Introduction to Surveying

Introduction to Surveying

Surveying is the art and science of determining the relative positions of points on, above, or beneath the surface of the earth by means of direct or indirect measurements of distance, direction, and elevation. It also involves laying out these points on the ground.

Classifications of Surveying

Surveying is primarily classified into two categories based on the consideration of the earth's curvature:

Types of Surveys

• Cadastral Survey: For defining property lines and boundaries.
• Topographic Survey: To determine the relief of the ground and location of natural and artificial features.
• Hydrographic Survey: dealing with bodies of water (depth, shoreline, etc.).
• Route Survey: For planning and design of linear projects like roads, railways, and pipelines.
• Construction Survey: Layout of engineering structures.

Precision vs. Accuracy

These terms are often used interchangeably but have distinct meanings in surveying.

A set of measurements can be precise (consistent) but not accurate (if there is a systematic error).

Types of Errors

Errors are the difference between the observed value and the true value.

1. Systematic Errors (Cumulative Errors):

   • Errors that follow a definite physical law or mathematical pattern.
   • They can be corrected or computed.
   • Example: Tape expansion due to temperature.

2. Accidental Errors (Random Errors):

   • Errors that remain after all mistakes and systematic errors have been removed.
   • They follow the laws of probability.
   • Example: Slight inability to read a scale exactly.

3. Mistakes (Blunders):

   • These are not errors but results of carelessness or confusion. They must be detected and removed.

Theory of Probability in Errors

For accidental errors, the Most Probable Value (MPV) of a set of observations is the arithmetic mean.

$\bar{x} = \frac{\sum x}{n}$

Standard Deviation ($\sigma$): A measure of precision.

$\sigma = \pm \sqrt{\frac{\sum v^2}{n-1}}$

Where $v$ is the residual ($v = x - \bar{x}$).

Probable Error ($PE$): A value that defines a range within which there is a 50% chance that the true error lies.

$PE_s = \pm 0.6745 \sqrt{\frac{\sum v^2}{n-1}} \quad \text{(Single Observation)}$ $PE_m = \pm 0.6745 \sqrt{\frac{\sum v^2}{n(n-1)}} \quad \text{(Mean)}$

Solved Problems