LEC11 Traversing Notes

Traversing

Introduction

  • Traversing is a fundamental aspect of land surveying used to accurately determine the position of points on the Earth's surface.
  • Historically, early surveyors in Mesopotamia, Egypt, and Greece used basic tools like ropes and sighting devices to create traverse surveys for land division, mapping, and construction.
  • A traverse consists of a series of consecutive straight lines forming a survey path. The endpoints of these lines are marked, and their lengths and directions are measured in the field.
  • Traversing is the process of evaluating these field measurements to determine the relative location of points.

Types of Traverses

  • There are two main types of traverses:
    • Closed Traverse
    • Open Traverse
Closed Traverse
  • Polygon:
    • The traverse returns to the starting point.
    • Forms a closed geometric figure that is mathematically and geometrically closed.
  • Link:
    • The traverse ends at a different station from the starting point.
    • Geometrically open but mathematically closed.
    • Requires a closing reference direction.
  • Closed traverses allow for checks on observed angles and distances.
Network
  • A network involves the interconnection of stations.
  • If the distance between points C and D is observed, the resultant set of observations is called a network.
  • Provides redundant observations.
  • Offers more geometric checks compared to a closed traverse.
Open Traverse
  • Geometrically and mathematically open.
  • Consists of a series of connected lines that do not return to the starting point or close upon a point of equal or greater accuracy.
  • Should be avoided because it lacks means for checking observational errors and mistakes.
  • If an open traverse is necessary, careful and repeated observations should be taken.
  • Traverse stations are also called angle points because angles are observed at each station.

Observation of Traverse Angles or Directions

  • Methods for observing angles or directions of traverse lines include:
    1. Interior angles
    2. Angles to the right
    3. Deflection angles
    4. Azimuths
Traversing by Interior Angles
  • Interior angles should be observed clockwise from the backsight station to the foresight station to reduce mistakes in reading, recording, and computing.
  • For example, angle EAB is observed at station A, with the backsight on station E and the foresight at station B.
  • Angles are read clockwise (except for deflection angles).
  • Accuracy may be improved by averaging equal numbers of direct and reversed readings.
Traversing by Angles to the Right
  • Angles observed clockwise from the backsight to the foresight are called angles to the right.
  • Traverse stations are numbered or lettered consecutively to increase in the forward direction.
  • Angles to the right can be interior or exterior angles of a polygon traverse, depending on the direction of traversing.
  • If traversing is counterclockwise, angles to the right are interior angles. If traversing is clockwise, angles to the right are exterior angles.
Traversing by Deflection Angles
  • Route surveys commonly use deflection angles, which are observed to the right or left from extended lines.
  • Each angle should be doubled or quadrupled, and an average value determined.
  • Deflection angles can be obtained by subtracting 180∘180^\circ from angles to the right.
  • Positive values indicate right deflection angles, and negative values indicate left deflection angles.
Traversing by Azimuths
  • Total station instruments allow traverses to be run using azimuths.
  • This method allows for direct reading of azimuths of all lines, eliminating the need to calculate them.
  • Azimuths are observed clockwise from the north end of the meridian through the angle points.

Angle Misclosure

  • The angular misclosure for an interior angle traverse is the difference between the sum of the observed angles and the geometrically correct total for the polygon.
  • The sum of the interior angles of a closed polygon should be: (n−2)×180∘(n-2) \times 180^\circ, where nn is the number of sides.
  • If the angles are measured clockwise to the right (exterior angles), then the sum of the observed angles should be: (n+2)×180∘(n+2) \times 180^\circ

Errors in Traverse

  • Sources of error in running a traverse include:
    • Poor selection of stations, resulting in bad sighting conditions caused by:
      • Alternate sun and shadow
      • Visibility of only the rod's top
      • Line of sight passing too close to the ground
      • Lines that are too short
      • Sighting into the sun
    • Errors in observations of angles and distances
    • Failure to observe angles an equal number of times direct and reversed

Balancing Angles

  • Methods for balancing angles:
    • Applying an average correction to each angle, assuming uniform observing conditions at all stations. The correction for each angle is the total angular misclosure divided by the number of angles.
    • Applying larger corrections to angles observed under poor conditions. The first method (average correction) is more commonly used.
  • Adjustments applied to angles are independent of the size of the angle.

Example: Balancing Angles

  • Compute the adjusted angles for the given interior angles.

Solution for the Balancing Angle Example

  • Two methods are demonstrated:
    • Method 1: Multiples of Average Correction
      • Involves rounding and successive differences to adjust the angles.
    • Method 2: Adjustment
      • Applies a direct adjustment to each angle.

References

  • Chapter 9, Elementary Surveying: An Introduction to Geomatics, 16th edition, 2022. Author: Charles D Ghilani.
  • The University of Memphis
  • AAIT, Department of Civil Engineering
  • Donald Parnell, P.E.; Land Surveying Principles – Traverse Surveys; CEDengineering.com