Assignment 2023 Solution updated

Adjusted elevations: /2 Correct number of readings /2 Correct adjustment 𝑁????? ?? ???????? ?? ?? ???????? = 12 𝐴????????? = ??????? ????? / 𝑁????? ?? ???????? ?? ?? ???????? = 0.170 / 12 = 0.014 /2 Explanation for how the error was adjusted Because the final BM1 value was higher than the first, the adjustment will be subracted to each elevation equally. /0.5 Correct values in the table (0.5 x 52) /2 No adjustment on the first benchmark reading /2 The adjustment is cumulative If calculations are done on Excel (with no rounding): Table 2: Adjusted elevations Location Elevation Adjustments Adjusted Elevations BM1 100.000 0.000 100.000 TP1 96.940 0.014 96.926 TP2 94.340 0.028 94.312 TP3 90.700 0.043 90.658 TP4 88.860 0.057 88.803 TP5 85.410 0.071 85.339 TP6 88.035 0.085 87.950 TP7 90.505 0.099 90.406 TP8 91.110 0.113 90.997 TP9 93.990 0.128 93.863 TP10 96.690 0.142 96.548 TP11 99.970 0.156 99.814 BM1 100.170 0.170 100.000 If calculations are done by hand (with rounding): Table 3: Adjusted elevations Location Elevation Adjustments Adjusted Elevations BM1 100.000 0.000 100.000 TP1 96.940 0.014 96.926 TP2 94.340 0.028 94.312 TP3 90.700 0.042 90.658 TP4 88.860 0.056 88.804 TP5 85.410 0.070 85.340 TP6 88.035 0.085 87.950 TP7 90.505 0.099 90.406 TP8 91.110 0.113 90.997 TP9 93.990 0.127 93.863 TP10 96.690 0.141 96.549 TP11 99.970 0.155 99.815 BM1 100.170 0.170 100.000 /2 Ensured that the loop was balanced

𝑇ℎ????????? ??? ?? ???????? ?????? = (? − 2) × 180° = (6 − 2) × 180° = 720° Latitudes and departures: (22.5 points) /0.5 Correct values in the table (0.5 x 35) /2 All values are given to three decimal places /0.25 Latitude and departure values are in the right column (0.25 x 12) Table 3: Latitudes and departures Side Bearing Length (m) Latitude (m) Departure (m) North (+) South (-) East (+) West (-) AB S 44°36’ W 112.700 80.245 79.133 BC S 11°05’ E 149.062 146.282 28.655 CD N 82°22’ E 145.085 19.272 143.799 DE N 34°55’ E 149.415 122.518 85.523 EF N 22°24’ W 121.592 112.417 46.335 FA S 80°16’ W 134.451 22.731 132.516 Σ = 812.305 254.208 249.258 257.977 257.983 Error of latitudes and departures: (6 points) /2 Latitude error (one point for the formula, one for the number) /2 Departure error (one point for the formula, one for the number) /2 Total error (one point for the formula, one for the number) ? 𝑙𝑎?𝑖???? = |∑ 𝐿??????? 𝑁 − ∑ 𝐿??????? 𝑆 | = |254.208 − 249.258| = 4.950 ? ??𝑝𝑎𝑟??𝑟? = |∑ ????????? 𝐸 − ∑ ????????? 𝑊 | = |257.977 − 257.983| = −0.006 ????? = √? 𝑙𝑎?𝑖???? 2 + ? ??𝑝𝑎𝑟??𝑟? 2 = √4.950 2 + (−0.006) 2 = 4.950 PART E: (63 points) Accuracy ratio: (2 points) /2 Accuracy ratio (one point for the formula, one for the number) 𝐴??????𝑦 ????? = ????? ∑ 𝐿????ℎ = 4.950 812.305 = 0.006 Adjustment using the compass rule: (31 points)