Reciprocal Leveling
Prob. – In leveling across a deep and wide river, reciprocal level readings were taken
between two points, X and Y, as follows:
A – With instrument near X, the rod readings on X are 1.280m and 1.300m; on the distant
point Y, the rod readings are 2.620m, 2.610m, 2.650m and 2.600m.
B – With the instrument near Y, the rod readings on Y are 3.480m and 3.500m; on the
distant point X, the rod readings are 2.110m, 2.140m, 2.130m and 2.100m.
Determine the true difference in elevation between the two points and the elevation of Y if
the known elevation of X is 100m.
Inverse Leveling
Prob. – A tall concrete wall is an obstruction along a level route between points A and B.
To proceed with the leveling work, an inverse method of leveling was executed at
the vicinity of the obstruction where rod readings were taken with the rod held
upside down. Determine the elevation of B.
Units of Angular Measurements
A – The degrees – 0o to 360o
B – The grad – 100 centesimal secs
100 centesimal mins
C – The mil – 6400 mils 1600 mils = 90o
D – The radian – π = 360o 1rad = 180o/π 1o = π/180o
400 grads
Conversion of Angles
Prob. – Convert 301o to grads, mils and rads
Prob. – Convert 310 grads to mils, degrees and rads
Magnetic Declinations
Prob. – In 1970, a line had a magnetic bearing of N80o23’E. At that time the magnetic
declination was 3o45’ west. In a new survey performed in 2020, the declination in
the same locality changed to 2o50’ east. Determine the:
A – True bearing
C – New magnetic bearing
B – True azimuth
D – New magnetic azimuth
To determine the back azimuth when the forward azimuth is known:
Rule 1 – If the forward azimuth of the line is greater than 180o, subtract 180o to obtain the
back azimuth.
Rule 2 – If the forward azimuth of the line is less than 180o, add 180o to determine the
back tangent.
Traversing
A – Interior angle traverse
B – Deflection angle traverse
Course
Dist.
Bearing
AB
BC
CD
DE
EA
445.660
326.730
434.500
427.000
301.950
S06o35’W
N17o48’W
N70o59’W
N59o33’E
S39o18’E
C – Angle-to-the-right traverse (Exterior angle)
D – Azimuth traverse
Int.
angles
Angleto-theright
Deflection Azimuth
angle