ABSTRACT
Despite great progress in neuroscience, there are still fundamental unanswered questions about the brain, including the origin of subjective experience and consciousness. Some answers might rely on new physical mechanisms. Given that biophotons have been discovered in the brain, it is interesting to explore if neurons use photonic communication in addition to the well-studied electro-chemical signals. Such photonic communication in the brain would require waveguides. Here we review recent work [S. Kumar, K. Boone, J. Tuszynski, P. Barclay, and C. Simon, Scientific Reports 6, 36508 (2016)] suggesting that myelinated axons could serve as photonic waveguides. The light transmission in the myelinated axon was modeled, taking into account its realistic imperfections, and experiments were proposed both in vivo and in vitro to test this hypothesis. Potential implications for quantum biology are discussed.
INTRODUCTION
Over the past decades a substantial number of facts has been discovered in the field of brain research. However, the fundamental question of how neurons, or more specifically all particles involved in the biological processes in the brain, contribute to mental abilities such as consciousness is still unanswered. The true explanation to this question might rely on physical processes other than those that have been discovered so far. One interesting candidate to focus on is biophotons, which might serve as supplementary information carriers in the brain in addition to the well established electro-chemical signals. Biophotons – which are photons ranging from near-IR to near-UV frequency and emitted without any enhancement or excitation– have been observed in many organisms such as bacteria (1), fungi (2), germinating seeds (3), plants (4), animal tissue 1 arXiv:1708.08887v1 [physics.bio-ph] 23 Aug 2017 Are there optical communication channels in the brain? cultures (5), and different parts of the human body (6–9), including the brain (10–15). These biophotons are produced by the decay of electronically excited species which are created chemically during oxidative metabolic processes (16, 17) and can contribute to communication between cells (18). Moreover, several experimental studies show the effects of light on neurons’ and, generally, the brain’s function (19–21). The existence of biophotons and their possible effects on the the brain along with the fact that photons are convenient carriers of information raises the question whether there could be optical communication in the brain. For the sources and detectors of the optical communication process in the brain, mitochondrial respiration (22, 23) or lipid oxidation (24), and centrosomes (25) or chromophores in the mitochondria (26) have been proposed, respectively. It has also been observed that opsins, photoreceptor protein molecules, exist in the brains of birds (27, 28), mammals (29–32), and more general vertebrates (33) and even in other parts of their bodies (34, 35) as well. Another essential element for this optical communication, which is not well established yet, is the existence of physical links to connect all of these spatially separated agents in a selective way. In the dense and (seemingly) disordered environment of the brain, waveguide channels for traveling photons would be the only viable way to achieve the targeted optical communication processes. Mitochondria and microtubules in neurons have been introduced as the candidates for such waveguides (36–39). However, they are not suitable in reality due to their small and inhomogeneous structure for light guidance over proper distances in the brain. Ref. (40) proposed myelinated axons as potential biophoton waveguides in the brain. The proposal is supported by a theoretical model and numerical results taking into account real imperfections. Myelin sheath (formed in the central nervous system by a kind of glia cell called oligodendrocyte) is a lamellar structure surrounding the axon and has a higher refractive index (41) than both the inside of the axon and the interstitial fluid outside (see Fig. 1a) which let the myelin sheath to guide the light inside itself for optical communications. This compact sheath also increases the propagation speed of an action potential (via saltatory conduction) based on its insulating property (42). There has been a few indirect experimental evidence for light conduction by axons (12, 43, 44). Another related and interesting experiment has shown that a certain type of glia cells, known as Muller cells, ¨ guide light in mammalian eyes (45, 46). Ref. (40) also proposed experiments to test the existence of the optical waveguides in the brain. One interesting property of optical communication channels is that they can also transmit quantum information. Quantum effects in biological systems are being studied in different areas such as photosynthesis (47, 48), avian magnetoreception (49, 50), and olfaction (51, 52). There is an increasing number of conjectures about the role of quintessential quantum features such as superposition and entanglement (53) in the brain (15, 38, 54–56). The greatest challenge when considering quantum effects in the brain or any biological system in general is environmentally induced decoherence (57), which leads to the suppression of these quantum phenomena. However, some biological processes can be fast and may show quantum features before they are destroyed by the environment. Moreover, nuclear spins can have coherence times of tens of milliseconds in the brain (58, 59). A recent proposal on “quantum cognition” suggests even longer coherence times of nuclear spins (56), but relies on quantum information transmission via molecule transport, which is very slow. In contrast, photons are the fastest and most robust carriers for quantum information over long distances, which is why currently man-made quantum networks rely on optical communication channels (typically optical fibers) between spins (60, 61).
