Guide to grid references and geographic co-ordinates

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The purpose of this page is to describe the grid reference system used at the battle
of Otterloo and to make some sense of the grid reference numbers that appear in much
of the primary source material.
Most of these have been converted to more understandable geographical latitude
and longitude values that appear in tool tips.
This page also explains the conversion between grid references and geographical
co-ordinates and how to view the co-ordinates.

The grid references used to specify specific locations on the ground during
the battle of Otterloo were based on what was called the “Modified
British System” of geographical co-ordinates.
The European theatre of operations was divided into zones.
The three low countries and sections of some other countries were part
of the “Nord de Guerre Zone”.
Each zone was divided into squares with 500 kilometre sides and each
of these was divided into 25 square blocks with 100 kilometre sides.

The battle of Otterloo took place in the 100 kilometre-square
“qE” block.
Both Arnhem and Otterloo were located within this block and all the
grid references for this battle are located within the qE block.
The grid references within this block will be consistent but each block
has its own origin so, even though the units of measurement are the same,
different blocks will have inconsistent grid references.

In the field, the grid references were referred to the map from which
they were obtained.
The documents on this site that contain grid references list the appropriate
map, usually an Otterloo map, rather than naming the grid block.

Military grid references are based on two-dimensional mathematical
co-ordinates but only the first quadrant is utilized.
Each block has its own co-ordinates and each has
an origin where the X and Y axes cross.
In the first quadrant, grid references are always zero or positive which
puts the origin in the lower left corner, that is, the southwest corner.
The origin of the qE block, at co-ordinates
qE000000,
is located in the village of Gierle, Belgium, near the border with
the Netherlands.
The diagonally opposite or northeast corner of this block at
qE999999
is located in a rural area northeast of Zutphen in the Netherlands.

Numeric co-ordinates consist of a single string of an even number
of digits.
The first half of the digits gives the X co-ordinate, usually called
the “easting” while the second half of the digits gives
the Y co-ordinate, usually called the “northing”.
Although this order corresponds to that of mathematical co-ordinate systems,
in which the X co-ordinate comes before the Y co-ordinate,
it reverses the order of modern global positioning systems in which
the latitude usually precedes the longitude.
This distinction becomes important when converting between the two.

For example, the grid reference for the old church in Otterloo,
qE654910,
indicates that it is 65.4 kilometres east of the origin and 91.0 kilometres
north of the origin.
Grid references do not contain decimal points; instead the number of
digits indicates the precision of the measurement.
Had it been expressed as qE6591, the corresponding distances would have
been 65 and 91 kilometres.
The six-digit grid reference specifies the location to the nearest one
hundred metres in each of the easterly and northerly directions,
but the four-digit reference is accurate only to the nearest kilometre
in each of these directions.
The expressed precision of the easting and the northing must be the same
to prevent ambiguity.
The grid reference of the old church, expressed to the nearest ten metres
in each direction, would be
65439097
in the qE block of the Nord de Guerre Zone.
We can assume that the maximum error in each direction would be plus or minus
five metres.
The Pythagorean theorem dictates the maximum linear error,
in this case about seven metres.

In the Otterloo materials, the precisions of grid references vary from
four digits to ten digits.
A ten digit precision implies that the position was known to the nearest
metre in each of the easterly and northerly directions.
With the technology available to them at the time, achieving precisions
of ten metres would have been challenging so a precision of one metre
must be considered an exaggeration.

The omission of decimal points has important side effects.
Eastings and northings below 10 kilometres must contain a leading zero;
those below one kilometre must contain a second leading zero; and so on
down to the origin which will be of a string consisting entirely
of zeros.
To convert a grid reference to kilometres east and north of the
origin, the numeric string must be split in the middle and a decimal point
placed after the second digit in each of the easting and northing.
Points located 100 kilometres or more east or north of the origin cannot
be represented but such points would not be in the same block and so will
have grid references measured from different origins.
Finally, the eastings and northings of two points cannot simply be
subtracted to get the X and Y distances without noting the precisions
and inserting the decimal points where needed.

Each grid reference of six digits or more in the Otterloo materials contains
a tool tip that gives the corresponding latitude and longitude, in that order,
expressed as a whole number of degrees followed by decimal minutes.
With decimal minutes, seconds are not used.
Each latitude begins with a letter indicating the northern or southern hemisphere,
always “N” for northern for the Otterloo materials.
Each longitude begins with a letter indicating the eastern or western hemisphere,
always “E” for eastern for the Otterloo materials.
The presence of the tip creates a light line under the grid reference.
The latitude and longitude will appear in a small box when the cursor is held
stationary over the grid reference for a second or so.

The conversions from grid references to geographical co-ordinates was done at
the website
“http://www.echodelta.net/mbs/eng-translator.php”.
An explanation for this grid reference system and the logic of the conversions
can be found at
“http://www.echodelta.net/mbs/eng-overview.php”.

The page sources for pages with grid references contain HTML5 geocoordinate
microdata intended for use by search engines.
These include signed latitudes and longitudes in decimal degrees as required
by HTML5 standards.
The latitudes and longitudes are signed to represent the hemispheres with
northern latitudes being positive and eastern longitudes being positive.
Since Otterloo in in the northern hemisphere and the eastern hemisphere,
all signs are positive and are not included explicitly.
Each geocoordinate microdata set includes an HTML comment giving the co-ordinates
in degrees on one line suitable for pasting into Google Earth.

In most web browsers, right clicking in an empty area of a page and left clicking
on “View page source” in the popup menu will open a page-source
window.