Leveling and Distance Measurement Techniques in Surveying

Posted on Feb 9, 2025 in Other subjects

Leveling and Distance Measurement in Surveying

Error Analysis in Leveling

Error Level:

ENH (Horizontal Error): This error arises from an imperfect horizontal visual axis (collimation) at the instrument level, analogous to the vertical axis error in a theodolite. It depends on the spirit level’s sensitivity and is expressed in seconds.

Error of Aim:

ENP: Similar to the theodolite, this error results from inaccurate readings on the sight and is expressed in seconds.

Increasing the telescope’s magnification (A) increases the level of error.

Total Error:

ENT: The total error is the sum of the individual errors.

Angle Measurement Techniques

Methods to increase the accuracy of measuring angles include:

  • Bessel’s Rule
  • Method of Repeatability
  • Method of Iteration

Bessel’s Rule

Bessel’s Rule involves observing the same point twice. First, with the telescope in the normal (direct) position, record the vertical and horizontal angles. Second, reverse the telescope (circle reverse) after a somersault and twist of 200 gon (grades), and re-record the horizontal and vertical angles.

Measuring characteristics between forward and reverse circle:

  • Horizontal: Readings differ by 200 gon. To obtain the mean, convert the reading in the inverse circle by ± 200 gon (LH = …).
  • Vertical: Readings should add up to 400 gon. To obtain the mean, convert the reading in the inverse circle (LV = …).

To identify whether a device is in forward or reverse circle, observe the overhead reading:

  • If the angle shown on the screen is between 0-200 gon: Direct circle.
  • If the angle shown on the screen is between 200-300 gon: Reverse Circle.

Distance Measurement Methods

Distance measurement can be done using:

  • Direct Methods:
    • With tape (metal, cloth, or synthetic)
    • With Invar wires
  • Indirect Methods:
    • Using optical technologies
    • Through distance meters

Direct Methods

We will focus on tape measures. Measuring the horizontal projection, or the reduced distance, is done for solar buildings or approximately horizontal surfaces. When using tape measures, horizontal projections must be triangulated to allow for representation in computer-aided design software, as tape measures only measure distance, not angles.

Indirect Methods

Indirect methods involve measuring other quantities and then calculating the distance. Distance meters measure magnitudes of waves, such as the phase angle difference, by emitting a wave. Electronic distance measurement (EDM) involves emitting electromagnetic waves. The fundamental equation of wave distance meters includes instrumental and reflecting prism corrections.

Distance meters emit waves to measure distances by measuring the magnitudes of the waves themselves. Depending on the method, they can be grouped into:

  • Pulse
  • Phase Comparison

Precision Instruments

The accuracy of distance meters depends on the accurate measurement of the phase difference and the accuracy of wave generation. The accuracy of phase measurement is approximately / 1,000, and the accuracy in wave generation is / 1,000,000.

For infrared instruments, the range is from:

3 mm + 3 ppm to 5 mm + 5 ppm

Note: ppm stands for parts per million of a millimeter. For example, at a distance of 1000 meters (1,000,000 mm), an EDM can be accurate to within 3 mm + 3 mm.