Engineering Surveying Chapter 5

Theodolite Instrument

• Theodolite is a precision instrument used for angular measurement.
• Parts of a theodolite include the tripod, optical piece, and plummet or laser.

Setting up the Theodolite

• Stand the tripod over the survey station, keeping the head reasonably horizontal.
• Attach the plumb-bob to the tripod head (may not be used).
• Move the whole tripod or unclamp a tripod leg and slide it in or out until the plumb-bob is exactly over the station.
• Put the theodolite on the tripod and clamp it.
• Move the pair of tripod feet or extend individual legs until the center of the optical piece or laser is near to the nearest location of the station.
• Determine the bearings of side AB and side BC, and check the bearing of CA.

Measuring Angles

• Angles can be measured in two cases, and then determining the average reading for angles at face right and face left.
• Horizontal angle: Set up the instrument on survey point A, direct the instrument on target point B, and bisect the target point carefully.
• Change of zero: Set zero at point one and read point two, then set zero at point two and read point one, and determine average data for two readings.
• Change of face: Measure the angle in two cases and determine the average reading for angles.

Vertical Angles

• A vertical angle is an angle between the inclined line of sight and the horizontal.
• It can be an angle of elevation or depression, depending on whether the object is above or below the horizontal plane.

Radian System (Circular System)

• Radian is a central angle for the circle arc that is equal to the radius of the circle.
• The circle circumference is (2π R).
• Relation between the three systems: 360° 00’ 00 “ = 400ᵍ 00ᶜ 00ᶜ ͨ = 2π.

Uses of Theodolite

• Measuring horizontal angles.
• Measuring vertical angles.
• Measuring deflection angles.
• Measuring the horizontal distance between two points.
• Finding the vertical height of an object.
• Finding the difference in elevation between various points.
• Ranging of a line.

Plane Rectangular Coordinates

• In surveying, coordinates are used to provide an address for a point.
• Coordinates in a plane system are split into four quadrants with the typical mathematical convention of the axis to the north and east being positive and to the south and west being negative.
• In surveying, the x-axis is referred to as the east-axis (E) and the y-axis as the north-axis (N), with angles (θ) measured clockwise from the N-axis.

Determination of Coordinates

• Assume one coordinate, based on corrected ΔE and ΔN, determine other coordinates.
• E2 = E1 + ΔECor. E3 = E2 + ΔECor. N2 = N1 + ΔNCor. N3 = N2 + ΔNCor. ….etc

Error of Closure and Relative Accuracy

• Find the error of closure for latitude and departure, and relative accuracy.
• Find closing error: e = dE² + dN².
• Find relative accuracy: β = σ / L.
• If the tolerance of work permits the relative accuracy, it is OK. If the tolerance of work did not permit the relative accuracy, correction must be applied.

Correction for Latitude and Departure

• Bowditch method (Compass method):
  • δ1 = σ 1 dE = σ 1 dN.
  • δ2 = σ 2 dE = σ 2 dN.
  • δLast = σ Last dE = σ Last dN.
• These values are added to calculated ΔE or ΔN with opposite signs.