978-0134604657 Chapter 4

18 Instructor’s Solution Manual

Elementary Surveying: An Introduction to Geomatics

4 LEVELING THEORY, METHODS, AND EQUIPMENT

4.1 Define the following leveling terms: (a) vertical line, (b) level surface, and (c)

benchmark.

From Section 4.2:

(a) Vertical line: “A line that follows the local direction of gravity as indicated by a

plumb line”

(b) Level surface: “. A curved surface that at every point is perpendicular to the local

plumb line (the direction in which gravity acts).”

(c) Benchmark: “A relatively permanent object, natural or artificial, having a marked

point whose elevation above or below a reference datum is known or assumed.”

*4.2 How far will a horizontal line depart from the Earth’s surface in 1 km? 5 km? 10 km?

4.3 Visit the website of the National Geodetic Survey, and obtain a data sheet description of

4.4 Create plot of the curvature and

refraction correction for sight lines

going from 0 ft to 10,000 ft in 500 ft

1.50

Curvature and Refraction

Correction

4.11 Describe how readings are determined in a digital level when using a bar coded rod.

From Section 4.11: “At the press of a button, the image of bar codes in the telescope’s

and 4.13. The values represent the horizontal distances between the instrument and either the

plus or minus sights. What error results from curvature and refraction?

*4.12 20, 225; 50, 195; 40, 135; 30, 250 ft.

Plus

CR (ft)

Minus

CR (ft)

20

0.00000824

225

0.001043

50

0.0000515

195

0.000783

40

0.00003296

135

0.000375

30

0.00001854

250

0.001288

Sum

0.00011124

0.003489

Combined

−0.003 ft

4.13 20, 70; 25, 60; 20, 55; 15, 60 m.

Plus

CR (mm)

Minus

CR (mm)

20

0.027

70

0.33075

25

0.042188

60

0.243

20

0.027

55

0.204188

15

0.015188

60

0.243

0.111375

1.020938

Combined: –0.91 mm

4.14 What error results if the curvature and refraction correction is neglected in trigonometric

leveling for sights: (a) 3000 ft long (b) 1200 m long (c) 4500 ft long?

1000)2=𝟎.𝟏𝟖 𝐟𝐭

(b) ℎ𝑚=0.0675(1200

1000)2=𝟎.𝟒𝟐 𝐟𝐭

*4.15 The slope distance and zenith angle observed from point P to point Q were 2406.787 m

and 84°13′07″ respectively. The instrument and rod target heights were equal. If the

elevation of point P is 30.245 m, above datum, what is the elevation of point Q?

4.16 The slope distance and zenith angle observed from point X to point Y were 2907.45 ft

and 97°25’36″. The instrument and rod target heights were equal. If the elevation of

point X is 6547.89 ft above datum, what is the elevation of point Y?

4.17 Similar to Problem 4.15, except the slope distance was 1543.853 m, the zenith angle

was 83°44’08″ and the elevation of point P was 1850.567 m above datum.

4.18 In trigonometric leveling from point A to point B, the slope distance and zenith angle

measured at A were 5462.46 ft and 94°08’36″. At B these measurements were 5462.58

ft and 85°51‘47″, respectively. If the instrument and rod target heights were equal,

4.19 Describe how parallax in the viewing system of a level can be detected and removed.

From Section 4.7:

4.20 What is the sensitivity of a level vial with 2-mm divisions for: (a) a radius of 13.75 m

(b) a radius of 10.31 m?

10.31(1000)]206264.8=𝟒𝟎″

*4.21 An observer fails to check the bubble, and it is off two divisions on a 500-ft sight. What

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Elementary Surveying: An Introduction to Geomatics

error in elevation difference results with a 10-sec bubble?

4.22 An observer fails to check the bubble, and it is off two divisions on a 300-m sight. What

error results for a 20-sec bubble?

4.23 Similar to Problem 4.22, except a 30-sec bubble is off three divisions on a 300-ft sight.

4.24 With the bubble centered, a 100-m sight gives a reading of 1.352 m. After moving the

bubble three divisions off center, the reading is 1.396 m. For 2-mm vial divisions, what

is: (a) the vial radius of curvature in meters (b) the angle in seconds subtended by one

division?

4.25 Similar to Problem 4.24, except the sight length was 300 ft, the initial reading was 5.132

ft, and the final reading was 5.176 ft.

4.26 Sunshine on the forward end of a 20″/2 mm level vial bubble draws it off 2 divisions,

giving a plus sight reading of 4.63 ft on a 250-ft sight. Compute the correct reading.

4.27 List in tabular form, for comparison, the advantages and disadvantages of an automatic

*4.28 If a plus sight of 3.54 ft is taken on BM A, elevation 850.48 ft, and a minus sight of 7.84

Instructor’s Solution Manual 23

1.564 m is read on point X, calculate the HI and the elevation of point X.

4.30 Similar to Problem 4.28, except a plus sight of 8.98 ft is taken on BM A, elevation

606.33 ft, and a minus sight of 4.32 ft read on point X.

4.31 Describe the procedure used to test if the level vial is perpendicular to the vertical axis

4.32 A horizontal collimation test is performed on an automatic level following the

procedures described in Section 4.15.5. With the instrument setup at point 1, the rod

reading at A was 5.548 ft, and to B it was 5.126 ft. After moving and leveling the

instrument at point 2, the rod reading to A was 5.540 ft and to B was 5.126 ft. What is

the collimation error of the instrument and the corrected reading to A from point 2?

4.33 The instrument tested in Problem 4.32 was used in a survey immediately before the test

where the observed elevation difference between two benchmarks was +44.65 ft. The

sum of the plus sight distances between the benchmarks was 250 ft and the sum of the

minus sight distances was 490 ft. What is the corrected elevation difference between the

two benchmarks?

point 2. The distance between the points in the test was 100 m.

1.923 1.894 1.100 1.083 0.006 m

2



  

Correct reading at A = 1.083 – 2(0.006) = 1.071 m

4.35 The instrument tested in Problem 4.34 was used in a survey immediately before the test

where the observed elevation difference between two benchmarks was −13.068 m. The

sum of the plus sight distances between the benchmarks was 1540 m and the sum of the

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Elementary Surveying: An Introduction to Geomatics

minus sight distances was 545 m. What is the corrected elevation difference between the

two benchmarks?