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AERIAL PHOTOSDesign Engineering SoftwareGeodetic DatumSolving spherical trianglesTRAVERSE CALCULATIONS

TRAVERSE CALCULATIONS- PROCEDURE

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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:
      Make larger corrections where mistakes were most likely
      Apply an average correction to each angle
      Or a combination
  • 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

    

    

    StationBearingLengthLatitudeDeparture
    

    A
    

    N 26° 10'E285.10+255.88+125.72
    

    B
    

    S 75° 25'E610.45-153.70+590.78
    

    C
    

    S 15° 30'W720.48-694.28-192.54
    

    D
    

    N 1° 42'W203.00+202.91-6.02
    

    E
    

    N 53° 06'W647.02+388.48-517.41
    

    A
    

    MISCLOSURE-0.71+0.53

    CALCULATION OF LATITUDES AND DEPARTURES

    Using azimuths

    

    

    StationAzimuthLengthLatitudeDeparture
    

    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

    

    

    StationAzimuthLengthLatitudeDeparture
    

    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
    

    TOTALS2466.05-0.71+0.53

    ADJUSTMENT OF LATITUDES AND DEPARTURES

    

    

    BalancedBalanced
    

    StationLatitudeDepartureLatitudeDeparture
    

    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+0.530.000.00

    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

    

    

    BalancedBalanced
    

    StationLatitudeDepartureY-coordX-coord
    

    A10000.0010000.00
    

    +255.96+125.66
    

    B10255.9610125.66
    

    -153.52+590.65
    

    C10102.4410716.31
    

    -694.07-192.69
    

    D9408.3710523.62
    

    +202.97-6.07
    

    E9611.3410517.55
    

    +388.66-517.55
    

    A10000.0010000.00
    

    TOTALS0.000.00

    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
      0.89 / 2466.05 = 0.00036090
      1 / 0.00036090 = 2770.8

      Precision = 1/2771

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