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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 geodetic distances and the principles of the plane surveying are not applicable here. The corrections for the curvature and refraction are applied directly to the angles directly.
Now we will discuss the various cases to find out the difference in elevation between the two.
(1) The two points are at known distance: The base of the object is accessible.
When the two points are at a known horizontal distance then we can find out the distance between them by taking the vertical angle observations.
If the vertical angle of elevation from the point to be observed to the instrument axis is known we can calculate the vertical distance using trigonometry.
Horizontal distance*tangent(vertical angle) = Vertical difference between the two.
If the points are at small distance apart then there is no need to apply the correction for the curvature and refraction else you can apply the correction as given below:
Where D is the horizontal distance between the given two points in Kilometers.
but the Correction is in meters (m).
(2) The base of the object is not accessible :
(a)( When the instrument is shifted to the nearby place and the observations are taken from the same level of the line of sight: In such case we have to take the two angular observations of the vertical angles. The instrument is shifted to a nearby place of known distance, and then with the known distance between these two and the angular observations from these two stations, we can find the vertical differencein distance between the line of sight of the instrument and the top point of the object.
(b) When the line of sights of the two instrument setting is different :
Here again there are two cases: (i) When the line of sights are at a small vertical distance which can be measured through the vertical staff readings. (ii) When the difference is larger than the staff height.
(i) In first case, It is advised to apply the formula for the difference in the height of the top of the object from these two lines of sights. The difference in lines of sights is same as the staff readings difference, when the staff is kept at a little distance from these two points. So we can get the solution for the vertical distance easily.
(ii) In the second case, there is a need to put a vane staff at the first instrument station and the angle of elevation is measured from the second point of observation. This gives us the difference in the line of the sights between the two points of instrument station. Then again we do the same.
(c) When the instrument station and the top of object are not in same vertical plane:
In this case there is a need to measure at-least two horizontal angles of the horizontal triangle formed by the two instrument stations and the base of the object.
Again we will take the vertical angular observations from the two instrument stations also and then we can apply the sine rule to solve the horizontal distances of the triangle. With the help of these angles and the distances we can get the vertical distance between any two point(Instrument station and the top of object).
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