Results
To show that myelinated axons could serve as the waveguides for traveling biophotons in the brain, Ref. (40) solved the three dimensional electromagnetic field equations numerically in different conditions, using Lumerical’s software packages FDTD (Finite Difference Time Domain) Solutions and MODE Solutions. These software packages solve Maxwell’s equations numerically, allowing the optical properties of dielectric structures defined over a mesh with subwavelength resolution to be simulated. The refractive indices of the fluid outside of the axon, the axon, and the myelin sheath were taken close to 1.34, 1.38 and 1.44 respectively (see Fig. 1a), which are consistent with their typical values (41, 62, 63). These indexes let the myelin sheath guide the light inside itself. The ratio of the radius of the axon, r to the outer radius of the myelin sheath r 0 (g-ratio) is taken equal to 0.6 for the most of the simulations, close to the experimental values (64). In reality, the radius of the myelinated axons in the brain changes from 0.2 microns to close to 10 microns (65). For the purpose of guiding light inside the myelin sheath, Ref. (40) considered the wavelength of the observed biophotons in the brain which is from 200 nm to 1300 nm. Since several proteins in the environment of the axons strongly absorb at wavelengths close to 300nm, a wavelength range of the transmitted light from the shortest permissible wavelength, λmin = 400nm, to the longest one, λmax, was chosen to avoid the absorption and confine the light well in the myelin sheath. λmax is chosen to the upper bound of the observed biophoton wavelength (1300 nm) or the thickness of the myelin sheath (denoted by d), whichever is smaller. Besides λmin and λmax, an intermediate wavelength was considered, denoted by λint , corresponding to the central permissible frequency (mid-frequency of the permissible frequency range) in the simulations. In the following section we discuss the guided modes in the myelinated axons and their transmissions in nodal and paranodal regions and even in the presence of the imperfections such as bends, varying cross-sections, and non-circular cross-sections.
Optical transmission in myelinated axons
Within the neuron, one can identify numerous intra-cellular structures that can function as potential scatterers, i.e. sources of waveguide loss. They are located both inside the axon and outside of the axon. Intra-cellular structures include cell organelles, for example, mitochondria, the endoplasmic reticulum, lipid vesicles, as well as the many filaments of the cytoskeleton, namely microtubules, microfilaments and neurofilaments. Extra-cellular structures include microglia, and astrocytes. However, the electromagnetic modes which are spatially confined within the myelin sheath, should not be affected by the presence of these structures. These biophoton modes considered here would be able to propagate in a biological waveguide provided its dimension is close to or larger than the wavelength of the light. Fig. 1b shows the numerically calculated magnitude of the electric field of a cylindrically symmetric eigenmode of an axon with radius r = 3µm and myelin sheath radius r 0 = 5µm for the wavelength 0.612µm. This electric field is azimuthally polarized as depicted is Fig. 1c and it is similar to the TE01 mode of a conventional fiber (66) which has higher refractive index of the core than that of the cladding. It is important to note that azimuthal polarization would prevent modal dispersion in the birefringent myelin sheath. Importantly, its optical axes are oriented radially (67). It can be readily established that there are hundreds of potential guided modes allowed to exist given the thickness of myelin sheath. Consequently, biophotons that could be generated by a source in the axons (e.g. mitochondria or recombination of reactive oxygen species) could readily interact with these modes as determined by mode-specific coupling coefficients. While we lack detailed knowledge of the particulars for these interactions, for the sake of simplicity and ease of illustration we select a single mode and examine its transmission. It is interesting to analyze transmission in the presence of optical imperfections such as discontinuities, bends and varying cross-sectional diameters. In this connection, we simulated short axonal segments due to computational limitations and extrapolated the results for the full length of an axon.
