Co-Ordinate Calculation And used in mine measurement and surveying.

  • Upendra Kumar

Co-ordinates act the fundamental role in the mine measurement and surveying. For the co-ordinates

calculation, two measurements are needed (a) horizontal bearings (b) horizontal distance. In ancient

times vernier theodolite used for angle measurement but in nowadays, digital theodolite and Total

 station used for angles measurements. For horizontal measurements to utilized chain or tape and

Total station. First, we understand the quadrant system.

Image of quadrant system,

In the above figure shown quadrant are four types (I, II, III, IV and two lines NS, EW are drawn. NS

lines are called meridian lines. If the known length and bearing of a line. it's projections, on the line

 parallel to the meridian and on the perpendicular to it may be obtained. The projection P1 Q1 is

called Latitude of the line OP1 similarly R1 P1 is called Departure of the line O P1.

Latitude - length*cosine reduced bearing

Departure- length* sine reduced bearing

Latitude is positive when measured North or upward, Latitude is negative when measured South or

downward. Departure is positive when measured east, Departure is negative when measured West.

The bearing of a line is given as a whole circle bearing the following table may be referred to

determine the signs of latitude and departure 

W.C.B Between.      Quadrant.    Latitude.   Departure.

 0• and 90•                     I N.E             +                   -
 90•and 180•                 II S.E               -                 +                                                            

180•and 270•               III S.W             -                    -
 270•and 360•             IV N.W             +                   -

The latitude and departure of any point with reference to the recording point are called consecutive

coordinates. The coordinate of any point reference to common origin are called independent or Total

The following trigonometric relations of the course of a line with its latitude and departure should be

 used in computing the unknown quantities.

 1. Latitude =Length×cosine reduced bearing.
      Departure= Length×sine reduced bearing.
 2. Tangent reduced bearing = departure/Latitude

 3. (a) Length= √(Latitude)2+(Departure)2

 4.Length= latitude× sec reduced bearing

 5. Length= departure × cosec reduced bearing


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