SOLUTIONS
,Table of Contents
1 Introduction
2 Introduction to Measurements
3 Distance Measurement
4 Distance Corrections
5 Electronic Distance Measuring Instruments (EDMs)
6 Introduction to Leveling
7 Differential Leveling
8 Leveling, Continued
9 Angles and Directions
10 Measuring Angle and Directions With Total Stations
11 Miscellaneous Angle Discussion
12 Traverse Adjustment and Area Computation
13 Computer Calculations and Omitted Measurements
14 Topographic Surveying
15 The Global Positioning System (GPS)
16 GPS Field Applications
17 Geographic Information Systems (GIS)
18 GIS, Continued
19 Construction Surveying
20 Volumes
21 Land Surveying or Property Surveying
22 Horizontal Curves
23 Vertical Curves
24 Surveying-the Profession
,Chapter 1 Solutions
1-1. The groma, which was used for laying off right angles, consisted of two cross-arms
fastened together in the shape of a horizontal cross. It had plumb bobs hanging from
each of its four ends and was pivoted on a vertical staff. The groma could be leveled
and sights taken along its cross-arms in line with the plumb bob strings.
1-2. Surveying is the science of determining the dimensions and contour or roughness or
three dimensional characteristics of the earth’s surface by the measurements of
distances, directions and elevations.
1-3. Geomatics is defined as an integrated approach to the measurement, analysis,
management, storage, and presentation of the descriptions and locations of spatial
data. (The term “spatial data” refers to data that can be linked to specific locations in
geographic space.)
1-4. Plane surveys are those for which the curvature of the earth’s surface is neglected
while geodetic surveys are those for which it is taken into account.
1-5. Among the various types of surveys are land, topographic, route, city or municipal,
construction, hydrographic, marine, mine, forestry, geological, photogrammetric, as-
built, and so on.
1-6. A topographic survey is one in which the relief or three-dimensional variations of the
earth’s surface are measured. In addition, man-made and natural objects or features
are located.
1-7. Two types of aerial surveys are photogrammetric surveys and remote sensing.
Photogrammetric surveys are those in which photographs (generally aerial) are used
in conjunction with limited ground surveys. Remote sensing is another type of aerial
survey. It makes use of cameras or sensors which are transported in aircraft or in
artificial satellites.
1-8. Hydrographic surveys pertain to lakes, streams, and other bodies of water. Shorelines
are charted, shapes of areas beneath water surfaces are determined, water flow of
streams is estimated, and other information relative to navigations, flood control, and
development of water resources is obtained. Marine surveys are related to
hydrographic surveys, but they are thought to cover a broader area. They include the
surveying necessary for offshore platforms, the theory of tides, and the preparation of
hydrographic maps and charts.
1-9. Mine surveys are made to obtain the relative positions of underground shafts,
geological formations, and so on. It is obvious that the location of the shafts is
extremely important in relation to property lines. Furthermore their location with
2
, respect to other shafts and various water and soil situations is extremely important
from a safety standpoint.
1-10. Horizontal control surveys involve the establishment of a network of horizontal
measurements between property corners, towers, roads, and other prominent features.
Vertical control surveys consist of the establishment of relatively permanent points
(bench marks) and the determination of their elevations above or below a reference
datum (usually sea level).
1-11. It is extremely important for a surveyor to carry liability insurance for physical injury
to employees, as well as outsiders. Otherwise he or she is risking financial ruin.
Similarly, liability insurance is very important for mistakes that might cause financial
damage to clients. Surveyors who do not carry these types of insurance may be
denied consideration for many industrial jobs.
1-12. Some safety precautions are as follows: conduct regular safety meetings, have first
aid kits on hand, wear conspicuous clothing, wear hard hats and safety shoes when
working on construction projects, use flagmen when working on roads and parking
areas, avoid sighting on the sun through telescopes unless special filters are used,
wear gloves when working in briars or poison ivy, do not throw range poles and other
equipment, and so on.
1-13. Surveying jobs will be obvious from the job description. Jobs related to geoomatics
include work using global positioning systems or as a geographic information
systems analyst, Some land development jobs fall in the realm of geomatics.
