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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Determining TSI elev 3.
The length of this side is the difference in elevation DE. As an aid in computations, tables have been developed that provide the following data:.
Height of reflector at point i. With practice, stadia provides a rapid means of determining the horizontal distances and elevations. Electronic distance- measuring devices measure the straight-line horizontal or slope distance between instruments.
The corrections for the curvature and refraction are applied directly to the angles directly. This gives us the difference in the line of the sights between the two points of instrument station. On reconnaissance surveys the vertical angles may be measured with a clinometer, and distances maybe obtained by pacing.
You will see in each of these situations the reamer in which the computed DE is applied to determine the HI and required elevations. As an aid in computations, tables have been developed that provide the following levellig In the second way, i. Here again there are two cases: This method of indirect leveling is particularly adaptable to rough, uneven terrain where direct leveling methods are impracticable or too time consuming. The instrumentman trains the telescope on C, which is an easily read value usually a full foot on the rod.
In addition, you must convert the slope distance to a horizontal distance before computing the DE.
Trigonometric leveling is used when trigonomeyric number of elevations are measured from a single instrument set up. Now one side and one angle of a right triangle OCD are known. An elevation error could be in an individual sideshot measurement or a control trigonoetric elevation error which affects all the sideshots from that point.
Then again we do the same. 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. Under ordinary circumstances in the Seabees, corrections for earth curvature and refraction are not necessary.
Wednesday, February trigonometrkc, Trigonometrical Levelling. Points B, C, and D serve as control for trigonometric leveling. 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.
Figure F-2 Control Network and Sideshots. For each method, there are requirements and limitations that must be adhered to. 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. From your knowledge of trigonometry, you know that the other sides and angle can be computed. As mentioned earlier in this section, the horizontal or slope distances used for trigonometfic the DE may be obtained levellling various methods.
The method used in trigonometric leveling is described in the following paragraphs: Where D is the horizontal distance between the given two points in Kilometers. As-you can see in figure between the height of. However, in trigonometric leveling, you are concerned only with determining the length of the side opposite the measured angle side CD. 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 levellig study in chapter 8.
The measured vertical angle can be used to convert the measured slope distance to DE by multiplying by the sine of the vertical angle. We trkgonometric the observation of the vertical angles and then compute the distances using them.
Now we will discuss the various cases to find out the difference in elevation between the two. The rod is on point B below the instrumerit. The green shots at points B, Frigonometric, and D are all sideshots. Because sideshots are not connected to other points their elevations cannot be checked.
The rod is below the instrument, and the vertical angle is minus. The distances are measured directly as in the plane surveying or they are computed as in the geodetic surveying.
Surveying: Trigonometrical Levelling
Computing the DE consists of multiplying the measured distance by levellling proper trigonometric function of the measured angle sine, when slope distance OC is measured; tangent, when horizontal distance OD is measured.
If trigojometric vertical angle of elevation from the point to be observed to the instrument axis is known we can calculate the vertical distance using trigonometry. Using appropriate procedures, and controlling errors, elevation accuraciy can be better than 0.
As-you can see in figure between the height ofthe DE is the distance instrument HI and the intersection of your line of sight with the rod point C.
Then either the horizontal distance or the slope distance between the instrument and rod is determined. With the telescope trained on C, the vertical angle a is read. In figurea transit is setup and leveled at A.