Understanding Surveying Levels and Measurement Errors
Components of a Surveying Level
The image below illustrates the components of a typical surveying level:
- Ocular
- Reticulum Focus
- Image Focus
- ASA (presumably a brand or model designation) dismantled, with screws
- RS232 serial interface
- Leveling mechanism
- Screw
- Lens with electronic distance meter (EDM) integrated
- Exit measurement beam
- Display
- Spherical level
- Keyboard
- Trigger button
- Switch
- Fine measurement, horizontal
Types of Surveying Levels
Levels can be classified as follows:
- Tilt Levels: These levels are adjusted manually for each reading.
- Automatic Levels: These levels automatically compensate for minor misalignments.
- Digital Levels: These are EDM machines with built-in automatic data recording. The sight has a barcode and divisions in mm.
- Dual-Plane Laser Levels: These levels project two laser beams to establish horizontal and vertical planes.
Measurement Errors in Topographic Surveying
An error is the difference between the measured value of a quantity and its true value.
Classification of Errors
Excluding gross errors and mistakes, errors can be classified as actual errors and apparent errors. Actual errors are always unknown because the true value of the measured magnitude is never known. Apparent errors are determined by comparing the measurement to an approximate value.
Apparent errors can be further divided into:
Systematic Errors: These errors consistently affect the outcome in the same direction. They often result from poor instrument calibration or external factors like pressure and temperature. Systematic errors follow a specific pattern, accumulate in successive operations (resulting in a final error proportional to the measured quantity), and are therefore compensable. These errors can be eliminated through instrument calibration and mathematical netting of measurement procedures.
Accidental Errors: These errors are caused by limitations in human senses, measuring instruments, and uncontrollable environmental changes. Accidental errors are not compensable because the final error is not proportional to the measured quantity. In successive operations, they partially offset each other because errors of one sign are often counterbalanced by errors of the opposite sign. Small accidental errors are more frequent than large ones.
Probable Value of a Magnitude
When multiple measurements of the same magnitude are taken, the arithmetic mean of these measurements is considered the most probable value.
Apparent Error, Mean Error, and Accuracy
The apparent error of each measurement is the difference between the mean value and the individual measurement. Accuracy refers to the degree of approximation of a measurement to the mean value. Precision, on the other hand, is the degree of approximation of each measure to the true value.
To define the accuracy of a measurement, error theory uses the following error means:
- Probable Error: The error that has an equal number of larger and smaller errors, considered in absolute value. This error is not commonly used in surveying as it does not provide information about the accuracy of each individual measurement.
- Arithmetic Mean Error: The arithmetic mean of the absolute values of the errors of each measurement.
- Mean Squared Error (Standard Deviation): The square root of the sum of the squares of the accidental errors, divided by the number of errors minus one. This is often called the standard deviation and is widely used in surveying.
- Maximum Error or Tolerance: To eliminate outliers, measurements with errors exceeding a certain value are discarded. The maximum error, or tolerance, is typically set as 2.5 times the mean squared error.