3
,Chapter 2 Solutions
2-1. Precision = 0.27/4826.55 = 1/17,876
2-2 Precision = 0.38/6432.81 = 1/16,928
2-3. A probable error or 50% error is the magnitude of an error for which there is a 50% chance
that a particular measurement contains an error of lesser magnitude and a 50% chance that it
contains a larger one.
2-4. When a single quantity is measured several times or when a series of quantities is measured,
random errors will tend to accumulate in proportion to the square root of the number of
measurements. This is referred to as the Law of Compensation.
2-5.
Measured Residual
Values v v2
3.462 0.0008 0.000001
3.467 0.0058 0.000034
3.465 0.0038 0.000014
3.458 -0.0032 0.000010
3.463 0.0018 0.000003
3.457 -0.0042 0.000018
3.468 0.0068 0.000046
3.452 -0.0092 0.000085
3.464 0.0028 0.000008
3.456 -0.0052 0.000027
Avg = 3.4612 Σ v2 = 0.000246
a. Most probable value of the measured quantity
Mean = 3.461
b. Probable error of a single measurement.
E50 = + 0.6745*(0.000246/(10-1))(1/2) = ± 0.0035 ft
c. 90% error.
E90 = + 1.6449*(0.000246/(10-1))(1/2) = ± 0.0086 ft
d. 95% error.
E95 = + 1.9599*(0.000246/(10-1))(1/2) = ± 0.0102 ft
4
,2-6.
2
Measured Values Residual v V
154.70 0.052 0.002756
154.67 0.022 0.000506
154.68 0.032 0.001056
154.69 0.042 0.001806
154.62 -0.028 0.000756
154.66 0.012 0.000156
154.60 -0.048 0.002256
154.74 0.093 0.008556
154.55 -0.097 0.009506
154.58 -0.067 0.004556
154.65 0.002 0.000006
154.63 -0.018 0.000306
2
Avg = 154.648 Σ v = 0.0322
a. Most probable value of the measured quantity
Mean = 154.65
b. Probable error of a single measurement.
E50 = + 0.6745*(0.0322/(12-1))(1/2) = ± 0.04 ft
c. 90% error.
E90 = + 1.6449*(0.0322/(12-1))(1/2) = ± 0.09 ft
d. 95% error.
E95 = + 1.9599*(0.0322/(12-1))(1/2) = ± 0.11 ft
2-7.
a. Most Probable Error = (0.6745)( ±0.21)= ±0.14 ft
b. Error @ 2σ = (2.00)( ±0.21)= ±0.42 ft
Estimated Precision = 0.42/916.45=1/2182
c. Error @ 3σ = (3.00)( ±0.21)= ±0.63 ft
Estimated Precision = 0.63/916.45=1/1454
2-8.
Measured
2
Values Residual v V
736.352 -0.0072 0.000052
736.363 0.0038 0.000014
736.375 0.0158 0.000250
736.324 -0.0352 0.001239
736.358 -0.0012 0.000001
736.383 0.0238 0.000566
2
Avg = 736.3592 Σ v = 0.00212
a. Most probable value of the measured quantity
Mean = 736.359 ft
b. Standard Deviation = ±(0.004/(6-1))1/2 = ±0.0206 ft
c. Error @ 3.29σ = (±0.028 ft)(3.29) = ±0.0678 ft
5
,2-9.
Measured Residual
2
Values v V
201.658 -0.019 0.000342
201.642 -0.035 0.001190
201.660 -0.017 0.000272
201.732 0.055 0.003080
201.649 -0.028 0.000756
201.661 -0.016 0.000240
201.730 0.053 0.002862
201.680 0.004 0.000012
2
Avg = 201.677 Σ v = 0.008756
a. Most probable value of the measured quantity
Mean = 201.677 ft
b. Standard Deviation = ±(0.008756/(8-1))1/2 = ±0.035 ft
c. Error @ 3.29σ = (±0.035 ft)(3.29) = ±0.115 ft
2-10.
Measured Residual
2
Values v V
155.35 -0.09 0.0074
155.42 -0.02 0.0003
155.30 -0.14 0.0186
155.58 0.14 0.0207
155.47 0.03 0.0011
155.32 -0.12 0.0135
155.61 0.17 0.0302
155.44 0.00 0.0000
2
Avg = 155.44 Σ v = 0.0918
a. Most probable value of the measured quantity
Mean = 155.44 ft
b. Standard Deviation = ±(0.0918/(8-1))1/2 = ±0.11 ft
c. Error @ 3.29σ = (±0.11 ft)(3.29) = ±0.36 ft
6
,2-11.
