ENGI 3703 Surveying and Geomatics

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1 Angle Measurement: (Chapter 8) We have provided good coverage of distance measurement with total stations. However, our treatment of angle coverage will be light as this is covered adequately in the field course. You should now be familiar with setting up a total station, its component parts, note taking, horizontal and vertical angle measurement. If you need these concepts reinforced please read sections Some field methods for sighting objects, prolonging a straight line by doubling, balancing in a total station along an establish line, obstruction avoidance through random traversing and trigonometric leveling best practices are presented in These are useful laboratory exercises but will not be demonstrated in this course. Nor will we be concerned with the adjustment of total stations except to say that instruments should be serviced regularly by qualified technicians. The range of adjustments and operator strategies for checking total stations are presented in Instrument Errors Natural Errors Personal Errors 1. Plate Bubble Alignment 1. Wind 1. Instrument over Point 2. H-axis not to V-axis 2. Temperature 2. Bubble not centered 3. Sight not to H-axis 3. Refraction 3. Clamping & Tangent Screws 4. V-angle Index 4. Settlement 4. Parallax 5. Eccentricity 5. Too careful sighting 6. Circle Graduation 6. Rod Placing and Plumbing 7. Peripheral Equipment (optic plumb, tribachs, tripods) Mistakes: Using wrong points, Communicating values, Focus, Leaning on instrument. Lect 10 - Oct 3/07 Slide 1 of 10

2 Traversing: (Chapter 9) You have all now conducted a traverse survey in the field portion of the course. These surveys are a series of consecutive lines whose ends are marked in the field and whose lenghts and directions determined. There are two traverse types: closed and open Closed traverses are allow checks to be made on the angles and distances recorded by either geometric (polygon) closure or mathematical (link) closure. Polygon close is actually both geometrically close. Additional (superfluous) measurements within a closed traverse form networks which allow additional adjustment procedures to be applied. Open traverses do not end at a known point or form a closed geometric loop. Hence they have do means with which to allow for mistake identification or error adjustment. These should be avoided and if used should be double and tripled checked help identify mistakes. Closed traverse Open traverse Read about field methods in traversing (Sections & ) Lect 10 - Oct 3/07 Slide 2 of 10

3 Traversing Error: (Section 9.7 and 9.10) As we have seen in an earlier lecture close traverses allow checking by computing the sum of the interior angles is equal to (n-2)180 where n is the number of polygon sides. This check can be made by reoccupying the starting point of polygon traverse to complete the closed traverse. Like leveling, allowable error depends on the accuracy of error allowed. When setting horizontal control for national networks this error can be quite high. Like the US standard in the text, Canadian standard are similar. The maximum misclosure c is defined as: c = K n where K values are 2, 5, 10, and 20 for 1 s t, 2 end, 3 ed, 4 th Order surveys, respectively and n is the number of angles in the traverse survey. As such a 4th order misclosure error for a 5 sided traverse would be 20 x sqrt(5) = 45. Even in low accuracy surveys misclosure less greater then 03 indicate a mistake is likely. Source of Traverse Error are related to angle and distance measurement we have already discussed. Errors particular to transvering include: 1. Poor Station Selection (short lines, too close to ground, shade to sun, poor slighting on rod) 2. Errors in angle and distance measurement 3. Unequal angle measurement in forward and reverse directions Lect 10 - Oct 3/07 Slide 3 of 10

4 Traversing Computations: (Chapter 10) Closed traverses like closed level loops offer a opportunity to check ones work and make adjustments because extra measurements have been make to form a loop. Advanced least squares methods exist to incorporate additional network adjustments. For now, we will concentrate on simple but effective methods and will explore least squares method timepermitting in the course. Adjustment steps include: 1. Balance Interior Angles 2. Determine Azimuths (preliminary) 3. Calculate latitudes and departures and adjust misclosure 4. Compute rectangular coordinates (x,y) 5. Calculate new length and azimuths coodinates Example Traverse B C 080 o o A 101 o o D 092 o E Lect 10 - Oct 3/07 Slide 4 of 10

5 Balancing Angles: (Section 10.2) Misclosure errors must be distributed over the interior angles of the traverse by: 1. Dividing the total error by the number of angle and appling the same error to each interior angle. 2. Making larger corrections for poor setup locations such as areas where tripod might settle (boggy spot), or instrument step up was difficult. Five Sided Example Station Field Interior Angle A 101 o B 149 o C 080 o D 116 o E 092 o sum 538 o =539 o Error = 01 Arbitrary Balance 101 o o o o o o =540 o Balanced Equally Balanced 101 o o o o o o =540 o Balanced Mathematical Closure = (5-2)180 = 540 o Equal Correction angle = 60 /5 = 12 / Lect 10 - Oct 3/07 Slide 5 of 10

6 Calculate Azimuths: (Section 10.3) To calculate latitudes and departures preliminary azimuths are required these azimuths will be adjusted later. Here s a clockwise example where we N51 o E (Given) B 149 o o C A 101 o o D 092 o E Bg AB = N E Az AB = Az BA = B Az BC = Az CB = C = Az CD = Az DC = D = Az DE = Az DE = Az ED = E Az EA = Flip Az CB = A = Az AB = CHECK OK Lect 10 - Oct 3/07 Slide 6 of 10

ENGI 3703 Surveying and Geomatics

ENGI 3703 Surveying and Geomatics Differential Level Errors We discussed the Canadian datum used in leveling and leveling methods and equipment in the field practice. However, there are a number of errors that we should consider in more