Tiêu đề MSTE 31 Solutions.pdf ✅

31 Surveying: Curvature, Refraction, and Stadia Solutions ▣ 1. How wide would a river be if a man 1.8 m tall stands on the other bank of the river and still could see a tower on the opposite bank of the river which is 30.5 m high considering the effect of curvature and refraction? [SOLUTION] hcr = 0.0675k 2 1.8 m = 0.0675k1 2 → k1 = 5.164 km 30 m = 0.0675k2 2 → k2 = 21.0819 km w = k1 + k2 = 26.246 km ▣ 2. Three hills, A, B, and C have elevations 660 m, 625 m, and 600 m, respectively. B is in between A and C and is 10 km from A and 12 km from C. Considering the effect of curvature and refraction, what is the clearance or obstruction of the line of sight at B considering that C is visible from A? [SOLUTION] Consider the vertical distances as the elevations measured based from sightings. Note that the sighting is at A. dA = 660 m dC = 600 m − 0.0675(22) 2 = 567.33 m

For the horizontal distance: HAB = (23.7015 m) cos 15°25′ + (32.2285 m) cos(−09°07′ ) HAB = 54.67 m ▣ 5. Determine the difference in elevation between A and B. [SOLUTION] Since the vertical angle from the instrument to A is positive, it means that the direction is upward while that of B is downward. ElevB = ElevA + MiddleA − VA + VB − MiddleB ElevA − ElevB = −1.175 + (23.7015 m) sin 15°25′ − (32.2285 m) sin(−09°07′ ) + 1.854 ElevA − ElevB = 12.086 m ▣ 6. An engineer’s level uses a level tube with a radius of curvature of 4 m. during observation the bubble is off centered through 4 spaces. What is the error on the observed vertical distance on a station 120 m away if one space on the tube is 0.5 mm long? [SOLUTION] From length of arc: C = Rθ 0.5 mm = (4000 mm)θ θ = 1 8000 Error in the vertical distance: θ = h L 1 8000 = h 120 m → h = 0.15 m ▣ 7. The top of the tower signal at B, 2 km away from A, was sighted through a transit with a recorded vertical angle 3°30′. The height of the mast is 12 m and the height of the transit above the point where it is set is 1.1 m. The elevation of the point under the transit A is 133.33 m. Compute the elevation of the base of the signal B. [SOLUTION]