Measured Residual
2
Values v V
613.27 -0.04 0.0012
613.24 -0.07 0.0042
613.34 0.03 0.0012
613.29 -0.02 0.0002
613.43 0.12 0.0156
613.22 -0.09 0.0072
613.39 0.08 0.0072
613.40 0.09 0.0090
613.26 -0.05 0.0020
613.21 -0.10 0.0090
2
Avg = 613.31 Σ v = 0.0570
a. Most probable value of the measured quantity
Mean = 613.31 ft
b. Standard Deviation = ±(0.0570/(12-1))1/2 = ±0.07 ft
c. Error @ 3.29σ = (±0.07 ft)(3.29) = ±0.23 ft
2-12. Etota l= ±0.008*(32)1/2 = ±0.045 ft
2-13. a) Etota l= ±0.007*(24)1/2 = ±0.034 ft
b) Etota l= ±0.004*(24)1/2 = ±0.020 ft
2-14. Etota l= ±0.020*(15.2744)1/2 = ±0.0781 ft
Etota l= ±0.020*(18.1237)1/2 = ±0.0851 ft
E for both sides = [(0.0781)2 + (0.0851)2]1/2 = 0.116 ft
2-15. Etotal = ±0.004*(25)1/2 = ±0.020 ft
2-16. n = # of tape lengths = 1500/30= 50
Etotal= ±0.003*(50)1/2 = ±0.0212 m
2-17. Area = (158.46)*(212.71) = 33,706.03 sq ft
Eproduct= ±[(158.46)2*(0.04)2 + (212.71)2*(0.03)2]1/2 = 8.99 sq ft
Say 9 sq ft
2-18. a) n=22 tape lengths
± E (22)1/2 = ±0.20
E = ±0.04 ft / tape length
b) n=40 tape lengths
± E95 (40)1/2 = ±0.24
E = ±0.0379 = 1.9599*σ = 1.9599*Estandard
Estandard = ±0.0194 ft Say ±0.02 ft
2-19. Eseries = ± E *n1/2
± 1’ = ± E *91/2
E = ± (1/3)’ = 20”
7
,Chapter 3 Solutions
3-1.
a) Pacing (convenient for estimating distances and for checking distances measured by other
methods—very inaccurate.)
b) Odometers (convenient for measuring on smooth surfaces such as pavements and for initial
route location surveys—quite inaccurate.)
c) Stadia (convenient for locating details for maps and for estimating other distances—poor
accuracy.)
d) Subtense bar (convenient for measuring across rough terrain and for relatively short distances
under about 500 ft. Has been made obsolete by the far more accurate and quickly used
EDMs.)
e) Taping (convenient and quite accurate for short distances up to a few hundred feet but tedious
and slow compared to EDMs. May have to make quite a few corrections as for temperature,
slope sag, pull, etc.)
f) Electronic distance measuring instruments (EDMs) (quick and accurate for short and long
distances. May have to make corrections for humidity and slopes.)
3-2.
a) Pacing (estimating distances as for lots and checking distances made by more precise means.)
b) Odometer (measurements of amounts of paving for roads and parking lots. Initial location
surveys and quick checks on other measurements.)
c) Stadia (locating details for maps, making rough surveys and for checking more precise
surveys.)
d) Taping (short distances, accurate work.)
e) EDMs (quick, accurate, long or short distances, difficult terrain.)
