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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Figure F-2 Control Network and Sideshots. We take the observation of the vertical angles and then compute the distances using them.

Besides the way the elevations are determined, another major difference between trigonometric and differential leveling is point connectivity. The measured vertical angle can be used to convert the measured slope distance to DE by multiplying by the sine of the vertical angle. On reconnaissance surveys the vertical angles may be measured with a clinometer, and distances maybe obtained trigonimetric pacing. These requirements and limitations are discussed as follows:.

When you use the same setup for slopes, replace the electronic equipment with a theodolite and either a target or a rod to measure the vertical angle.

### Surveying: Trigonometrical Levelling

Figure F-2 b depicts a trigonometric network referenced to the differential network. Article Index Chapter F. Now one side and one angle of a right triangle OCD are known. Inclination corrections for foot tape b.

The distances are measured directly as in the plane surveying or they are computed as in the geodetic surveying. Measured distances obtained by slope chaining also should be corrected as discussed above. What we want, however is the elevation of the ground point at the reflector location. Lveelling 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.

That is the basic principle of trigonometric leveling. Points B, C, and D serve as control for trigonometric leveling.

### Chapter F. Trigonometric Leveling

Trigonometric leveling is used when a number of elevations are measured from a single instrument set up. Vertical distance, V, is the elevation difference between the TSI and the reflector.

The known distances are either assumed to be horizontal or the geodetic lengths at the mean sea level MSL. The rod is above the instrument and the angle is plus. 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 difference in elevation between the points.

Determining TSI elev 3. With practice, stadia provides a rapid means of determining the horizontal distances and elevations. Here again there are two cases: 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.

For each method, there are requirements and limitations that must be adhered to. The corrections triognometric the curvature and refraction are applied directly to the angles directly. 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.

Electronic distance- measuring devices measure the straight-line horizontal or slope distance between instruments.

To determine that, we need two additional pieces of information: 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. In addition, you must convert the slope distance to a horizontal distance before computing the DE.

The instrumentman trains the telescope trigonomegric C, which is an easily read value usually a full foot on the rod. Newer Post Older Post Home. The rodman trigoometric a rod on B. The green shots at points B, C, and D trigonometrkc all sideshots. From your knowledge of trigonometry, you know that the other sides and angle can be computed. The base of the object is accessible. Now we will discuss the various cases to find out the difference in elevation between the two.

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.

## Trigonometric leveling

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. The rod is above the instrument, and the vertical angle is plus.

The method used in trigonometric leveling is described in the following paragraphs:. However, methods to perform these corrections can be found in commercial publicationssuch as Surveying Theory and Practice, by Davis, Foote, Anderson, and Mikhail. Because sideshots are not connected to other points their elevations cannot be checked.

In figurea transit is setup and leveled at A. These requirements and limitations are discussed as follows: So we can get the solution for the vertical distance easily. As an aid in computations, tables have been developed that provide the following data:. The rod is below the instrument, and the vertical angle is minus. The X and Y co-ordinates in trigonomerric of station Shore are