TRAVERSE CALCULATIONS

PROCEDURE FOR TRAVERSE CALCULATIONS

  • Adjust angles or directions
  • Determine bearings or azimuths
  • Calculate and adjust latitudes and departures
  • Calculate rectangular coordinates

    BALANCING ANGLES OF CLOSED TRAVERSES



    An example of a calculation involving interior angles is available.

    ADJUSTING ANGLES

  • Adjustments applied to angles are independent of the size of the angle
  • Methods of adjustment:
  • Never make an adjustment that is smaller than the measured accuracy

    DETERMINING BEARINGS OR AZIMUTHS

  • Requires the direction of at least one line within the traverse to be known or assumed
  • For many purposes, an assumed direction is sufficient
  • A magnetic bearing of one of the lines may be measured and used as the reference for determining the other directions
  • For boundary surveys, true directions are needed

    LATITUDES AND DEPARTURES

  • The latitude of a line is its projection on the north-south meridian and is equal to the length of the line times the cosine of its bearing
  • The departure of a line is its projection on the east-west meridian and is equal to the length of the line times the sine of its bearing
  • The latitude is the y component of the line and the departure is the x component of the line

    LATITUDES AND DEPARTURES



    CLOSURE OF LATITUDES AND DEPARTURES

  • The algebraic sum of all latitudes must equal zero or the difference in latitude between the initial and final control points
  • The algebraic sum of all departures must equal zero or the difference in departure between the initial and final control points

    CALCULATION OF LATITUDES AND DEPARTURES

    Using bearings
    Station Bearing Length Latitude Departure
    A
    N 26° 10'E 285.10 +255.88 +125.72
    B
    S 75° 25'E 610.45 -153.70 +590.78
    C
    S 15° 30'W 720.48 -694.28 -192.54
    D
    N 1° 42'W 203.00 +202.91 -6.02
    E
    N 53° 06'W 647.02 +388.48 -517.41
    A
    MISCLOSURE -0.71 +0.53

    CALCULATION OF LATITUDES AND DEPARTURES

    Using azimuths
    Station Azimuth Length Latitude Departure
    A
    26° 10' 285.10 +255.88 +125.72
    B
    104° 35' 610.45 -153.70 +590.78
    C
    195° 30' 720.48 -694.28 -192.54
    D
    358° 18' 203.00 +202.91 -6.02
    E
    306° 54' 647.02 +388.48 -517.41
    A
    MISCLOSURE -0.71 +0.53

    ADJUSTMENT OF LATITUDES AND DEPARTURES

    Compass (Bowditch) Rule

    ADJUSTMENT OF LATITUDES AND DEPARTURES

    Station Azimuth Length Latitude Departure
    A +0.08 -0.06
    26° 10' 285.10 +255.88 +125.72
    B +0.18 -0.13
    104° 35' 610.45 -153.70 +590.78
    C +0.21 -0.15
    195° 30' 720.48 -694.28 -192.54
    D +0.06 -0.05
    358° 18' 203.00 +202.91 -6.02
    E +0.18 -0.14
    306° 54' 647.02 +388.48 -517.41
    A
    TOTALS 2466.05 -0.71 +0.53

    ADJUSTMENT OF LATITUDES AND DEPARTURES

    Balanced Balanced
    Station Latitude Departure Latitude Departure
    A +0.08 -0.06
    +255.88 +125.72 +255.96 +125.66
    B +0.18 -0.13
    -153.70 +590.78 -153.52 +590.65
    C +0.21 -0.15
    -694.28 -192.54 -694.07 -192.69
    D +0.06 -0.05
    +202.91 -6.02 +202.97 -6.07
    E +0.18 -0.14
    +388.48 -517.41 +388.66 -517.55
    A
    TOTALS -0.71 +0.53 0.00 0.00

    RECTANGULAR COORDINATES

  • Rectangular X and Y coordinates of any point give its position with respect to a reference coordinate system
  • Useful for determining length and direction of lines, calculating areas, and locating points
  • You need one starting point on a traverse (which may be arbitrarily defined) to calculate the coordinates of all other points
  • A large initial coordinate is often chosen to avoid negative values, making calculations easier.

    CALCULATING X AND Y COORDINATES

    Given the X and Y coordinates of any starting point A, the X and Y coordinates of the next point B are determined by:


    COORDINATES

    Balanced Balanced
    Station Latitude Departure Y-coord X-coord
    A 10000.00 10000.00
    +255.96 +125.66
    B 10255.96 10125.66
    -153.52 +590.65
    C 10102.44 10716.31
    -694.07 -192.69
    D 9408.37 10523.62
    +202.97 -6.07
    E 9611.34 10517.55
    +388.66 -517.55
    A 10000.00 10000.00
    TOTALS 0.00 0.00

    LINEAR MISCLOSURE

    The hypotenuse of a right triangle whose sides are the misclosure in latitude and the misclosure in departure.


    TRAVERSE PRECISION

  • The precision of a traverse is expressed as the ratio of linear misclosure divided by the traverse perimeter length.
  • expressed in reciprocal form
  • Example