Transmission in nodal and paranodal regions
A myelinated axon has periodically unmyelinated segments, called Nodes of Ranvier, which are approximatly 1µm long (68) (while the whole axon length varies from 1 mm to the order of a meter). Here, we discuss the transmission in the Ranvier nodes and at the edges of the nodes, the paranodes. The configuration of myelin sheath is special in the paranodal regions (see Fig. 2a). There are many layers making up the compact myelin sheath and at the edge of each node, almost all of the layers are in contact with the core (bared axon) with a small pocket of cytoplasm. That’s because each layer moving from the innermost outward is longer than the one below. However, for thick myelin sheaths, many cytoplasmic pockets cannot reach the surface of the bare axon, but end on inner layers. Thus, the length of paranodal regions is dependent on the thickness of the myelin sheath. We call the ratio of the length of paranode, lparanode, to the thickness of the myelin sheat, d, p-ratio and take its value close to 5 in our simulations based on the realistic values (69). Fig. 2a displays the model of Ref. (40) for two adjacent paranodal regions with the node in between, and Fig. 2b shows the magnitude of the electric field profile in the longitudinal direction (along the length of the axon), EFPL, as a cylindrically symmetric input mode crosses this region. Fig. 2c shows the power transmission in the guided modes as a function of p-ratio for three wavelengths, 0.40 µm, 0.61 µm, and 1.30 µm. For the transmission, there are two main losses: divergence or scattering of the light beam. Shorter wavelengths scatter more but diverge less. Thus, in Fig. 2c, for small p-ratios, shorter wavelengths have higher transmission and as the effect of divergence is dominant in this region and the shorter wavelengths diverge less. However, for the large p-ratios, the effect of scattering is dominant and since the higher wavelengths scatter less, and have a higher transmission. Fig. 2d–f compares the transmission percentage for different axon radii, wavelengths, and p–ratios. Although in Fig. 2d, the behavior of the transmission as a fuction of axon radius is independent of p–ratios for the longest permissible wavelength, it can be concluded that for the most loosely confined modes (λmax) transmission increases in thicker axons. It’s also possible that for long wavelengths, a fraction of the light diverging into the axon comes back into the myelin sheath at the end of the paranodal region and not all the light that diverges is lost. This can be an explanation for not well-defined dependency of the transmission on the paranodal lengths (see Fig. 2d). In, Fig. 2e, and Fig. 2f, for p-ratio = 2.5, based on our intuition from Fig. 2c, the divergence is dominant. Here, the thickness of the axon plays a role in the transmission such that the thicker the axon the divergence is less and the light is transmitted more. However, for larger p–ratios, the scattering is dominant and the light scatters more in thick axons. To summarize, for small p–ratios (∼2.5), the well confined modes (shorter wavelengths) transmit better while for large p–ratios (∼5 or greater), the loosely confined ones (longer wavelengths) transmit better. Thicker axons yield higher transmission for all wavelengths with small p–ratios while it’s inverse only for the shorter wavelengths with large p–ratios. The transmission after several paranodal regions can be roughly estimated by following the intuition of exponentiating the transmission through one (see Supplementary Information of Ref (40))...
