Balance the following interior angles (angles-to-the-right) of a five-sided clos

Question

Balance the following interior angles (angles-to-the-right) of a five-sided closed polygon traverse using Method 1 of Section 10.2. If the azimuth of side AB is fixed at 218 degree 59'30", calculate the azimuths of the remaining sides: A = 132 degree 47'04'', B = 108 degree 46'18'', C = 107 degree 19'37" D = 81 degree 50'34'', E = 109 degree 16'18". Also, Convert the azimuths to bearings (Draw a sketch of the figure using a straight edge). Compute the latitudes and departures, linear misclosure, and the relative precision of problem 2. If the lengths of the sides (in feet) are as follows: AB = 202.74: BC = 283.87: CD = 498.37: DE = 320.33: and EA = 380.78. Use the converted bearings of the previous problem for this problem.

Explanation / Answer

Part I: Questions: 1- What are the purposes, as mentioned in the lecture, of establishing a traverse? 2- List the considerations that affect the choice of the locations of traverse stations. 3- When selecting traverse stations locations, why should the lines be as equal as possible?
Gras
N (mag)
A
C
D
E
B
4- What is the best range of each of the interior angles of traverses? Why? 5- In the traverse below, why was point E necessary? Could the traverse be ABCDA?

6- When adjusting measured traverse angles, why aren’t the adjustments made in proportion to angle sizes? 7- What is the criteria that is used to adjust the linear misclosure using Bowditch method? 8- Explain, using an example, how adjustment using the compass rule may distort the direction of a line. 9- Explain the difference between closed and open traverse. Comment on the advisability of using open traverses. 10- What is the allowed linear closing error a function of? Why? 11- Adjustments are given equally to angles in a closed traverse. When would you give unequal adjustments to angles? 12- After you adjust angles and lengths, if you re-compute the lengths of the sides and measure them again onsite “precisely” will the measured and adjusted lengths be the same? Why? 13- If all measurements were correct with the exception of one angle, will that error result in a linear closing error if angles were not adjusted? Use a sketch to explain your answer.

Part II: Closed Traverse Computations 14- What is the theoretical sum of the interior angles of a closed polygon traverse that has a) 6sides b) 8 sides and c) 12 sides? 15- The interior angles in a five sided closed polygon traverse were measured and found to be: A = 139°10”11”, B = 126°17’43”, C = 94°28’30”, D = 71°04’59” and E = 108°58’31”. a) Compute the angular misclosure. b) Will you accept the observations if a 1” theodolite was used? c) Adjust the angles and explain why you adjusted them the way you did. d) For what order and class is this survey? “ specifications will be given in exams”. 16- Given the measured lengths and angles of the counter-clockwise polygon ABCDEA, calculate the adjusted coordinates of the points, assume angles were already adjusted.

Corrections Balance (adjusted) Balanced Coordinates Pt. Line Azimuth Length Departure Latitu de Cdep.ClatDepartures Latitudes E N A 1000.00 1000.00 AB 71° 11’ 164.95 156.13 53.20 0.03 -0.04 +156.16 +53.16 B 1156.16 1053.16 BC 149° 00’ 88.41 45.53 -75.78 0.02 -0.02 +45.55 -75.80 C 1201.71 977.36 CD 224° 18’ 121.69 -84.99 -87.09 0.03 -0.03 -84.96 -87.12 D 1116.75 890.24 DE 291° 13’ 115.89 -108.03 41.94 0.02 -0.03 -108.01 +41.91 E 1008.74 932.15 EA 352° 39’ 68.42 -8.75 67.86 0.11 -0.01 -8.74 +67.85 A 1000.00 1000.00 sum 559.36 -0.11 +0.13 +0.11 -0.13 0.00 0.00 Error = (0.13)2 +(0.11)2 = 0.17m Relative Precision = 0.17 / 559.36 = 1/ 3,290 (to be rounded to 1:3,000 which is less accurate) Three checks:



17- Compute and tabulate for the following closed-polygon clockwise traverse: (a) Azimuths then bearings (reduced azimuths) (b) adjusted angles (c) departures and latitudes (d) linear misclosure (e) relative precision (f) adjust the traverse using the Bowditch (Compass) rule assuming the coordinates of A are 5000.00E and 5000.00N, determine the coordinates of all other points. Perform all checks. (g) the area of the traverse.
Hints for the answer: sum (dep) = 1.23, sum (lat) = 0.38, area = 2,818,400 m2

line length(m) measured angle Adjustment adjusted angle bearing Azimuth
AB 701.82 A = 128°58' N32° 21'E BC 1009.91 B = 138°04' CD 1109.91 C = 110°24' DE 1320.51 D = 125°57' EF 1447.66 E = 85°57' FA 785.74 F = 130°46' sum
Adjustments(corrections) Balanced(Adjusted) Point Coordinatesline PT . Departures L sin(Az) Latitudes L cos(AZ) Departure Departure Latitude Latitude E N
A 5000 5000 AB
B BC
C CD
D DE
E EF
F FA
A Sum



Part III Problem of a missing side A technique applied in two cases: a- One side is totally missing, no length or azimuth measured such as AF in the previous problem. b- Two values are missing in a traverse: two azimuths, two sides, or a length and an azimuth. Assume a closed traverse with no error, apply the two equations of closing error: Ew = E and Nw = N If a side is missing, the closing error between A and F for example is the line AF, notice the direction. Otherwise, establish two equations in two unknowns and solve them.

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