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Consecutive Co-ordinates:

Consecutive Co-ordinates: The northing and easting of any point with reference to the preceding point are called the consecutive co-ordinates of that point. Independent or Total Co-ordinates:

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Consecutive Co-ordinates:

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  1. Consecutive Co-ordinates: The northing and easting of any point with reference to the preceding point are called the consecutive co-ordinates of that point. Independent or Total Co-ordinates: The co-ordinates of any point with respect to a common origin are known as the independent co-ordinates or total co-ordinates of that point.

  2. Horizontal Control TRAVERSE By : - a) Bowditch Method - proportional to line distances D N values and D E b) Transit Method - proportional to c) Numerous other methods including Least Squares Adjustments We have started to compute the traverse station coordinates from an anticlockwise polygon traverse. We tested the sum of the observed angles against the sum of the internal angles of the polygon, and if within an acceptable value we distributed the misclosure. We established the bearings of all the traverse lines and then calculated the changes in Easting and Northing for each line. The algebraic sum of these changes should be ZERO. The values give the error eE and the error eN. The linear misclosure e =  (eE2 + eN2)was calculated and used to find the FLM. If acceptable then distribute the errors.

  3. Bowditch Method - proportional to line distances • This rule, also termed as the compass rule, is used to balance the traverse • when the angular and linear measurements are equally precise. The eE and the eN have to be distributed For any line IJ the adjustments are dEIJ and dNIJ dEIJ= [ eE / perimeter of traverse ] x DIJ Applied with the opposite sign to eE dNIJ= [ eN / perimeter of traverse ] x DIJ Applied with the opposite sign to eN

  4. CO-ORDINATE DIFFERENCES WHOLE HORIZONTAL CIRCLE DISTANCE CALCULATED BEARING D q D E D N 638.57 +638.570 0.000 00 00 00 +931.227 -1271.701 1576.20 306 12 51 -3677.764 -1047.754 3824.10 195 54 06 +2107.313 +2319.361 3133.72 47 44 33 9172.59 -0.094 -0.654 3 3 eE eN e =  (eE2 + eN2) =  (0.0942 + 0.6542) = 0.661m Fractional Linear Misclosure (FLM) = 1 in SD / e = 1 in 9172.59 / 0.661 = 1 in 13500 Check 2

  5. dEIJ= [ eE / SD ] x DIJ Applied with the opposite sign to eE Store this in the memory For line AB dE AB = +0.0000102479…x D AB For line BC dE BC = +0.0000102479…x D BC For line CD For line DA dE CD = +0.039m dE DA = +0.032m eE= -0.094mSD = 9172.59 m dE IJ = [+0.094/ 9172.59 ] x D IJ = +0.0000102479…... x D IJ = +0.0000102479…x 638.57 dE AB = +0.007m = +0.0000102479…x 1576.20 dE BC = +0.016m

  6. CO-ORDINATE DIFFERENCES S T CO-ORDINATES A CALCULATED ADJUSTMENTS ADJUSTED T I O N D D d d D D E N E N E N E N +638.570 0.000 +931.227 -1271.701 -3677.764 -1047.754 +2107.313 +2319.361 -0.094 -0.654 eE eN +0.007 +0.016 +0.039 +0.032

  7. Store this in the memory dNIJ= [ eN / SD ] x DIJ Applied with the opposite sign to eN eN= -0.654m dN IJ = [+0.654/ 9172.59 ] x D IJ = +0.000071299…... x D IJ dN AB = + 0.000071299… x D AB = + 0.000071299…x 638.57 dN AB = +0.046m dN BC = +0.112m dN CD = +0.273m dN DA = +0.223m

  8. 4000.00 3000.00 B +638.570 0.000 C +931.227 -1271.701 D -3677.764 -1047.754 A +2107.313 +2319.361 Check 3 CO-ORDINATE DIFFERENCES S T CO-ORDINATES A CALCULATED ADJUSTMENTS ADJUSTED T I O N N D D d d D D E E N E N E N A +638.616 +0.007 4638.62 3000.01 +0.007 +0.046 5569.96 1728.32 +931.339 -1271.685 +0.016 +0.112 1892.46 680.61 +0.039 -3677.491 +0.273 -1047.715 +2107.536 +2319.393 4000.00 3000.00 +0.032 +0.223 S= 0 S= 0 -0.094 -0.654 eE eN

  9. Transit Method The transit rule may be employed to balance the traverse when the angular measurements are more precise than the linear measurements. The eE and the eN have to be distributed For any line IJ the adjustments are dEIJ and dNIJ dEIJ= [ eE / arithmetical sum of all eastings ] x easting of that side Applied with the opposite sign to eE dNIJ= [ eN / arithmetical sum of all northings ] x northing of that side Applied with the opposite sign to eN