Discussion
In this review of Ref. (40) we have discussed how light conduction in a myelinated axon is feasible even in the presence of realistic imperfections in the neuron. We have also described future experiments that could validate or falsify this model of biophoton transmission (40). It is also worth addressing a few related questions. It is of interest to identify possible interaction mechanisms between biophotons and nuclear spins within the framework of quantum communication. Spin chemistry research (87) determined effects whereby electron and nuclear spins affect chemical reactions. These effects can also involve photons. In particular, a class of cryptochrome proteins can be photo-activated resulting in the production of a pair of radicals per event, with correlated electronic spins. This effect has been hypothesized to explain bird magnetoreception (49). It has been recently shown by theoretical considerations that interactions between electron and nuclear spins in cryptochromes are of critical importance to the elucidation of the precision of magnetoreception effects (50). Importantly for this topic, cryptochrome complexes are found in the eyes of mammals and they are also magnetosensitive at the molecular level (88). Therefore, if similar proteins can be found in the inner regions of the human brain, this could provide the required interface between biophotons and nuclear spins. However, for individual quantum communication links to form a larger quantum network with an associated entanglement process involving many distant spins, the nuclear spins interfacing with different axons must interact coherently. This, most likely, requires close enough contact between the interacting spins. The involvement of synaptic junctions between individual axons may provide such a proximity mechanism. We should also address the question of the potential relevance of optical communication between neurons with respect to consciousness and the binding problem. A specific anatomical question that arises is whether brain regions implicated in consciousness (89) (e.g. claustrum (90, 91), the thalamus, hypothalamus and amygdala (92), or the posterior cerebral cortex (89)) have myelinated axons with sufficient diameter to allow light transmission. A major role of the myelin sheath as an optical waveguide could provide a better understanding of the causes of the various diseases associated with it (e.g. multiple sclerosis (93)) and hence lead to a design and implementation of novel therapies for these pathologies. Let us note that, following Ref. (40), we have focused our discussion here on guidance by myelinated axons. However, light guidance by unmyelinated axons is also a possibility, as discussed in more detail in the supplementary information of Ref. (40). Finally, with the advantages optical communication provides in terms of precision and speed, it is indeed a wonder why biological evolution would not fully exploit this modality. On the other hand, if optical communication involving axons is harnessed by the brain, this would reveal a remarkable, hitherto unknown new aspect of the brains functioning, with potential impacts on unraveling fundamental issues of neuroscience.
Source: https://arxiv.org/pdf/1708.08887.pdf
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Table of Contents
1 • INTRODUCTION 1
1.1 Definition of Surveying 1
1.2 Geomatics 3
1.3 History of Surveying 4
1.4 Geodetic and Plane Surveys 9
1.5 Importance of Surveying 10
1.6 Specialized Types of Surveys 11
1.7 Surveying Safety 13
1.8 Land and Geographic Information Systems 14
1.9 Federal Surveying and Mapping Agencies 15
1.10 The Surveying Profession 16
1.11 Professional Surveying Organizations 17
1.12 Surveying on the Internet 18
1.13 Future Challenges in Surveying 19
Problems 20
Bibliography 21