3-3. Avg. # of paces = (95+93+97+98+92) / 5 = 95 paces
Avg. pace = = 2.632 ft
Avg. # of paces for unknown dist. = (115+118+116+117) / 4 = 116.5 paces
Dist. Paced = (116.5 paces)(2.632 ft / pace) = 306.63 say 307 ft
3-4. Avg. # of paces = (140+143+141+142) / 4 = 141.5 paces
Avg. pace = .5 = 2.827 ft
# of paces req’d. for 525 ft = .827 = 185.7 say 186 paces
3-5. a) (632.18 m)(3.280840 ft / m) = 2074.08 ft
b) (895.49 m)(3.280840 ft / m) = 2937.96 ft
c) (1254.3 m)(3.280840 ft / m) = 4115.16 ft
3-6. a) 24°19′12″ = 24°19′ + 12′/60 = 24°19.2′ = 24° + 19.2°/60 = 24.32°
b) 59°44′37″ = 59°44′ + 37′/60 = 59°44.616666′ = 59° + 44.616666°/60 = 59.7436°
c) 123°10′09″ = 123°10′ + 9′/60 = 123°10.15′ = 123° + 10.15°/60 = 123.1692°
3-7. a) 99.4871° = 99° + (0.4871)(60′) = 99°29.226′ = 99°29′ + (0.226)(60″) = 99°29′13.6″
b) 51.9534° = 51° + (0.9534)(60′) = 51°57.204′ = 51°57′ + (0.204)(60″) = 51°57′12.2″
c) 148.6736° = 148° + (0.6736)(60′) = 148°40.416′ = 148°40′ + (0.416)(60″) = 148°40′25″
8
, 3-8. Avg. angle reading on the subtense bar =
0°44′20″ + 0°44′18″ + 0°44′21″ + 0°44′19″
4
Avg.= 0°44′20″
Horizontal length of line = cot α / 2 = cot( 0°44′20″ / 2) = cot(0°44.333333′ / 2)
= cot( 0.73888888° / 2) = 155.08 m
3-9. Distance = 83.00 – 0.48 = 82.52 ft
3-10. Cross-sectional area of tape
= (1/40)(5/16) = 0.0078125 sq. in.
Volume of tape in cubic ft.
= (0.)(100) = 0.0054253472222 ft3
Wt. of tape = (0.0054253472222)(490) = 2.66 lb
3-11. Cross-sectional area of tape
= (0.030)(3/8) = 0.01125 sq. in.
Volume of tape in cubic ft.
= (0.)(100) = 0.0078125 ft3
Wt. of tape = (0.0078125)(490) = 3.83 lb
3-12. Changing angle A to decimal form
=26° + (18/60) ° = 26.3°
Cos(26.3°) = 415.77 ft / LAC
LAC = 415..896486430 = 463.78 ft
LBC = [(463.78)2 – (415.77)2] ½ = 205.49 ft
3-13. Sin A = 126..83 = 0.655196963
Angle A = 40°56.075′
9
,Table of Contents
1 Introduction
2 Introduction to Measurements
3 Distance Measurement
4 Distance Corrections
5 Electronic Distance Measuring Instruments (EDMs)
6 Introduction to Leveling
7 Differential Leveling
8 Leveling, Continued
9 Angles and Directions
10 Measuring Angle and Directions With Total Stations
11 Miscellaneous Angle Discussion
12 Traverse Adjustment and Area Computation
13 Computer Calculations and Omitted Measurements
14 Topographic Surveying
15 The Global Positioning System (GPS)
16 GPS Field Applications
17 Geographic Information Systems (GIS)
18 GIS, Continued
19 Construction Surveying
20 Volumes
21 Land Surveying or Property Surveying
22 Horizontal Curves
23 Vertical Curves
24 Surveying-the Profession
,Chapter 1 Solutions
1-1. The groma, which was used for laying off right angles, consisted of two cross-arms
fastened together in the shape of a horizontal cross. It had plumb bobs hanging from
each of its four ends and was pivoted on a vertical staff. The groma could be leveled
and sights taken along its cross-arms in line with the plumb bob strings.
1-2. Surveying is the science of determining the dimensions and contour or roughness or
three dimensional characteristics of the earth’s surface by the measurements of
distances, directions and elevations.
1-3. Geomatics is defined as an integrated approach to the measurement, analysis,
management, storage, and presentation of the descriptions and locations of spatial
data. (The term “spatial data” refers to data that can be linked to specific locations in
geographic space.)
1-4. Plane surveys are those for which the curvature of the earth’s surface is neglected
while geodetic surveys are those for which it is taken into account.
1-5. Among the various types of surveys are land, topographic, route, city or municipal,
construction, hydrographic, marine, mine, forestry, geological, photogrammetric, as-
built, and so on.
1-6. A topographic survey is one in which the relief or three-dimensional variations of the
earth’s surface are measured. In addition, man-made and natural objects or features
are located.
1-7. Two types of aerial surveys are photogrammetric surveys and remote sensing.
