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Error due to Refraction and Curvature
Finally, today I thought to write about this particular topic, which is important to study when we are talking about Geodetic Surveying.
As we know, in Geodetic Surveying we have to consider the error due to the curvature of the earth and the refraction too. Reason is because a larger area is surveyed in Geodetic Surveying, more than about 256 km2. In such large areas, the error due to curvature of the earth has to be considered to calculate the linear distances and also in case of the angular measurements.
We have to consider the refraction error too, because here we are dealing with the large distances and in order to get the correct results we have to apply these correction.
What is the Error due to Curvature?
To understand this simple concept of error due to curvature of the earth, first you have to understand the shape of the earth and the methods and instruments which we employ for calculating these distances.
When we do leveling with Theodolite or Autolevel, the line of sight first is set horizontal. Then we measure the vertical angle to the target and by applying some trigonometrical formulae we can calculate the vertical distance of the target from that horizontal line.
Error due to curvature comes into play, because in the cases of long distances, the horizontal line and level line do not coincide. Level line is a curved line, parallel to the level surface, but the horizontal lines goes straight.
This means that the vertical distance of that target from the level line is going to be larger than the distance which we calculate from the horizontal line. Please refer the figure given above, the amount of correction depends upon the magnitude of the horizontal distance between the target and the instrument station.
What is Error due to Refraction?
Error to refraction can be understood easily once you understand the phenomenon which takes place when light passes from one density system to another density system. Refraction is nothing but the phenomenon by which when light travels from a denser media to the lighter media, it deflects away from the normal to the plane of the media.
Phenomenon occurs vice-versa when light travels from lighter media to denser media. This phenomenon has to be considered in the calculation of the distances in case of Geodetic Surveying. Suppose a man is taking the observation of the top of a hill from a point, which is at a considerable down far vertical distance from it to change the density of the air.
We know that density of air decreases with the height, this will effect your line of sight. The line of sight of a person who is taking observation to a point at a quite higher distance, will be a curved path, because light will continuously change its direction due to the continuous change in the density of the air.
Imporant question to ask is, how does it effect our observations? Well, the observed angle will be to high in case of taking the observation of an elevated object and the observed angle will be small in case of taking observations to an object in depressions.
Correction for the Error due to Curvature and Refraction:
There are a numbers of textbooks, which explains the procedure to calculate the correction for the refraction and curvature.
Curvature correction, Cc = - 0.07849.D^2 meter
Refraction Correction, Cr = 0.01121.D^2 meter
Combined Correction C = Cc+Cr= -0.06728. D^2 meter; here D is in kilometer
Tacheometry is the branch of Surveying in which we determine the horizontal and vertical distances with the angular measurements with an instrument , Tachemometer. It is not so accurate method of finding the horizontal distances as the Chaining is, but it is most suitable for carrying out the surveys to find the distances in the hilly area where other methods are quite difficult being carried out. It is generally used to locate contours, hydrographic surveys and laying out routes of highways, railways etc.
The instruments required for carrying out the Tacheometric survey are: (1) A Tacheometer (2) A Stadia Rod. Tacheometer: Tacheometer is more or less a Theodolite installed with a stadia diaphragm. Stadia diaphragm is equiped with three horizontal hairs and one vertical hair. So we can take three vertical staff reading at the same instruments setting, lower most hair reading, central hair reading and the top hair reading. The difference between the lower hair reading and the upper ha…
A short introduction to plane tabling- A graphical method of Surveying.
Plane Table Survey: Plane Table Survey is a method of Surveying in which field work and the office work are done simultaneously. It is also known as the graphical method of Surveying. A manuscript map is made in the field and the topographic details can be filled in later.
List of Instruments used in Surveying:
(1) Plane Table(2) Alidade(3) Plumbing fork and Plumb bob(4) Spirit Level(5) Chain or Tape(6) Rain roof cover for the plane table(7) Compass(8) Ranging Rods(9) Drawing Sheets(10) Drawing equipment.
Procedure: To do the plane tabling one has to follow the following procedure at every plane table set-up: (a) Fixing the plane table to the tripod stand(b)Setting up and temporary adjustments:
Leveling the plane table with the help of spirit level Centering with the help of plumbing fork Orientation by trough compass or by back sighting
Trigonometric Leveling is the branch of Surveying in which we find out the vertical distance between two points by taking the vertical angular observations and the known distances. The known distances are either assumed to be horizontal or the geodetic lengths at the mean sea level(MSL). The distances are measured directly(as in the plane surveying) or they are computed as in the geodetic surveying.
The trigonometric Leveling can be done in two ways: (1) Observations taken for the height and distances (2) Geodetic Observations. In the first way, we can measure the horizontal distance between the given points if it is accessible. We take the observation of the vertical angles and then compute the distances using them. If the distances are large enough then we have to provide the correction for the curvature and refraction and that we provide to the linearly to the distances that we have computed. In the second way, i.e geodetic observations, the distances between the two points are g…