Elementary Surveying
UNITS OF ANGULAR MEASUREMENT
1. The Degree. The sexagesimal system is used in which the
circumference of a circle is divided into 360 parts or degrees.
The basic unit is the degree, which is further subdivided into
60 minutes, and the minute is subdivided into 60 seconds. The
, ‘ and “ are used to denote degrees, minutes, and seconds,
respectively.
2. The Radian. One radian is defined as the angle subtended at
the center of a circle by an arc length exactly equal to the
radius of the circle. One radian equals 180 /  or
approximately 57.2958 degrees.
3. The Grad
4. The Mil
360
0
270
2 rad
0 rad
90
180
Degree
Elementary Surveying Notes of AM Fillone
/2
3/2
 rad
Radian
Elementary Surveying
DESIGNATION OF NORTH POINTS
Map users are primarily concerned with the north point for the determination
of directions. The following are the commonly used reference points;
1. True North – is the north point of the true meridian. In maps and
sketches, it is portrayed in the direction of the actual location of the earth’s
north geographic pole and is always shown along a vertical line. A star, an
asterisk, or the letters TN symbolizes it. Figure 24-5a.
2. Magnetic North – a north point that is established by means of a
magnetized compass needle when there are no local attractions affecting it.
Magnetic north may be located either east or west of true north. A half
arrowhead or the letters MN usually symbolizes the point. Figure 24-5b.
3. Grid North – a north point, which is established by lines on a map, which
are parallel to a selected central meridian. It may coincide with lines
directed toward true north. A full arrowhead or the letters GN or Y may
symbolize grid north. Figure 24-5c.
4. Assumed North – is used to portray the location of any arbitrarily chosen
north point. It may be symbolized by a small-blackened circle or the letters
AN. Figure 24-5d.
TN
MN
GN
AN
*
W
E
W
E
W
E
W
E
S
S
S
S
(a)
(b)
(c)
(d)
Figure 24-5
Elementary Surveying Notes of AM Fillone
Elementary Surveying
DIRECTION OF LINES
The direction of a line is defined as the horizontal angle the line makes
with an established line of reference. There are various kinds of angles,
which can be used to describe the direction of lines. In surveying
practice, directions may be defined by means of,
a) Interior angles,
1
5
2
4
3
b) Exterior angles,
1
A
5
B 2
E
C
3
D
4
Elementary Surveying Notes of AM Fillone
Elementary Surveying
c) Deflection angles,
B
D
1
3
E
2
A
C
d) Angles to the right,
B
D
A
C
e) Bearings, and
f) Azimuths
N
a
c
4430’
50
W
P
E
2942’
b
Bearing Pa = _________
Bearing Pb = _________
Bearing Pc = _________
Azimuth (from South) Pa = ________
Azimuth (from South) Pb = ________
S Azimuth (from North) Pc = ________
Note: Azimuths will be based either from the South or North going
clockwise.
Elementary Surveying Notes of AM Fillone
Elementary Surveying
FORWARD AND BACK AZIMUTHS
- Any line established on the earth’s surface has two azimuths – a
forward azimuth and a back azimuth.
- These directions differ by 180 degrees from each other since the back
azimuth is the exact reverse of the forward azimuth.
- To determine the back azimuth when the forward azimuth is known,
the following rules are used:
Rule 1: If the forward azimuth of the line is greater than 180
degrees, subtract 180 degrees to obtain the back azimuth.
Rule 2: When the forward azimuth of the line is less than 180
degrees, add 180 degrees to determine the back azimuth.
- See Figure 25-10 and the Table as example below
N
N
E
345
314
B
Figure 25-10
50
N
165
N
230
D
N
75
255
A
C
134
LINE
AB
BC
CD
DE
Obs. Azimuth from south
Forward
Back
23000’
5000’
31400’
13400’
25500’
7500’
16500’
34500’
Elementary Surveying Notes of AM Fillone
Calc. azimuth from north
Forward
Back
5000’
23000’
13400’
31400’
7500’
25500’
34500’
16500’