DIRECTION & THE PROTRACTOR

SECTION 19
DESCRIBING DIRECTION

501. An observer sees his horizon as a circle with himself at the centre.
He normally describes the direction of any object by saying that
it is north, east, south, west, NE, NNE, etc.
When map reading, a more accurate method is required
in describing direction. Two commonly used methods are:

a. the degree system; and
b. the mil system.

THE DEGREE SYSTEM
502. In the degree system, the circle is divided into 360 degrees;
0 or 360 being the north point. The four quadrants of the circle are
each 90 degrees and, therefore, the east south and west points are at
90, 180 and 270 degrees respectively.

503. Each degree is subdivided into 60 minutes, and each minute into
60 seconds. Degrees are marked thus , minutes’, and seconds”. When map
reading, the subdivisions of a degree are too small for practical use
and measurements to one half of a degree are generally sufficient.

504. The degree system is commonly used outside the Army.
THE MIL SYSTEM

505. In the mil system, the circle is divided into 6400 mils; 0 or
6400 being the north point. East, south and west are at 1600, 3200,
4800 mils respectively. Accuracy to the nearest 10 mils is normally
sufficient in map reading.

506. The Australian Army uses the mil system. It is convenient for many
practical uses as one mil subtends approximately one unit of length at a
range of one thousand units. For example, 1 mil subtends 1m at 1000m.
The mil system will be used in explanation for the remainder of this
pamphlet. Figure 18 shows how direction is described.

NORTH POINTS

507. The purpose of a bearing is to give an accurate indication of the
direction of one point from another. A bearing is the angle, measured
clockwise, that a point makes from a fixed zero. In actual practice,
the zero point may be one of three north points:

a. True North (TN)
b. Grid North (GN)
c. Magnetic North (MN)

TRUE NORTH (TN)

508. TN is the direction of the geographic north pole from an observer
anywhere on the Earth’s surface. A line which passes through any point
and the north and south poles is called a meridian. These lines converge
towards each other at the poles and consequently, are not parallel.
509. In map reading, there is rarely a practical need for knowing the
direction of TN. As the direction of GN is more easily found and is
very close to TN, it is used in preference.

GRID NORTH (GN)

510. GN is the direction in which the north south point towards the top
of the map. Under the UTM grid reference system, the central grid line
of each grid column coincides with a particular meridian. Within each
grid column, this one grid line points to TN, but all other grid lines,
being parallel, point to an imaginary point either to the east or west of
the true north pole.

MAGNETIC NORTH (MN), MAGNETIC VARIATION & GRID MAGNETIC ANGLE

511. MN is the direction in which a compass needle points when affected
only by the earth’s magnetic field. As the magnetic pole is not the true
north pole, there is a variation between TN and MN at any place.
The angle made at the observer between TN and MN is called the magnetic
variation of that position.

512. As GN is used in map reading more often than TN, it is more useful
to know the size of the angle between GN and MN. This is called the grid
magnetic angle and its size is shown in the north point diagram.

ANNUAL CHANGE IN MN

513. The position of the magnetic pole is not fixed. The annual change
is not constant, although it can be forecast with sufficient accuracy
over a number of years. If the annual change is in the same direction
as the grid magnetic angle, it must be added. If they are in opposite
directions, the annual change must be subtracted. The annual change is
shown below the north point diagram, in the marginal information.
Figure 19 has two examples of a north point diagram.

CONVERTING BEARINGS

514. Compass bearings (magnetic bearings) taken on ground must be
converted to grid bearings for plotting on a map. Conversely,
grid bearings taken from a map will have to be converted to magnetic
bearings before they can be used with a compass on the ground.

515. To convert a bearing from grid to magnetic or magnetic to grid
is a simple matter of adding or subtracting the grid magnetic angle.
Unfortunately, it is easy to add when you should subtract, or subtract
when you should add. As can be seen in the two examples in Figure 19,
the north point diagram indicates the correct for converting bearings.
Particular note should be taken to observe that the procedure varies
depending on whether MN is to the east or west of GN. For this reason,
the north point diagram or a roughly drawn diagram should always be
used to avoid errors, although a guide is also given below the north
point diagram.

EXAMPLE 1

A magnetic bearing of 780 mils has to be converted to a grid bearing.
The year is 1984. From the north point diagram in Figure 19.a, the
grid magnetic angle is 170 mils east in 1975, and the annual change
is easterly 2 mils in three years.

