Question

With respect to plane table surveying, the terms 'triangle of error', 'great circle', 'great triangle' are related to

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Bessel method

बेसेल विधि

Two-point Problem

दो-बिंदु समस्या

Lehmann Method

लेहमैन विधि

Graphic Triangulation

ग्राफिक त्रिकोणीकरण

Answer ( Option C)

Lehmann Method

लेहमैन विधि

Solution

Methods of Resection in plane table surveying:

1. Back ray Method

2. Two-point Problem

3. Three-point Problem

Three point problem can be further divided into following methods.

1. Mechanical Methods

2. Graphical method (Bessel's Solution)

3. Trial Error Method (Lehmann's Method)

Lehmann's Method :

• This method is very commonly used in field and is quite quick and very accurate

• The plane table is stationed, set and levelled at station O and is oriented as nearly as possible into correct position either by visual judgment or by use of compass.

Steps includes in Lehman's method are as follows:

• Rays Aa Bb and Cc through plotted points a, b and c are drawn sighting stations A, B and C along aA, bB and cC respectively.

• If the table was oriented correctly to start with all these rays will intersect at common point O on the map indicating correct position of station O.

• However, since the initial orientation was only approximate, a small triangle O1 O2 O3 will be formed in place of a common point O.

• This triangle is called triangle of error.

• This triangle is attempted to shrink to a point by trial and error, so that initial positions lines aA, bB and cC pass through a single point o.

• The process applied to achieve this object is known as Lehmann's rule.

• The triangle formed by joining stations A, B and C is termed great triangle while the circle passing through A, B and C as great circle.