9 Jan Principles. Trigonometric leveling is so named because it uses a total station instrument’s (TSI) slope distance and zenith angle measurements. That is the basic principle of trigonometric leveling. This method of indirect leveling is particularly adaptable to rough, uneven terrain where direct leveling. Trigonometric leveling: surveying: Triangulation: Trigonometric leveling often is necessary where accurate elevations are not available or when the elevations of .

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Then either the horizontal distance or the slope distance between the instrument and rod is determined. What we want, however is the elevation of the ground point at the reflector location. Once we have those, levellijg the elevation of any observed point, i, is computed from:.

### Trigonometric leveling

In this case there is a need to measure at-least two horizontal angles of the horizontal triangle formed by trigoonometric two instrument stations and the base of the object.

With the telescope trained on C, the vertical angle a is read. In the second way, i. The rodman holds a rod on B.

Figure F-2 Control Trigonometgic and Sideshots. 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. The known distances are either assumed to be horizontal or the geodetic lengths at the mean sea level MSL.

These requirements and limitations are discussed as follows:. As-you can see in figure between the height of.

## Trigonometric leveling

The rod is above the instrument triyonometric the angle is plus. From your knowledge of trigonometry, you know that the other sides and angle can be computed. On reconnaissance surveys the vertical angles may be measured with a clinometer, and distances maybe obtained by pacing. Trigonometric leveling is so named because it uses a total station instrument’s TSI slope distance and zenith angle measurements to mathematically compute an elevation difference which, with a few more bits of information, can be used to determine a point’s elevation.

Electronic distance- measuring devices measure the straight-line horizontal or slope distance between instruments. The green shots at points B, C, and D are all sideshots. The base of the object is accessible. Because trigonometric leveling is not limited to a horizontal line of trigonoketric, it is more flexible and provides faster elevation data collection than differential leveling.

Adding V to the TSI elevation gives us the reflector elevation. As in any survey, the equipment that you will use in trigonometric leveling depends on the precision required.

Measured distances obtained by slope chaining also should be corrected as discussed above. Where D is the horizontal distance between the given two points in Kilometers. Now we will discuss the various cases to find out the difference in elevation between the two. The distances are measured directly as in the plane surveying or they are computed as in the geodetic surveying.

The measured vertical angle a is a depression minus angle. Each elevation point determined by trigonometric leveling is an open link, also known as a sideshot. Then again we do the same. The method used in trigonometric leveling is described in the following paragraphs:. 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: The length of this side is the difference in elevation DE.

Height of reflector at point i. With practice, stadia provides a rapid means leevelling determining the horizontal distances and elevations. For most trigonometric- leveling surveys of ordinary precision, angles are measured with a transit, or alidade, and distances are measured either with a tape or by stadia, which you will study in chapter 8.

Article Index Chapter F. In a closed differential level network, Figure F-2 aeach point has a BS and FS; each is connected to another point and their elevations are based on the BM.

Wednesday, February 6, Trigonometrical Levelling. When you know the vertical angle and either the horizontal or slope distance between two points, you can apply the fundamentals of trigonometry to calculate the levelljng in elevation between the points. The rod is on point B below the instrumerit.

Measured distances obtained by horizontal chaining should be corrected for standard error, temperature, and trigonoemtric before you compute the DE.

For each method, there are requirements and limitations that must be adhered to. If the vertical angle of elevation from the point to lwvelling observed to the instrument axis is known we can calculate the vertical distance using trigonometry. To determine that, we need two additional pieces of information: That is the basic principle of trigonometric leveling.

This gives us the difference in the line of the sights between the two points of instrument station. We take the observation of the vertical angles and then compute the distances using them. The measured vertical angle can be used to convert the measured slope distance to DE by multiplying trigonoometric the sine of the vertical angle. 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.

Inclination corrections for foot tape b. So we can get trigonomettic solution for the vertical distance easily. Electronic Distance Measurement VI. 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. Tfigonometric method used in trigonometric trigonoometric is described in the following paragraphs: Now one side and one angle of a right triangle OCD are known.

You will see in each of these situations the reamer in which the computed DE is applied to determine the HI and required elevations.

Computing the DE consists of multiplying the measured distance by the proper trigonometric function of the measured angle sine, when slope distance OC is measured; tangent, when horizontal distance OD is measured.