Therefore, the grid magnetic angle is 176 mils east in 1984.
(Note that map reading angles are normally rounded off to the
nearest 10 mils, therefore, for all practical purposes the grid
magnetic angle becomes 180 mils east). From figure 20, it is clear
that the angle GOA, the grid bearing = GOM + MOA = 180 + 780 = 960 mils

EXAMPLE 2

A grid bearing of 1570 mils has to be converted to a magnetic bearing.
The grid magnetic angle is 180 mils east. From figure 21, it is clear
that the angle MOA, the magnetic bearing = GOA - GOM = 1570 - 180 = 1390 mils

516. Figures 20 and 21 demonstrate how to convert bearings when the
grid magnetic angle is to the east, that is, when the magnetic north
is to the east of grid north. A simple way to remember these
conversions is as follows:

a. Magnetic to Grid Add MGA My Great Aunt
b. Grid to Magnetic Subtract GMS Grand Ma Sleeps

517. When the grid magnetic angle is to the west, magnetic north is
to the west of grid north. In this case the opposite conversions
are true, as follows:

a. Magnetic to Grid Subtract MGS
b. Grid to Magnetic Add GMA

NAV.5. INTERMEDIATE NAVIGATION STUDIES
THE SERVICE PROTRACTOR

518. To measure a bearing accurately on a map, a protractor must be
used. There are many different types of protractors available and,
although they differ in design and shape, they are used in much the
same way. They all consist of a scale around the outer edge which
radiates from an index mark located at the centre of the protractor
circle. The scale divides a circle into units of angular measure.

519. The present service protractor is the Protractor,
Semi-circular, RAA, Mils, F6 (Figure 22). The scale is
graduated in 10 mil intervals, 0 to 3200 mils outside and
3200 to 6400 (0) mils inside. The protractor includes metric
scales for measuring distance on 1:50 000 scale maps.
These are on the base and also radiate in concentric semicircles
from the index mark. A black thread radiates from the index mark
to aid in the reading of bearings.
520. To aid in reading grid references, the protractor includes
roamers for maps of the following scales:

a. 1:250 000m;
b. 1:63 360yards;
c. 1:100 000m;
d. 1:50 000m; and
e. an eight figure grid reference roamer for 1 000m maps.

MEASURING BEARINGS

521. To measure the grid bearing from the road junction at 0 to the
road junction at A in Map 19, proceed as follows:

a. Using a straight edge and a fine pencil, join 0 and A.
If the distance between the two points is less than 8cm, the
line should be extended so that it overlaps the scale when the protractor
is positioned on the map.

b. Place the protractor on the map and position it so that
the index mark is directly over the road junction at 0,
and the north line is pointing to grid north, that is,
parallel to the eastings. If the north line does not overlap an easting,
it will be pointing to grid north if an easting intersects the 10 mil
scale at the top of the protractor the same number of divisions from the
north line as at the bottom of the protractor (as arrowed in Map 19).

c. The grid bearing can now be read from the outside set of
figures on the 10 mil scale, where the pencil line meets it.
In Map 19, the grid bearing is 910 mils.

522. When bearings of between 3200 mils and 6400 mils are to be
measured, the protractor is rotated upside down or 3200 mils.
The same principles apply, except that the inside set of figures
is used on the 10 mil scale.

523. When time prevents the drawing of a fine pencil line on a map,
a bearing can be measured using the black thread attached to the
index mark. This method is not as accurate, although it has the
advantage of not marking the map.

NAV.5. INTERMEDIATE NAVIGATION STUDIES page 6 of 7

PLOTTING BEARINGS

524. To plot a grid bearing on a map, proceed as follows:

a. Place the protractor on the map and position the index
mark directly over the point on the map from which the
bearing is to be plotted, so that the north line is pointing to
grid north (such as point 0 in Map 19).

b. Read off the bearing required on the 10 mil scale and mark
the map with a pencil.

c. Draw a thin line through point 0 and the pencil mark.
This line is the required grid bearing.

BACK BEARINGS

525. A bearing gives the direction of a line from the point
of observation to an object. A back bearing gives the direction
from the object back to the point of observation. It is clear
from Figure 23 that the difference between the bearing and the
back bearing is 3200 mils. Therefore, given the bearing,
add 3200 mils to find the back bearing, or if more than 3200 mils,
subtract 3200 mils.

