5th RESOLUTION STEP -- My last step divides these boxes by squares that are 10 wide by 10 high, and labels them 00 through 99. These final
squares have a resolution of 0.125 seconds in Longitude by 0.0625 seconds in Latitude. All possible 12 cipher Grid addresses go from AA00AA00AA00
(at the South Pole, East side of the International Date Line) through RR99XX99XX99 (at the North Pole, on the West side of the International Date
Line), that's (18^2)*100*(24^2)*100*(24^2)*100 or 107.5E12 possible addresses. ............

I hope this information is useful. Please feel free to correct the mistakes. ...........

73 es Good VHF/UHF/SHF DX, ............
Dick, K2RIW ............

Grid FN30HT84DC27. ...........
40D 48' 31.7" North, 73D 20' 56.0" West. .............
web: <> ...................

Here is a copy of the Memo from Ron, W2IOL: ..............
At 10:22 AM 6/6/04 -0400, Ron McConnell wrote:
>Hello, Tony,
>Last night I was trying to thin out my piles of stuff, including old QSTs.
>One issue that surfaced and didn't get thinned, was the February 2003 issue.
>Your article,"VUCC - 20 Years and Counting", got reread. So much for the thinning out for a while...
>One statement caught my attention that I had either overlooked or forgotten,
> "The Maidenhead system actually extends beyond six characters..."
>Where is that specified?
>I found nothing at ARRL.
>In a google search
>I found what appears to be an "official" looking meeting report
> <>
>and, of course, Folke Rosvall, SM5AGM's own notes.
> <>
>There are _many_ hits in the google search.
>No where could I find a mention of more than the usual six characters.
>The Trimble Scout GPS receiver had 8-character grid locators I recall. Characters 7 and 8 are pretty obvious.
>Likewise subsequent alternate number pairs are obvious.
>Subsequent alphabetic letter pairs involve choices, some of which result in "nice" results and others less "nice" results.
>At least four of us are fiddling with locators longer than 6 charaters:
> Ekki Plicht DF0OR [8 characters],
> Dick Knadle K2RIW 12 characters],
> Dan Jacobson ( [ 22 characters !!]
>and me [12 characters, so far...].
>For characters 9 and 10 I personally favor a range of A to Y, providing a "nice" divisor of 25 for the character 7 & 8 area of 0.5' by 0.25'
>with "nice" dimensions for "9 & 10" of 0.025' by 0.01' and also "11 & 12" with 0.0025' by 0.0010' etc.
>Others favor a range of A to X which results in a divisor of 24 - not so "nice" in my humble opinion. :)
>Those are certainly usable, of course and make very little practical difference.
>Opinions, thoughts,...
>Know any one else that might be interested?
>Cheers, 73,
>Ron McConnell
> WGS-84: N 40 46' 57.5" +/-0.2"
> W 74 41' 22.1" +/-0.2"
> FN20ps.77GU58 +/-
>There are two secrets to success:
>(1) Don't tell all you know.