CONTENT
To orientate oneself in space, one must first of all know in
which direction one is looking with regard to a known
reference.
The basic partition of the space around oneself is thus
based on the four sides instinctly felt and described in all
languages, in front and behind, left and right of the own body.
Away from home, a possible reference point may be the sun's position
during the day: rising, zenith (highest position) at noon, setting. Although this
reference system varies during the day and the seasons, it is quite
reliable ... in sunny countries. The winds blowing allways in
the same direction at the same time also constitute a reference
system. But the only never changing reference is the
North star (in the Northern hemisphere). One of mankind's greatest achievements was to
realise that magnetized metal points to this star. From this
position, a circle around one's own position could be defined and the
other directional elements like the sun's positions were integrated
with precision in this circle. These form the basic
Cardinals.
The circle thus divided into four parts, each quarter can be halved
in its turn (1/8th) and so on until we obtain sectors measuring 1/32th
of the full circle. These are called
rhumbs. The result
of this is what we call the
rose of the winds.
It used to be beautifully drawn on early compasses. If the compass rose
is large enough, it is still possible to divide all divisions again by
two so that the precision is a 1/64th part of the circle. We will see
this number later again (see MILS below). However, the great difficulty to
steer a boat on a moving sea makes such a precision unnecessary.
Furthermore, the circle can be divided into other units
resulting of mathematical calculations (see also the
traditional Chinese divisions).
THE VARIOUS UNITS:
RHUMB, DEGREE, GRAD/GON, ANGULAR MIL
(Artillery)
RHUMB
This word with unclear etymology (does it come from "rhombus", the form
of the arrows on the picture at right?) designates a subdivision of the
circle. The rose of winds being divided into 32 rhumbs, each one equals
(360/32 =) 11 ° 5.
(360/32 =) 11° 15'.
Picture at right:
Ancient French compass rose, 18th C. - Click to enlarge
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The degree ist the most common division system of the circle.
It was first used by Ptolemy in his astronomy book called Almagest.
One degree is a 360th of the full circle.
A particular type of division used during a long time on big
survey and on small pocket compasses was the quadrant. Each quarter of
the circle is numbered separately, starting with zero at North and
South. Directions (bearings) were read and noted with only a small
figure starting from the next cardinal and by indicating the sense.
Example: 190 degrees is thus said 10 deg.
SW.
Picture at right:
Ancient British pocket compass, c1850 - Click to enlarge
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(Definitions according to Wikipedia - for more
details read the full
article)
The grad is a unit of plane angle, equivalent to 1/400 of a full
circle, dividing a right angle in 100. It is also known as gon, grade
or gradian, gradient or radian. One grad equals 9/10 of a degree or
pi/200 of a radian.
This is the application of the metric system on the division of the
circle : this division system was used for all geodesic measures of
France
(see examples like MERIDIAN or
STOPPANI in the category Survey Compasses
Picture
at right:
French Marching compass Modèle 1922
with 400 gon divisions - Click to enlarge
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Some compasses feature 24 hours in addition to the 360 degrees
on their chapter ring, i.e. 15 deg per hour (360/24) see example and
explanation
under ROSPINI.
Others are real sun-watches like L'Abée-Lunds'
Uhr-Kompass.
Picture
at right: detail view of ROSPINI's survey compass
early 20th C. - Click to enlarge
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ANGULAR MIL
Read also a comprehensive explanation on the website www.trademarklondon.com:
The
real Truth about Mil Dots.
(Definitions according to Wikipedia - for more details read the full
article)
The angular mil is commonly used by military organizations. Its
relationship to the radian gives rise to the handy property that an
object
of size s that subtends an angle theta angular mils is at a distance d
= 1000 s / theta. Alternatively, if the distance is known, we can
determine the size of an object by s = theta d/1000. The practical form
of this that is easy to remember is: an object located 1 km away and
seen within angle of 1 mil measures about 1
meter (2 pi/6.4 = 0.98 m to be more precise). Another example: an
object situated in 2 km distance and seen within an angle of 100
mils is 200 meters
long. Even on large compasses, the scales are only graduated in steps
of 10 mils. Marching compasses feature scales in 100 mils (see
pictures of examples below).
Comment: In the general case, where neither the distance nor the object
size is known, the formulae may be of little use. In practice, sizes of
observed objects are known with reasonable accuracy since they are
often people, buildings and vehicles. Using the formulae, distances of
the objects can be readily calculated without a calculator. In military
terms, distances are of course essential for artillery bombardments and
estimations of journey times.