THE COMPASS

SECTION 22

THE PRISMATIC COMPASS

601. The compass is an instrument used for measuring magnetic bearings.
Although there are different types, they all consist of a magnetised
needle accurately balanced on a pivot point set in the centre of a
non-ferrous or plastic box. One point of the compass aligns with the
direction of magnetic north (MN).

602. When closed, the prismatic compass is a black lacquered,
circular, brass box and consists of the following:

a. Lid
b. Body
c. Prism
d. Thumb Ring

Refer to Figure 24

USE OF THE PRISMATIC COMPASS

603. The methods of using the prismatic compass are detailed in brief
as follows:

a. Taking a Bearing - Hold the compass in both hands, with a
thumb through the ring (figure 25).
The compass must be held level and steady, so that
the compass card swings freely. The lid must
be vertical and the prism turned into the reading position.
Look through the sighting slit and line up the
hair-line in the lid with the object on which the bearing
is to be taken. By looking through the eyehole
when the card comes to rest, read off the bearing against
the hair-line.

b. Finding the Direction of a Given Bearing - Look through
the eyehole and turn the compass until the hair-line cuts
the required bearing. Note some distant object which is in
line with the hair-line. This object will be on the
required bearing.

c. Using the Compass Without the Prism - Either of the operations
outlined above can be carried out without using the prism,
but with much less accuracy. To take a bearing, open the
compass out flat and line it up so that the tongue
is directly in line with the object. The bearing is read
from the inner circle of the compass card against the lubber
line. To find direction of a bearing, turn the
compass until the inner circle below the lubber line reads
the given bearing. The tongue is then pointing in
the required direction.

NAV.6. INTERMEDIATE NAVIGATION STUDIES Page 2 of 4

SECTION 23

THE SILVA COMPASS

604. There are many different types of silva compasses available.
However, the basic construction for all types remains the same.
The compass enables the user to plot and calculate bearings rapidly
and accurately on a map without the use of a protractor. This is done
by combining, on a common base plate, both compass and a protractor.

USE OF THE SILVA COMPASS

605. Taking a Grid Bearing - Map 20 shows the procedure for calculating
a grid bearing from a map as follows:

a. Place the long edge of the base plate (or an aid line) along
the desired bearing, making sure that the direction arrow points in the
direction that it is wished to travel (that is along line ABin Map 20).

b. Turn the compass housing so that the meridian lines are
parallel with the eastings on the map.

c. Read the grid bearing on the graduated dial against the
lubber line.

d. Note that before marching, the grid bearing must be
converted to a magnetic bearing and the dial adjusted
appropriately.

606. Taking a Magnetic Bearing - The procedure for taking a magnetic
bearing to an object is detailed below:

a. Hold the compass in the position shown in Figure 27,
with the direction arrow pointing to the object.

b. Rotate the compass housing until the orienting arrow is
directly beneath the north (red) end of the compass
needle.

c. Read the magnetic bearing on the graduated dial against
the lubber line.
607. Setting the Compass on a Magnetic Bearing - The procedure for
setting a compass on a magnetic bearing is as follows:

a. Set the magnetic bearing on the compass by rotating the
compass housing until the required bearing on the
graduated dial is in line with the lubber line.

b. Hold the compass flat in the hand and turn around until
the north end of the compass needle is directly
above the orienting arrow.

c. The direction arrow now points along the required magnetic
bearing.

NAV.7. INTERMEDIATE NAVIGATION STUDIES Page 1 of 4

MAP SETTING & POSITION FINDING

SECTION 25
MAP SETTING
701. A map is said to be set, oriented, when the features on the map
are in the same relative position as the features on the ground.
This requirement is met when grid north on the map is pointing to
grid north. As a consequence, a map may be set by either:

a. Inspection; or
b. Compass.
702. The purpose of setting a map is to make the reading of it easier.
Sometimes, the lettering is not the right way up, but since place
names are usually irrelevant to the navigation task at hand, that
usually does not affect the use of the map.

SETTING A MAP BY INSPECTION

703. Usually, when map reading, your position is known, so the quickest
and simplest way of setting a map is by inspection of the map and the
ground (figure 28). If there is a linear feature such as a straight
road, turn the map until the road on the map is aligned with or
parallel to the road on the ground.

704. If there is no convenient road or railway, the map can be set by
lining up on distant objects, provided your position is known. Lay a
ruler, or any straight edge, on the map so that it passes through your
position and through that of one of the objects. Sight along the ruler
to the object on the ground to set the map.

