Lecture 11 traverse computations
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The lecture by Dr. Mahmood Arshad covers the methods for adjusting angles in traverse computations, including balancing angles, computing preliminary azimuths, and correcting for misclosure. It also discusses alternative methods for calculations, such as the least-squares method and the application of software for traverse computations. Examples and solutions are provided to illustrate the concepts presented.
Lecture 11 traverse computations
- 1. Traverse Computations Dr. Mahmood Arshad Assistant Professor, Dept. of Mining Engineering, Faculty of Earth Sciences and Engineering, University of Engineering & Technology, Lahore. smarshad@uet.edu.pk Min-E-240 Surveying Lecture 11 – Week 6
- 2. INTRODUCTION Adjusting angles or directions to fixed geometric conditions, Determining preliminary azimuths (or bearings) of the traverse lines, Calculating departures and latitudes and adjusting them for misclosure, Computing rectangular coordinates of the traverse stations, and Calculating the lengths and azimuths (or bearings) of the traverse lines after adjustment.
- 3. BALANCING ANGLES Method 1: Applying an average correction to each angle where observing conditions were approximately the same at all stations. The correction for each angle is found by dividing the total angular misclosure by the number of angles. Method 2: Making larger corrections to angles where poor observing conditions were present. Example 1: For the traverse of Figure (Next Slide), the observed interior angles are given in Table (Next Slide). Compute the adjusted angles using methods 1 and 2.
- 4. Example 10.1 – Method 1
- 5. Example 10.1 – Method 2
- 6. COMPUTATION OF PRELIMINARY AZIMUTHS OR BEARINGS Compute preliminary azimuths for the traverse courses of Figure 10.1, based on a fixed azimuth of 234°17’18” for line AW, a measured angle to the right of 151°52’24” for WAE, and the angle adjustment by method 1
- 7. Solution for Azimuth Problem
- 8. DEPARTURES AND LATITUDES departure = L sin α latitude = L cos α
- 9. DEPARTURE AND LATITUDE CLOSURE CONDITIONS Departure misclosure Latitude misclosure
- 10. TRAVERSE LINEAR MISCLOSURE AND RELATIVE PRECISION
- 11. TRAVERSE ADJUSTMENT Compass (Bowditch) Rule Least-Squares Method
- 13. ALTERNATIVE METHODS FOR MAKING TRAVERSE COMPUTATIONS Balancing Angles by Adjusting Azimuths or Bearings Balancing Departures and Latitudes by Adjusting Coordinates
- 14. Example 10.6 Table 10.5 lists observed angles to the right for the traverse of Figure 9.1(b). The azimuths of lines A-AzMk1 and E- AzMk2 have known values of 139°05’45” and 86°20’47”, respectively. Compute unadjusted azimuths and balance them to obtain geometric closure. Solution on next slide.
- 16. Example 10.7
- 17. Solution
- 18. INVERSING If only departure and latitudes are available.
- 19. COMPUTING FINAL ADJUSTED TRAVERSE LENGTHS AND DIRECTIONS Calculate the lengths and directions with the adjusted coordinates in the last example. Can we calculate the internal angles?
- 21. COORDINATE COMPUTATIONS IN BOUNDARY SURVEYS Compute the length and bearing of property line PQ.
- 22. Solution
- 24. USE OF OPEN TRAVERSES
- 25. STATE PLANE COORDINATE SYSTEMS We’ll study Pakistan’s Coordinate System someday and look in to Survey of Pakistan.
- 26. TRAVERSE COMPUTATIONS USING COMPUTERS We’ll get ourselves introduced with some software as well.