Traversing Chapter 9

Closed Traverse Showing Interior Angles

Open Traverse Showing Deflection Angles Computation of Interior and Exterior Angle at STA 1 + 43.26

Computation of Azimuths

Computation of Bearings

Traverse Computations Chapter 10

Step 1: Check Allowable Angle Misclosure where: c is the allowable misclosure in seconds K is a constant that depends on the level of accuracy specified for the survey n is the number of angles Federal Geodetic Control Subcommittee (FGCS) recommends: First order 1.7” Second-order class I 3” Second-order class II 4.5” Third-order class I 10” Third-order class II 20”

Step 2: Balance interior angles Sum of the interior angles must equal (n-2)180 degrees!

Procedures for Balancing Angles Method 1: Multiple Measurements: Use weighted average based on standard errors of angular measurements. Method 2: Single Measurements: Apply an average correction to each angle where observing conditions were approximately the same at all stations. The correction is computed for each angle by dividing the total angular misclosure by the number of angles. Method 3: Single Measurements: Make larger corrections to angles where poor observing conditions were present. This method is seldom used.

Step 3: Computation of Preliminary Azimuths or Bearings

Step 3: Computation of Preliminary Azimuths or Bearings (continued) Beginning at the reference meridian compute the azimuth or bearing for each leg of the traverse. Always check the last leg of the traverse to make sure that you compute the same azimuth or bearing as the reference meridian.

Step 4: Compute Departures and Latitudes

Step 4: Compute Departures and Latitudes (continued) departure = L sin (bearing) latitude = L cos (bearing)

Step 5: Compute Linear Misclosure Because of errors in the measured angles and distances there will be a linear misclosure of the traverse. Another way of illustrating this is that once you go around the traverse from point A back to point A’ you will notice that the summation of the departures and latitudes do not equal to zero. Hence a linear misclosure is introduced.

Step 5: Compute Linear Misclosure (continued) Linear misclosure = [(departure misclosure)2 + (latitude misclosure)2]1/2

Step 6: Compute Relative Precision relative precision = linear misclosure / traverse length expressed as a number 1 / ? read as 1’ foot error per ? feet measured Example: linear misclosure = 0.08 ft. traverse length = 2466.00 ft. relative precision = 0.08/2466.00 = 1/30,000 Surveyor would expect 1-foot error for every 30,000 feet surveyed

1984 FGCS Horizontal Control Survey Accuracy Standards Order and Class Relative Accuracy Required First Order 1 part in 100,000 Second Order Class I 1 part in 50,000 Class II 1 part in 20,000 Third Order Class I 1 part in 10,000 Class II 1 part in 5,000 From Table 19-3, page 557 in your textbook

Step 7: Adjust Departures and Latitudes Methods: Compass (Bowditch) Rule: correction in departure for AB = - [(total departure misclosure)/(traverse perimeter)](length of AB) correction in latitude for AB = - [(total latitude misclosure)/(traverse perimeter)](length of AB) Adjusts the departures and latitudes of the sides of the traverse in proportion to their lengths. Least Squares Adjustment: Rigorous but best method based on probabilistic approach which models the occurrence of random errors. Angle and distance measurements are adjusted simultaneously. Most computer programs employ a least square adjustment methodology. For more information on Least Squares Method see Chapter 15 in your textbook.

Step 8: Compute Rectangular Coordinates XB = XA + departure AB YB = YA + latitude AB

Step 8: Compute Rectangular Coordinates (continued) Compute the coordinates of all points on the traverse taking into account the signs of the latitudes and departures for each side of the traverse. Be sure to compute the coordinates of the beginning point (in this case A) so you can check to see if you have made any errors in your computations.

Signs of Departures and Latitudes North Departure (-) Latitude (+) Departure (+) Latitude (+) West East Departure (-) Latitude (-) Departure (+) Latitude (-) South

Step 9: Compute Final Adjusted Traverse Lengths and Bearings To compute adjusted bearing AB: tan (bearing) AB = (corrected departure AB)/(corrected latitude AB) To compute adjusted length AB: length AB = [(corrected departure AB)2 + (corrected latitude AB)2]1/2

Coordinate Geometry (COGO) Formulas: tan azimuth (or bearing) AB = departure AB/latitude AB length AB = departure AB/(sin azimuth (or bearing) AB) length AB = latitude AB/(cos azimuth (or bearing) AB) length AB = length AB = [(departure AB)2 + (latitude AB)2]1/2 departure AB = XB – XA = delta X latitude AB = YB – YA = delta Y A Bearing angle delta Y (latitude) B delta X (departure)

Coordinate Geometry (COGO) (continued) More formulas: tan azimuth (or bearing) AB = (XB – XA)/(YB – YA) = (delta x)/(delta y) length AB = (XB – XA)/(sin azimuth (or bearing) AB) length AB = (YB – YA)/(cos azimuth (or bearing) AB) length AB = [(XB – XA )2 + (YB – YA )2]1/2 Length AB = [(delta X)2 + (delta Y)2]1/2 These types of calculations are referred to as “inversing” between two points. i.e. if you know the coordinates of two points you can easily find the bearing between the two points and the distance between the two points by using the above formulas.

Area Computations Chapter 12

Step 10: Compute Area using Coordinate Method areaE’EDD’E’ = YE = E’ – C’ YD = D’ – C’ Each of the areas of trapezoids and triangles can be expressed by multiplying coordinates in a similar manner.

Step 10: Compute Area using Coordinate Method (continued) Double area = +XAYB+XBYc+XcYD+XDYE+XEYA -XBYA –XcYB –XDYC –XEYD -XAYE An easy way to remember how to compute the area using the coordinate method: Be sure to begin and end at the same coordinate. The products are computed along the diagonals with dashed arrows considered plus and solid ones minus. This method computes the DOUBLE AREA so you need to divide the result by 2 to get the area.