Latitudes and Departures

Latitude (ΔY) = distance(H) cos α Departure (ΔX) = distance(H) cos α Latitude : is the north /south rectangular components of the line(ΔN). Departure : is the east /west rectangular components of the line(ΔE).

Compass Rule – distributes the errors in lat/dep. C lat AB= Σ lat AB P C dep AB = Σ dep AB The sign of correction is opposite from that of the error

Example 1 A four-sided closed traverse has the following angles. The lengths of the sided are as follows: AB= 636.45 m BC= 654.45 m CD= 382.65 m DA= 469.38 m The bearing of AB is S17o 17/ W BC is in the NE quadrant

Example 1 a) Balance the field angles b) Compute the bearings or Azimuths c) Compute the latitudes and departures d)Determine the linear error of closure and the accuracy ratio. e) Balance the latitudes and Departures by use of the compass rule. f) Compute the coordinates of stations A,C,and D if the coordinates of station B are 1000.00 N ,1000.00 E.

Example 2 The two frontage corners of a large land were joined by the following traverse: Compute the distance and bearing of the property frontage AD.

Homework4 1) A four-sided closed traverse has the following angles. The lengths of the sided are as follows: AB=713.93 m BC= 606.06 m CD= 391.27 m DA= 781.18 m The bearing of AB is S17o 17/ W BC is in the NE quadrant

a) Balance the field angles b) Compute the bearings or Azimuths c) Compute the latitudes and departures d)Determine the linear error of closure and the accuracy ratio.

Homework4 2) Figure 1 shows the field data for a five-sided closed traverse. If the bearing of line A-B is N 51° 22/ 00// E and the coordinates of station A are (1000.000 mN, 1000.000 mE), compute the coordinates of the remaining stations. Distance AB=401.58m, BC=382.20m,CD=368.28m, DE=579.03m and EA= 350.10m.