Angle Measurement

Determining the relative positions of points often involvesmeasurements of both angles and distances.

Angles are classified as either horizontal or vertical.

Vertical(zenith)

Horizontal(bearings or azimuths)

O

Basic Components of an Angle

• Reference or starting line (J)• Angular value (O) usually in DMS

Figure 8.9 Measurement of horizontal angles. (textbook)

Closing the Horizon:Measure all the anglesaround a point

Kinds of Angles

Clockwise InteriorAngles

Counter-clockwiseInterior Angles

Kinds of Angles

Deflection Angles

• Deflection angles are measured from anextension of the back line, to the forwardstation.

• Angles may be measured to the right(clockwise) or to the left (counterclockwise).

Azimuths and Bearings

AzimuthsBearings

Azimuths are horizontal anglesmeasured clockwise from anyreference meridian (North).

The bearing is the actual horizontalangles between a reference meridian(North or South) and the line.

N---E

S--ES--W

N--W

Units• Generally angles are measured in degrees, mins, secs (DMS)

• 2 PI Radians = 3600

Converting Angular ValuesConvert α = 390 41’ 54” to radians

2 π radians = 3600 OR π radians = 1800

α = (39 + 41/60 +54/3600) degs / (180/π)α = 39.698 radians

• DMS must usually be converted to D.DD before they can beoperated on in a calculator or computer.

• Most calculators will have a hard-wired function to go betweenDMS (HMS) and D.DD (H) and vice versa.

Two Types of Theodolites:• Repeating - has both upper and

lower motion• Directional - no lower motion

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

Instruments for Angle Measurement

Components of a Theodolite

Components of a Theodolite

Total Station InstrumentsIt is a combination of:

• EDM• Electronic angle measurements.• A microprocessor.

Lab procedure• Setup the instrument at the a point.• Choose four different points around 3600 sweep.• Measure and record the clockwise horizontal angles between the points

with the provided instrument.• Make one set of measurement with normal scope position (single) and

another one with turned over (‘Plunged’) position (double).

A B

C

D

O• Measure the vertical angle between the

horizontal plane and the top of theconfederation building.

• Follow the procedure given in the manual.

Sample field note

A B

C

D

O