German artillery compass (WWII)
Divisions: 6400 mils, every 10
Click
on pictures for
enlarged views
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Conversion table on the
rear side of a German
light artillery compass
(no manufacturer indicated)
Columns:
- Grad / %
- Mils
- Gon |
Marching compass
Model 1922
(France, WWII)
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Conversion table of a
French
marching compass Model 1922
Abbr. (at the right end beside the scales):
- "D" for degré
(degree)
- "G" for grade
(gon)
- "M" for millième
(Mils). |
The official symbol (at least in France) is the letter "m" with a bar making an
angle of 30
degrees across it :
.
This letter "m" was chosen for the French word "millième"
(i.e. "thousandth"). In the angloamerican world, the word MILS ist used
(see the BRUNTON M2 compass in the category Survey Compasses).
On older German compasses and in their relevant documentation, the
symbol used was
an apostrophe (') or an horizontal bar placed as exponent. Example in table above:
rear side
of a German artillery compass - unfortunately without maka er's name
(click on picture to enlarge).
The mil being one thousandth of a radian, the exact figure would thus be
6283.
The more practical figure used in the Western world (NATO) is 6400.
Such a precision is not achievable on hand-held compasses. The last two
digits are thus not indicated. This is the division one can see on the
western military compasses (0-64). It used to be indicated
counterclockwise on older German Bézard compasses for
instance. Until 1933, the zero/6400 marking was at the South cardinal
point and 3200 at North. The Soviet Union and Eastern European
countries (Warsaw pact) used the lower practical figure 6000. This is
the division 0-60 seen on Russian, Yugoslavian, Hungarian, Romanian,
Czech and Polish compasses. China, Vietnam and Arab countries also use it.
This division system was used by a French Artillery officer called
Emile Rimailho* for canon type that he developed in 1904 and dubbed
155 CTR (
court à tir rapide / short barrel, fast shooting).
This canon was the ancestor of the anti-aircraft FLAK canons.
This unit is therefore sometimes called in France
"Rimailho-millième".
*
French officer and engineer
(born in Paris 1864, died 1954 in Pont-Erambourg,
département Calvados).
Measurement of distances with angular mils
The division in angular mils makes it possible to calculate a distance
even when no parameter is known.
Major Rudolf Gallinger serving in the imperial Austrian Army had
known very well the inventor Johann von Bézard during WW I
and he wrote in the years 1920-1930 several manuals for "tourists" (see
definition)
and soldiers. He described in them how to use this compass in order to
compute the distance of an object and the size of objects at known
distance.
There are several methods:
- a) moving on a strait line in the direction of the target or
- b) moving sideways from line of sight to the target.
- Method a)
Assessing the distance between the present position
A and a target located in
c. Measure first the angle built by two
representative points (
a and
ab) located on both sides of c (i.e.
s = 91
mils in the figure). Move then in the direction of
c up to a point
B which is located at a known distance of
A -for instance 100 m and which we call
M (for move). Measure there again the angle built by
the two points left and right of
c (i.e.
s1 = 99.2 mils). The formula
is as follows:
To calculate the distance
D (between
B and
c), multiply the value of
the move
M (100 m) by the angle
s (91 mils) and divide the result by
the difference
d between both angles (i.e. 8.2 mils.):
D = M x s / d = 100 x 91 / 8.2 = 1100 m.
Add then the value of the first move from
A to
B (100 m) to obtain
distance
A-c (1200 m).
NOTE: It is also possible to go back from the observation point. One must
then substract the moving distance.
- Method b)
In the present case only one additional point is necessary: it should
be situated 100 mils sideways of the line of sight (
A-B) to the target.
One goes a certain distance in the direction of the additional aid
point and measure again the angle between
c and the target. With these
distance measures and angle values, one can calculate the distance to
the target with the same formula as with method a).
One can also estimate a distance without computing it. For instance the
broadth of a river. The method is as follows: One must draw hereto a
sketch with a certain scale. First, chose an easily recognizable object
on the opposite bank and take a bearing of it against the next cardinal
point. Move then sideways by a certain distance (100 m for instance),
at a 90 degrees angle and take again the bearing. The difference
between both is the angular value of the line B-C that is to be drawn
on the sketch. Since the distance A-B is known, one can measure on the
sketch the length of the line A-C at the cross point with B-C.
- Special devices in compass lids and tools
Some compasses
have one or several rulers located besides the sighting slots in the
lid (picture right: TELEOPTIK M49 - click to enlarge).
These compasses must be held at a certain distance from the eye, for
example 25 cm or 50 cm. To this purpose, the compass' lanyard has a
knot at the right place, that you can hold with one hand against your
cheek while holding the compass at eye's level with the other hand. The
size of the observed objects is also measured in mils.
The Bézard
Universalkompass (BUK) had an additional system: attached to
the compass was a foldable ruler comprising two halves of 8 cm each,
i.e. 16 cm when open. The first 10 cm were also mils and read:
0-20-40-...-200-11-12...! |
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