Describe the concept of “Trigonometric Heighting” with the aid of diagram?

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Expert Solution

The difference in elevation/heights between two objects can be determined by using the Trignometric Heighting. The heights of control points can be established using this method while traversing. The only two observations made in this method are

(i) Inclined or horizoontal distance between them

(ii) Zenith or vertical angle between the two objects

This two observations help in finding out of height of instrument and the height of target. As long as strict field procedure is adhered to this method prves to be highly reliable. The ccuracy is this method is 1 cm to 2 cm.

When carrying out a detailed surveying, Trignometric Heighting as ameans of obtaining heights for working points is very economical. It also proves to be a faster method as far as vertical control of profiling is considered, especially for electrical power lines.

Principle of Trignometric Heighting

A total station is setup over a peg A and sights a reflector rod set up over peg B. Height of instrument HI has been measured using a small tape. The length of the reflector rod or the Height of signal (Hsig) has been measured using a small tape. The Zenith angle V and the slope distance Sslope has been measured using TotalStation. Height difference between the two stations is then calculated. This calculation is done similar to that of rise and fall method of spirit levelling.

R+C is a small correction due to refraction and curvaature of the earth and of the line of sight

k is relative ray curvature = 0.13

R is the earth radius = 6400 km approx.

S is the slope distance in meters

If instead of slope distance, the horizontal distance HD is given, then the formula becomes:

VD =HD/tanZ

Ally Wells answered 4 months ago

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