Photogrammetric surveys are those in which photographs (generally aerial) are used
in conjunction with limited ground surveys. Remote sensing is another type of aerial
survey. It makes use of cameras or sensors which are transported in aircraft or in
artificial satellites.
1-8. Hydrographic surveys pertain to lakes, streams, and other bodies of water. Shorelines
are charted, shapes of areas beneath water surfaces are determined, water flow of
streams is estimated, and other information relative to navigations, flood control, and
development of water resources is obtained. Marine surveys are related to
hydrographic surveys, but they are thought to cover a broader area. They include the
surveying necessary for offshore platforms, the theory of tides, and the preparation of
hydrographic maps and charts.
1-9. Mine surveys are made to obtain the relative positions of underground shafts,
geological formations, and so on. It is obvious that the location of the shafts is
extremely important in relation to property lines. Furthermore their location with
2
, respect to other shafts and various water and soil situations is extremely important
from a safety standpoint.
1-10. Horizontal control surveys involve the establishment of a network of horizontal
measurements between property corners, towers, roads, and other prominent features.
Vertical control surveys consist of the establishment of relatively permanent points
(bench marks) and the determination of their elevations above or below a reference
datum (usually sea level).
1-11. It is extremely important for a surveyor to carry liability insurance for physical injury
to employees, as well as outsiders. Otherwise he or she is risking financial ruin.
Similarly, liability insurance is very important for mistakes that might cause financial
damage to clients. Surveyors who do not carry these types of insurance may be
denied consideration for many industrial jobs.
1-12. Some safety precautions are as follows: conduct regular safety meetings, have first
aid kits on hand, wear conspicuous clothing, wear hard hats and safety shoes when
working on construction projects, use flagmen when working on roads and parking
areas, avoid sighting on the sun through telescopes unless special filters are used,
wear gloves when working in briars or poison ivy, do not throw range poles and other
equipment, and so on.
1-13. Surveying jobs will be obvious from the job description. Jobs related to geoomatics
include work using global positioning systems or as a geographic information
systems analyst, Some land development jobs fall in the realm of geomatics.
3
,Chapter 2 Solutions
2-1. Precision = 0.27/4826.55 = 1/17,876
2-2 Precision = 0.38/6432.81 = 1/16,928
2-3. A probable error or 50% error is the magnitude of an error for which there is a 50% chance
that a particular measurement contains an error of lesser magnitude and a 50% chance that it
contains a larger one.
2-4. When a single quantity is measured several times or when a series of quantities is measured,
random errors will tend to accumulate in proportion to the square root of the number of
measurements. This is referred to as the Law of Compensation.
2-5.
Measured Residual
Values v v2
3.462 0.0008 0.000001
3.467 0.0058 0.000034
3.465 0.0038 0.000014
3.458 -0.0032 0.000010
3.463 0.0018 0.000003
3.457 -0.0042 0.000018
3.468 0.0068 0.000046
3.452 -0.0092 0.000085
3.464 0.0028 0.000008
3.456 -0.0052 0.000027
Avg = 3.4612 Σ v2 = 0.000246
a. Most probable value of the measured quantity
Mean = 3.461
b. Probable error of a single measurement.
E50 = + 0.6745*(0.000246/(10-1))(1/2) = ± 0.0035 ft
c. 90% error.
E90 = + 1.6449*(0.000246/(10-1))(1/2) = ± 0.0086 ft
d. 95% error.
E95 = + 1.9599*(0.000246/(10-1))(1/2) = ± 0.0102 ft
4
,2-6.
2
Measured Values Residual v V
154.70 0.052 0.002756
154.67 0.022 0.000506
154.68 0.032 0.001056
154.69 0.042 0.001806
154.62 -0.028 0.000756
154.66 0.012 0.000156
154.60 -0.048 0.002256
154.74 0.093 0.008556
154.55 -0.097 0.009506
154.58 -0.067 0.004556
154.65 0.002 0.000006
154.63 -0.018 0.000306
2
Avg = 154.648 Σ v = 0.0322
a. Most probable value of the measured quantity
Mean = 154.65
b. Probable error of a single measurement.
E50 = + 0.6745*(0.0322/(12-1))(1/2) = ± 0.04 ft
c. 90% error.
E90 = + 1.6449*(0.0322/(12-1))(1/2) = ± 0.09 ft
d. 95% error.
