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Join Calculation

Join Calculation. calculation of the 1) whole circle bearing (or azimuth); . 2) distance. between two points (or stations) if the coordinates of them are known on a grid system. Join Calculation. N = North direction Sta. A and Sta. B = stations A and B AB = Bearing AB,

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Join Calculation

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  1. Join Calculation • calculation of the 1) whole circle bearing (or azimuth); 2) distance between two points (or stations) if the coordinates of them are known on a grid system

  2. Join Calculation • N = North direction • Sta. A and Sta. B = stations A and B • AB = Bearing AB, = Azimuth AB or = WCB AB • WCB = Whole circle bearing

  3. Procedures • draw a sketch showing the relative positions of the two stations to determine in which quadrant the line falls • the greatest source of error in this type of calculation is wrong identification of quadrant

  4. Quadrants • 1st Quadrant : • E = +; N = + • 2nd Quadrant : • E = +; N = - • 3rd Quadrant : • E = -; N = - • 4th Quadrant : • E = -; N = +

  5. Bearing Determination AB = tan -1 (EAB/NAB) = tan -1 (EB - EA) / (NB - NA) • final value of AB will depend on: the quadrant of the line and a set of rules, based on the quadrant in which the line falls.

  6. I II III IV Quadrant no change Formula E/N must be calculated ignoring the respective signs of E and N + - - q q q 360 180 180 Bearing Determination (con’t)

  7. Distance Determination • LAB = E2 +N2 To check the result against gross error use: LAB = (EAB/sin AB) = (NAB/ cos AB) • small differences occur between the two results, the correct answer is given by the trigonometrical functions

  8. Bearing Determination • if  = 5, L found from (N/ cos ) gives the more accurate answer than (E/ sin ) since the cosine function is changing less rapidly than the sine function at this angle value • inspection of the different columns in the trigonometrical values for the two functions will show which is the slower changing

  9. Example - Join Calculation In a road scheme, let the coordinates of a point X on the road centreline be 8 612 910.74 mE, 8 157 062.28mN. This point is to be set out by polar coordinates from a nearby control station Y with coordinates 8 613 112.33mE, 8 157 238.91mN.

  10. Example - Join Calculation EYX = 8 612 910.74 - 8 613 112.33 = -201.59 m NYX = 8 157 062.28 - 8 157 238.91 = -176.63 m distance YX = (-201.59)2 +(-176.63)2 = 268.02 m

  11. Example - Join Calculation YX = tan-1 (201.59 /176.63) = 48 46’ 32” Since YX is in the 3rd quadrant, therefore bearing of YX = 180 + 48 46’ 32” =228 46’ 32” To avoid gross error, check distanceYX using the following formulae: LAB = (EAB/sin AB) = (NAB/ cos AB) =268.02 m

  12. Polar Ray Calculation • Name given to the process of determining coordinates of one point (EA and NA) based on the following known information: coordinates of another point (EB and NB), the bearing bA, and the distance BA (dBA)

  13. Polar Ray Calculation The formulae are as follows: NA = NB + dBA cos BA and EA = EB + dBA sin BA • all additions being algebraic. The result can be checked by doing a join calculation

  14. Example - Polar Ray Calculation If NB = 1068.263 m and EB = 2135.920 m; bearing BA = 25 30’ 41” and distance BA = 100.023m, calculate the coordinates of A. • NA = NB + d cos BA = 1068.263 + (100.023 x cos 25 30’ 41”) = 1158.534 m • EA = EB + d sin BA = 2135.920 + (100.023 x sin 25 30’ 41”) =2178.999 m

  15. Coordinates Computations using Electronic Calculators • useful for computing coordinates because the sine and cosine of the bearing need not be entered • coordinate difference of E and N; or bearing and distance are then displayed at the press of several keys (normally less than the conventional keystrokes)

  16. Coordinates Computations using Electronic Calculators • built-in functions : PR and RP • PR is the conversion of polar coordinate into rectangular coordinates (Polar Ray Calculation) • RP is the reverse conversion (Join Calculation)

  17. Example: P  R • Enterhorizontal distance • PressP  R • Enterbearing (or azimuth) • Press= • Display N • PressX  Y • Display E

  18. Example: R  P • Enter N • PressR P • Enter  E • Press= • Displayhorizontal distance • PressX  Y • Displayangle

  19. Where do you want to go? Traversing Back to Traverse - Main Menu

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