  10. CO-ORDINATE DIFFERENCES WHOLE HORIZONTAL CIRCLE DISTANCE CALCULATED BEARING D q D E D N 638.57 +638.570 0.000 00 00 00 +931.227 -1271.701 1576.20 306 12 51 -3677.764 -1047.754 3824.10 195 54 06 +2107.313 +2319.361 3133.72 47 44 33 9172.59 -0.094 -0.654 3 3 eE eN e =  (eE2 + eN2) =  (0.0942 + 0.6542) = 0.661m Fractional Linear Misclosure (FLM) = 1 in SD / e = 1 in 9172.59 / 0.661 = 1 in 13500 Check 2

  11. Store this in the memory For line AB dE AB = +0.0000202637…x E AB For line BC dE BC = +0.0000202637…x E BC For line CD For line DA dE CD = + 0.0212 m dE DA = +0.047m dEIJ= [ eE / arithmetical sum of all easting ] x easting of that side Applied with the opposite sign to eE eE= -0.094m arithmetical sum of all eastings =4638.816 = +0.0000202637…... x D IJ dE IJ = [+0.094/ 4638.816 ] x easting of that side = +0.0000202637…x 0 dE AB = +0 m = +0.0000202637…x 1271.701 dE BC = + 0.0257 m

  12. CO-ORDINATE DIFFERENCES S T CO-ORDINATES A CALCULATED ADJUSTMENTS ADJUSTED T I O N D D d d D D E N E N E N E N +638.570 0.000 +931.227 -1271.701 -3677.764 -1047.754 +2107.313 +2319.361 -0.094 -0.654 eE eN +0 +0.0257 +0.0212 +0.047

  13. Store this in the memory dNIJ= [ eN / arithmetical sum of all northings ] x northing of that side Applied with the opposite sign to eN eN= -0.654m dN IJ = [+0.654/ 7354.874 ] x northing of that side = +0.00008892…... x D IJ dN AB = + 0.00008892… x D AB = + 0.00008892…x 638.570 dN AB =+0.0567m dN BC = dN CD = dN DA =

  14. CO-ORDINATE DIFFERENCES WHOLE HORIZONTAL CIRCLE DISTANCE CALCULATED BEARING D q D E D N 638.57 +638.570 0.000 00 00 00 +931.227 -1271.701 1576.20 306 12 51 -3677.764 -1047.754 3824.10 195 54 06 +2107.313 +2319.361 3133.72 47 44 33 9172.59 -0.094 -0.654 3 3 eE eN e =  (eE2 + eN2) =  (0.0942 + 0.6542) = 0.661m Fractional Linear Misclosure (FLM) = 1 in SD / e = 1 in 9172.59 / 0.661 = 1 in 13500 Check 2

  15. CO-ORDINATE DIFFERENCES S T CO-ORDINATES A CALCULATED ADJUSTMENTS ADJUSTED T I O N D D d d D D E N E N E N E N +638.570 0.000 +931.227 -1271.701 -3677.764 -1047.754 +2107.313 +2319.361 -0.094 -0.654 eE eN +0 +0.0257 +0.0212 +0.047

  16. SURVEYING – I(CE- 128) Local Attraction The magnetic needle does not point towards the magnetic north under the influence of the external attractive forces. Such a disturbing influence is known as Local Attraction. Compass bearings cannot, therefore, be relied upon unless means are taken to detect the presence of local attraction and eliminate its effects. To detect its presence, it is only necessary to observe the bearing of each line from both its ends. If the for and back bearings differ by 180o, there is no local attraction at either station, provided the compass is free from instrumental errors, and no observational errors are made. If the fore and back bearings differ by 180o nearly, the back bearing is increased or decreased by 180o to get the corresponding fore bearing, and the mean is taken between this and the observed fore bearing, e.g. the observed fore and back bearings are 90o0’ and 276o30’. The fore bearing calculated from the back bearing is= 96o30’. The mean of the observed and calculated fore bearings= 96o15’, which is the corrected bearing of the line.

  17. SURVEYING – I(CE- 128) • The amount of local attraction is the same for each of the bearings observed at the affected station. It may, therefore, be remembered that the differences between the bearings of the lines observed at the station will give the correct values of the angles between the lines even though the station is affected by local attraction provided they are taken at the same time with the same instrument. • There are two methods of correcting the observed bearings of the lines. • In the first method the true included angles at the affected stations are computed from the observed bearings. Commencing from the unaffected line and using these included angles, the correct bearings of the successive lines are computed as already explained.

  18. SURVEYING – I(CE- 128) Example:- Suppose, for example, the observed bearings of the lines AB, BC, CD, & DA are:

  19. SURVEYING – I(CE- 128) (2) In the second method, which is in most common use, the included angles are not computed, but the amount and direction of error due to local attraction at each of the affected stations is found. Starting from a bearing unaffected by local attraction, the bearings of the successive lines are adjusted by applying the corrections to the observed bearings. Example:-

  20. SURVEYING – I(CE- 128)

  21. SURVEYING – I(CE- 128)

  22. SURVEYING – I(CE- 128)

  23. SURVEYING – I(CE- 128)

  24. SURVEYING – I(CE- 128)

  25. SURVEYING – I(CE- 128)

  26. SURVEYING – I(CE- 128)

  27. SURVEYING – I(CE- 128)

  28. SURVEYING – I(CE- 128)

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