Horizontal Angle Measurement

Theodolites or Transits can Measure:• horizontal angles• vertical angles• distances (stadia)• elevations

Components of a Theodolite

Vertical axis

Horizontal axisLine o

f sightVertical circle

Plate bubble

Horizontal circle

MicrometerOptical Plummet

Tribrach

Tribrach (detachable)Eye piece ofoptical plummet

Foot Screw

Horizontal circlehousing

Horizontal CircleAdjustmentFor Orientation(Orientation Driver)

Circular Bubble

Standard

Optical Switch for Horizontal/ VerticalCircle Readings

Micrometer forCircle Readings

Vertical Circle

Objective ofTelescope

Fine Horizontal Adjustment for TelescopeAlignment (Tangent Screw)

HORIZONTAL AXIS

Ver

tica

l Axi

so

f R

ota

tio

n

LINE OF SIGHT

Precise Hor. Bubble(Plate Bubble)

TURN

PLUNGE

COMPONENTS OF A TYPICAL ‘OPTO-MECHANICAL’ THEODOLITE

Fine VerticalAdjustment forTelescopeAlignment(Tangent Screw)

Basic Components of an Angle

• reference or starting line (A)• direction of turn (B)• angular value (C) usually in DMS

A

B

C

Kinds of Angles

1. Clockwise Interior

2. Counter-clockwise Interior

3. Deflection Angles

L

R

L

180

0

270 0

90 0

Measuring Angles

113000

B

A

C

Azimuth

FIRSTQUAD

2NDQUAD

3RDQUAD

4THQUAD

0

180

270 90

45315

225 135

N

EW

S

3100

490

A

BC

Measuring Azimuths

“CLOSING THE HORIZON”

B

D

CA

Measure all the angles around a point

Units• Generally angles/azimuths measured in degrees, mins, secs

90

9090

90 100

100100

100

DMS(sexagesimal)

Grads/Gons

1600

16001600

1600

Mils (Russia uses 6000)

• 2 PI Radians = 3600

Converting Angular Values

Convert a = 390 41’ 54” to radians

2 p radians = 3600 OR p radians = 1800

a = (39 + 41/60 +54/3600) degs / (180/p) ……. radians

DMS must usually be converted to D.DD before they can be operated on in a calculator or computer. In some cases (e.g.Excel) angular values must be converted to radians for trigfunctions.Most calculators will have a hard-wired function to go betweenDMS (HMS) and D.DD (H) and vice versa.