Question

Differential leveling between BMs AA, BB, CC, DD, and AA gives elevation differences (in meters) of -15.242, +32.068, +37.824, and -54.635, and distances in kmkm of 2.0, 3.0, 1.0, and 4.0, respectively. The elevation of AA is 634.597.

Part A

Compute the adjusted elevations of BMs BB, CC, and DD.

Express your answers in meters to six significant figures. Enter your answers separated by commas.

Answer 1

Hi,

Solution as follows:

Elevation of a Stations = Elevation of Previous station + elevation difference

Accordingly Given readings are reproduced in tabular form below. Their respected elevations are also calculated:

Station	Elevation difference (meter)	Distance (km)	Elevation (meter)	Remarks
BMAA			634.597	Given
BMBB	-15.242	2	619.355	634.597 - 15.242
BMCC	32.068	3	651.423	619.355 + 32.068
BMDD	37.824	1	689.247	651.423 + 37.824
BMAA	-54.635	4	634.612	689.247 - 54.635
Sum	0.015	10

1. Error in measurements:

Since this is a closed loop survey, sum of elevation differences must be zero. Any remainder is error or misclosure.

In level surveys, it is observed that the error in a reading is directly proportional to distance between stations. Accordingly we will calculate the correction for each elevation based on below formula:

Correction=-1×total error×distance between stationsTotal Distance

Accordingly results are furnished below:

Station	Elevation difference (meter)	Distance (km)	Correction (meter)	Adjusted Elevation difference (meter)	Adjusted Elevation (meter)
BMAA					634.597000
BMBB	-15.242	2	-0.003000	-15.245000	619.352000
BMCC	32.068	3	-0.004500	32.063500	651.415500
BMDD	37.824	1	-0.001500	37.822500	689.238000
BMAA	-54.635	4	-0.006000	-54.641000	634.597000
Sum	0.015	10	-0.015000	0.000000

Hence the answers are: 619.352000, 651.415500, 689.238000

Hope the solution provided above is clear. In case of any clarifications, please leave comment in comments section.

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