705. In both the methods outlined in paragraphs 703 and 704, a check
should be conducted against other features. If none can be recognised,
at least the slope of the land can be checked.

SETTING A MAP BY COMPASS

706. If you are not aware of your exact position and it is difficult
to identify sufficient detail on the map and on the ground, a map may
be set very accurately by use of a compass. The compass should be placed
so that its axis lies along any easting. The map and compass are then
turned until the north point of the compass is east or west of the lubber
line by the amount of the grid magnetic angle.

707. The map should not be set by placing the axis of the compass on
MN in the north point diagram, as this diagram may only be
representational and not accurately drawn.
NAV.7. INTERMEDIATE NAVIGATION STUDIES Page 2 of 4

SECTION 28

POSITION FIND & RESECTION
FINDING YOUR POSITION FROM LOCAL OBJECTS

708. Once the map has been set, if the area is well developed and fully
mapped, it is relatively easy to locate your position by comparison of
the map detail with the features on the ground. Your position should
be fixed roughly in relation to the major features around, such as hills
and towns. If the map was set by use of a road, an approximate position
can be obtained as its direction is already known and the distance can
be estimated. Your exact position is found by use of minor features,
such as creeks, tracks, fences and houses. Remember that the shape of
the ground is most helpful when locating your position, and it is far
more reliable than artificial features.

RESECTION

709. A resection is a means of locating your position on a map if you
are unable to do so by comparison of detail on the map with the features
on the ground. The method of carrying out a resection is as follows:

a. Select three prominent, widely spaced features that can be
recognised on the map and on the ground. Two features can be
used to obtain an approximate position.

b. On the ground, take magnetic bearings to these features
with a compass.

c. Convert these magnetic bearings to grid bearings.

d. Convert the grid bearings to back bearings.

e. Using a protractor, plot on the map the back bearings from
the identified features.

f. These lines will either intersect to locate your position
or form a small triangle of error.
710. Triangle of Error - If a triangle of error is formed, your true
position can be determined by the following rules:

a. If the triangle of error is inside the triangle formed by the
three features (ABC) your true position will be inside the triangle of
error. If the triangle of error is outside the triangle ABC, then your
true position will be outside the triangle of error.


b. If the triangle of error is outside the triangle formed
by the three features ABC, then your true position will be either
to the left or right when facing the fixed points of all the lines drawn
on the map from the respective features through the triangle of error.
For example, in figure 30, of the six sectors formed by the lines
drawn from the three known features, there are only two sectors
(sectors III and VI), which are either to the left or right of all the lines.

c. Regardless of whether your true position is inside or
outside the triangle of error, the distance from that position
to the lines will be directly proportional to the length of the
lines (ie, your position will be nearest to the shortest
line and furthest from the longest line). Depending on the size
of the triangle of error in figure 29, your position within the
triangle can be worked out exactly by this method. In figure 30,
the only sector in which these conditions are fulfilled is
sector VI. By approximations, your true position is at P and can
be confirmed by relating the map to the ground.

NAV.7. INTERMEDIATE NAVIGATION STUDIES Page 3 of 4

RESECTION BY OVERLAY

711. A resection can be conducted on a piece of clear plastic or
tracing paper and using that as an overlay. Provided the clear
plastic is available, this method is relatively simple and is detailed
as follows:

a. Take magnetic bearings to three features as was done for
the previous method.

b. Mark a north south line and a zero point on the plastic
with indelible pencil.

c. Working from the zero point on the north south line,
rule in the magnetic bearings (map 22). Note that magnetic
bearings are not converted to grid bearings at any stage.

d. Now place the marked plastic on the map, and bring the
three rays into alignment with their corresponding features.
Once they are aligned, your position is indicated by the zero point on
the north south line. When the rays are aligned with their corresponding
features, the north south line will automatically be offset from grid
north by an angle equal to the grid magnetic angle.

LOCAL MAGNETIC ATTRACTION

712. Local magnetic attraction is due to the presence of iron or
iron ore nearby. The compass is a delicate instrument and quite
small quantities of iron have a surprisingly large effect on its behaviour.
A wrist watch, steel framed spectacles or steel radio frames will effect
the compass reading. Precautions should be taken to see that all iron or steel
objects are at a safe distance before using the compass. Small articles will
be safe in a trouser pocket but larger articles should be placed 2 or 3 metres away.