E95 = + 1.9599*(0.0322/(12-1))(1/2) = ± 0.11 ft
2-7.
a. Most Probable Error = (0.6745)( ±0.21)= ±0.14 ft
b. Error @ 2σ = (2.00)( ±0.21)= ±0.42 ft
Estimated Precision = 0.42/916.45=1/2182
c. Error @ 3σ = (3.00)( ±0.21)= ±0.63 ft
Estimated Precision = 0.63/916.45=1/1454
2-8.
Measured
2
Values Residual v V
736.352 -0.0072 0.000052
736.363 0.0038 0.000014
736.375 0.0158 0.000250
736.324 -0.0352 0.001239
736.358 -0.0012 0.000001
736.383 0.0238 0.000566
2
Avg = 736.3592 Σ v = 0.00212
a. Most probable value of the measured quantity
Mean = 736.359 ft
b. Standard Deviation = ±(0.004/(6-1))1/2 = ±0.0206 ft
c. Error @ 3.29σ = (±0.028 ft)(3.29) = ±0.0678 ft
5
,2-9.
Measured Residual
2
Values v V
201.658 -0.019 0.000342
201.642 -0.035 0.001190
201.660 -0.017 0.000272
201.732 0.055 0.003080
201.649 -0.028 0.000756
201.661 -0.016 0.000240
201.730 0.053 0.002862
201.680 0.004 0.000012
2
Avg = 201.677 Σ v = 0.008756
a. Most probable value of the measured quantity
Mean = 201.677 ft
b. Standard Deviation = ±(0.008756/(8-1))1/2 = ±0.035 ft
c. Error @ 3.29σ = (±0.035 ft)(3.29) = ±0.115 ft
2-10.
Measured Residual
2
Values v V
155.35 -0.09 0.0074
155.42 -0.02 0.0003
155.30 -0.14 0.0186
155.58 0.14 0.0207
155.47 0.03 0.0011
155.32 -0.12 0.0135
155.61 0.17 0.0302
155.44 0.00 0.0000
2
Avg = 155.44 Σ v = 0.0918
a. Most probable value of the measured quantity
Mean = 155.44 ft
b. Standard Deviation = ±(0.0918/(8-1))1/2 = ±0.11 ft
c. Error @ 3.29σ = (±0.11 ft)(3.29) = ±0.36 ft
6
,2-11.
Measured Residual
2
Values v V
613.27 -0.04 0.0012
613.24 -0.07 0.0042
613.34 0.03 0.0012
613.29 -0.02 0.0002
613.43 0.12 0.0156
613.22 -0.09 0.0072
613.39 0.08 0.0072
613.40 0.09 0.0090
613.26 -0.05 0.0020
613.21 -0.10 0.0090
2
Avg = 613.31 Σ v = 0.0570
a. Most probable value of the measured quantity
Mean = 613.31 ft
b. Standard Deviation = ±(0.0570/(12-1))1/2 = ±0.07 ft
c. Error @ 3.29σ = (±0.07 ft)(3.29) = ±0.23 ft
2-12. Etota l= ±0.008*(32)1/2 = ±0.045 ft
2-13. a) Etota l= ±0.007*(24)1/2 = ±0.034 ft
b) Etota l= ±0.004*(24)1/2 = ±0.020 ft
2-14. Etota l= ±0.020*(15.2744)1/2 = ±0.0781 ft
Etota l= ±0.020*(18.1237)1/2 = ±0.0851 ft
E for both sides = [(0.0781)2 + (0.0851)2]1/2 = 0.116 ft
2-15. Etotal = ±0.004*(25)1/2 = ±0.020 ft
2-16. n = # of tape lengths = 1500/30= 50
Etotal= ±0.003*(50)1/2 = ±0.0212 m
2-17. Area = (158.46)*(212.71) = 33,706.03 sq ft
Eproduct= ±[(158.46)2*(0.04)2 + (212.71)2*(0.03)2]1/2 = 8.99 sq ft
Say 9 sq ft
2-18. a) n=22 tape lengths
± E (22)1/2 = ±0.20
E = ±0.04 ft / tape length
b) n=40 tape lengths
± E95 (40)1/2 = ±0.24
E = ±0.0379 = 1.9599*σ = 1.9599*Estandard
Estandard = ±0.0194 ft Say ±0.02 ft
2-19. Eseries = ± E *n1/2
± 1’ = ± E *91/2
E = ± (1/3)’ = 20”
7
,Chapter 3 Solutions
3-1.