2 • UNITS, SIGNIFICANT FIGURES, AND FIELD NOTES 23
PART I UNITS AND SIGNIFICANT FIGURES 23
2.1 Introduction 23
2.2 Units of Measurement 23
2.3 International System of Units (SI) 25
2.4 Significant Figures 27
2.5 Rounding Off Numbers 29
PART II FIELD NOTES 30
2.6 Field Notes 30
2.7 General Requirements of Handwritten Field Notes 31
2.8 Types of Field Books 32
2.9 Kinds of Notes 33
2.10 Arrangements of Notes 33
2.11 Suggestions for Recording Notes 35
2.12 Introduction to Data Collectors 36
2.13 Transfer of Files from Data Collectors 39
2.14 Digital Data File Management 41
2.15 Advantages and Disadvantages of Data Collectors 42
Problems 43
Bibliography 44
3 • THEORY OF ERRORS IN OBSERVATIONS 45
3.1 Introduction 45
3.2 Direct and Indirect Observations 45
3.3 Errors in Measurements 46
3.4 Mistakes 46
3.5 Sources of Errors in Making Observations 47
3.6 Types of Errors 47
3.7 Precision and Accuracy 48
3.8 Eliminating Mistakes and Systematic Errors 49
3.9 Probability 49
3.10 Most Probable Value 50
3.11 Residuals 51
3.12 Occurrence of Random Errors 51
3.13 General Laws of Probability 55
3.14 Measures of Precision 55
3.15 Interpretation of Standard Deviation 58
3.16 The 50, 90, and 95 Percent Errors 58
3.17 Error Propagation 60
3.18 Applications 65
3.19 Conditional Adjustment of Observations 65
3.20 Weights of Observations 66
3.21 Least-Squares Adjustment 67
3.22 Using Software 68
Problems 69
Bibliography 71
4 • LEVELING–THEORY, METHODS, AND EQUIPMENT 73
PART I LEVELING–THEORY AND METHODS 73
4.1 Introduction 73
4.2 Definitions 73
4.3 North American Vertical Datum 75
4.4 Curvature and Refraction 76
4.5 Methods for Determining Differences in Elevation 78
PART II EQUIPMENT FOR DIFFERENTIAL LEVELING 85
4.6 Categories of Levels 85
4.7 Telescopes 86
4.8 Level Vials 87
4.9 Tilting Levels 89
4.10 Automatic Levels 90
4.11 Digital Levels 91
4.12 Tripods 93
4.13 Hand Level 93
4.14 Level Rods 94
4.15 Testing and Adjusting Levels 96
Problems 100
Bibliography 102
5 • LEVELING–FIELD PROCEDURES AND COMPUTATIONS 103
5.1 Introduction 103
5.2 Carrying and Setting Up a Level 103
5.3 Duties of a Rodperson 105
5.4 Differential Leveling 106
5.5 Precision 112
5.6 Adjustments of Simple Level Circuits 113
5.7 Reciprocal Leveling 114
5.8 Three-Wire Leveling 115
5.9 Profile Leveling 117
5.10 Grid, Cross-Section, or Borrow-Pit Leveling 121
5.11 Use of the Hand Level 122
5.12 Sources of Error in Leveling 122
5.13 Mistakes 124
5.14 Reducing Errors and Eliminating Mistakes 125
5.15 Using Software 125
Problems 127
Bibliography 129
6 • DISTANCE MEASUREMENT 131
PART I METHODS FOR MEASURING DISTANCES 131
6.1 Introduction 131
6.2 Summary of Methods for Making Linear Measurements 131
6.3 Pacing 132
6.4 Odometer Readings 132
6.5 Optical Rangefinders 133
6.6 Tacheometry 133
6.7 Subtense Bar 133
PART II DISTANCE MEASUREMENTS BY TAPING 133
6.8 Introduction to Taping 133
6.9 Taping Equipment and Accessories 134
6.10 Care of Taping Equipment 135
6.11 Taping on Level Ground 136
6.12 Horizontal Measurements on Sloping Ground 138
6.13 Slope Measurements 140
6.14 Sources of Error in Taping 141
6.15 Tape Problems 145
6.16 Combined Corrections in a Taping Problem 147
PART III ELECTRONIC DISTANCE MEASUREMENT 148
6.17 Introduction 148
6.18 Propagation of Electromagnetic Energy 149
6.19 Principles of Electronic Distance Measurement 152
6.20 Electro-Optical Instruments 153
6.21 Total Station Instruments 156
6.22 EDM Instruments Without Reflectors 157
6.23 Computing Horizontal Lengths from Slope Distances 158
6.24 Errors in Electronic Distance Measurement 160
6.25 Using Software 165
Problems 165
Bibliography 168
7 • ANGLES, AZIMUTHS, AND BEARINGS 169
7.1 Introduction 169
7.2 Units of Angle Measurement 169
7.3 Kinds of Horizontal Angles 170
7.4 Direction of a Line 171
7.5 Azimuths 172
7.6 Bearings 173
7.7 Comparison of Azimuths and Bearings 174
