Introduction
In Geodetic Surveying, it is crucial to account for the errors arising from the curvature of the Earth and refraction. This consideration becomes particularly significant when surveying larger areas exceeding approximately 256 km², where ignoring the Earth’s curvature is not permissible. The error resulting from the Earth’s curvature must be taken into account when calculating linear distances and also when making angular measurements in such expansive regions. Additionally, the refraction error must be considered due to the substantial distances involved. To obtain accurate results, both of these corrections need to be applied.
What is the Error Due to Curvature?
To understand the concept of error due to the curvature of the Earth, it is important to familiarize yourself with the shape of the Earth and the methods and instruments used for measuring and calculating distances.
During leveling with a Theodolite or Auto level, the line of sight is initially set as horizontal. By measuring the vertical angle to the target and applying relevant trigonometric formulas, we can determine the vertical distance between the target and the horizontal line.
The error due to curvature arises because, in the case of long distances, the horizontal line and the level line do not coincide. While the level line is a curved line parallel to the Earth’s surface, the horizontal lines are straight.
Consequently, the vertical distance from the level line to the target will be greater than the distance calculated from the horizontal line. Please refer to the provided figure, as the magnitude of the correction depends on the horizontal distance between the target and the instrument station.”
This revised version maintains the clarity of the original paragraph while improving readability. It also ensures that the information flows smoothly and clearly presents the concept of error due to curvature in geodetic surveying.
What is Error Due to Refraction?
Understanding the concept of error due to refraction becomes straightforward once you grasp the phenomenon that occurs when light passes between different density systems. Refraction refers to the deflection of light away from the normal when it transitions from a denser medium to a lighter medium, and vice versa.
In Geodetic Surveying, this phenomenon must be taken into account when calculating distances. For instance, when observing the top of a hill from a point located significantly below it, where the density of the air changes, the density gradient affects the line of sight. As the density of air decreases with height, the path of the line of sight becomes curved due to the continuous change in air density.
The crucial question to consider is how this phenomenon affects our observations. When observing an elevated object, the observed angle will be higher, while observing objects in depressions will yield smaller observed angles
Correction for the Error due to Curvature and Refraction
There are numerous textbooks that provide explanations on how to calculate the correction for refraction and curvature.
Formulas:
Curvature correction: Cc = -0.07849 * D2 meter
Refraction correction: Cr = 0.01121 * D2 meter
Combined correction: C = Cc + Cr = -0.06728 * D2 meter, where D is in kilometers.
Concluding Thoughts:
Understanding and accounting for the error due to curvature and refraction are fundamental in geodetic surveying. By considering the shape of the Earth, employing proper measurement techniques, and applying the appropriate corrections, accurate results can be achieved. Awareness of these concepts, their effects on observations, and the formulas for correction are crucial for geodetic surveyors to ensure reliable and precise surveying outcomes.