a) Pacing (convenient for estimating distances and for checking distances measured by other
methods—very inaccurate.)
b) Odometers (convenient for measuring on smooth surfaces such as pavements and for initial
route location surveys—quite inaccurate.)
c) Stadia (convenient for locating details for maps and for estimating other distances—poor
accuracy.)
d) Subtense bar (convenient for measuring across rough terrain and for relatively short distances
under about 500 ft. Has been made obsolete by the far more accurate and quickly used
EDMs.)
e) Taping (convenient and quite accurate for short distances up to a few hundred feet but tedious
and slow compared to EDMs. May have to make quite a few corrections as for temperature,
slope sag, pull, etc.)
f) Electronic distance measuring instruments (EDMs) (quick and accurate for short and long
distances. May have to make corrections for humidity and slopes.)
3-2.
a) Pacing (estimating distances as for lots and checking distances made by more precise means.)
b) Odometer (measurements of amounts of paving for roads and parking lots. Initial location
surveys and quick checks on other measurements.)
c) Stadia (locating details for maps, making rough surveys and for checking more precise
surveys.)
d) Taping (short distances, accurate work.)
e) EDMs (quick, accurate, long or short distances, difficult terrain.)
3-3. Avg. # of paces = (95+93+97+98+92) / 5 = 95 paces
Avg. pace = = 2.632 ft
Avg. # of paces for unknown dist. = (115+118+116+117) / 4 = 116.5 paces
Dist. Paced = (116.5 paces)(2.632 ft / pace) = 306.63 say 307 ft
3-4. Avg. # of paces = (140+143+141+142) / 4 = 141.5 paces
Avg. pace = .5 = 2.827 ft
# of paces req’d. for 525 ft = .827 = 185.7 say 186 paces
3-5. a) (632.18 m)(3.280840 ft / m) = 2074.08 ft
b) (895.49 m)(3.280840 ft / m) = 2937.96 ft
c) (1254.3 m)(3.280840 ft / m) = 4115.16 ft
3-6. a) 24°19′12″ = 24°19′ + 12′/60 = 24°19.2′ = 24° + 19.2°/60 = 24.32°
b) 59°44′37″ = 59°44′ + 37′/60 = 59°44.616666′ = 59° + 44.616666°/60 = 59.7436°
c) 123°10′09″ = 123°10′ + 9′/60 = 123°10.15′ = 123° + 10.15°/60 = 123.1692°
3-7. a) 99.4871° = 99° + (0.4871)(60′) = 99°29.226′ = 99°29′ + (0.226)(60″) = 99°29′13.6″
b) 51.9534° = 51° + (0.9534)(60′) = 51°57.204′ = 51°57′ + (0.204)(60″) = 51°57′12.2″
c) 148.6736° = 148° + (0.6736)(60′) = 148°40.416′ = 148°40′ + (0.416)(60″) = 148°40′25″
8
, 3-8. Avg. angle reading on the subtense bar =
0°44′20″ + 0°44′18″ + 0°44′21″ + 0°44′19″
4
Avg.= 0°44′20″
Horizontal length of line = cot α / 2 = cot( 0°44′20″ / 2) = cot(0°44.333333′ / 2)
= cot( 0.73888888° / 2) = 155.08 m
3-9. Distance = 83.00 – 0.48 = 82.52 ft
3-10. Cross-sectional area of tape
= (1/40)(5/16) = 0.0078125 sq. in.
Volume of tape in cubic ft.
= (0.)(100) = 0.0054253472222 ft3
Wt. of tape = (0.0054253472222)(490) = 2.66 lb
3-11. Cross-sectional area of tape
= (0.030)(3/8) = 0.01125 sq. in.
Volume of tape in cubic ft.
= (0.)(100) = 0.0078125 ft3
Wt. of tape = (0.0078125)(490) = 3.83 lb
3-12. Changing angle A to decimal form
=26° + (18/60) ° = 26.3°
Cos(26.3°) = 415.77 ft / LAC
LAC = 415..896486430 = 463.78 ft
LBC = [(463.78)2 – (415.77)2] ½ = 205.49 ft
3-13. Sin A = 126..83 = 0.655196963
Angle A = 40°56.075′
9