7.8 Computing Azimuths 175
7.9 Computing Bearings 177
7.10 The Compass and the Earth’s Magnetic Field 179
7.11 Magnetic Declination 180
7.12 Variations in Magnetic Declination 181
7.13 Software for Determining Magnetic Declination 183
7.14 Local Attraction 184
7.15 Typical Magnetic Declination Problems 185
7.16 Mistakes 187
Problems 187
Bibliography 189
8 • TOTAL STATION INSTRUMENTS; ANGLE OBSERVATIONS 191
PART I TOTAL STATION INSTRUMENTS 191
8.1 Introduction 191
8.2 Characteristics of Total Station Instruments 191
8.3 Functions Performed by Total Station Instruments 194
8.4 Parts of a Total Station Instrument 195
8.5 Handling and Setting Up a Total Station Instrument 199
8.6 Servo-Driven and Remotely Operated Total Station Instruments 201
PART II ANGLE OBSERVATIONS 203
8.7 Relationship of Angles and Distances 203
8.8 Observing Horizontal Angles with Total Station Instruments 204
8.9 Observing Horizontal Angles by the Direction Method 206
8.10 Closing the Horizon 207
8.11 Observing Deflection Angles 209
8.12 Observing Azimuths 211
8.13 Observing Vertical Angles 211
8.14 Sights and Marks 213
8.15 Prolonging a Straight Line 214
8.16 Balancing-In 216
8.17 Random Traverse 217
8.18 Total Stations for Determining Elevation Differences 218
8.19 Adjustment of Total Station Instruments and Their Accessories 219
8.20 Sources of Error in Total Station Work 222
8.21 Propagation of Random Errors in Angle Observations 228
8.22 Mistakes 228
Problems 229
Bibliography 230
9 • TRAVERSING 231
9.1 Introduction 231
9.2 Observation of Traverse Angles or Directions 233
9.3 Observation of Traverse Lengths 234
9.4 Selection of Traverse Stations 235
9.5 Referencing Traverse Stations 235
9.6 Traverse Field Notes 237
9.7 Angle Misclosure 238
9.8 Traversing with Total Station Instruments 239
9.9 Radial Traversing 240
9.10 Sources of Error in Traversing 241
9.11 Mistakes in Traversing 242
Problems 242
10 • TRAVERSE COMPUTATIONS 245
10.1 Introduction 245
10.2 Balancing Angles 246
10.3 Computation of Preliminary Azimuths or Bearings 248
10.4 Departures and Latitudes 249
10.5 Departure and Latitude Closure Conditions 251
10.6 Traverse Linear Misclosure and Relative Precision 251
10.7 Traverse Adjustment 252
10.8 Rectangular Coordinates 255
10.9 Alternative Methods for Making Traverse Computations 256
10.10 Inversing 260
10.11 Computing Final Adjusted Traverse Lengths and Directions 261
10.12 Coordinate Computations in Boundary Surveys 263
10.13 Use of Open Traverses 265
10.14 State Plane Coordinate Systems 268
10.15 Traverse Computations Using Computers 269
10.16 Locating Blunders in Traverse Observations 269
10.17 Mistakes in Traverse Computations 272
Problems 272
Bibliography 275
11 • COORDINATE GEOMETRY IN SURVEYING CALCULATIONS 277
11.1 Introduction 277
11.2 Coordinate Forms of Equations for Lines and Circles 278
11.3 Perpendicular Distance from a Point to a Line 280
11.4 Intersection of Two Lines, Both Having Known Directions 282
11.5 Intersection of a Line with a Circle 284
11.6 Intersection of Two Circles 287
11.7 Three-Point Resection 289
11.8 Two-Dimensional Conformal Coordinate Transformation 292
11.9 Inaccessible Point Problem 297
11.10 Three-Dimensional Two-Point Resection 299
11.11 Software 302
Problems 303
Bibliography 307
12 • AREA 309
12.1 Introduction 309
12.2 Methods of Measuring Area 309
12.3 Area by Division Into Simple Figures 310
12.4 Area by Offsets from Straight Lines 311
12.5 Area by Coordinates 313
12.6 Area by Double-Meridian Distance Method 317
12.7 Area of Parcels with Circular Boundaries 320
12.8 Partitioning of Lands 321
12.9 Area by Measurements from Maps 325
12.10 Software 327
12.11 Sources of Error in Determining Areas 328
12.12 Mistakes in Determining Areas 328
Problems 328
Bibliography 330
13 • GLOBAL NAVIGATION SATELLITE SYSTEMS—INTRODUCTION AND PRINCIPLES OF OPERATION 331
13.1 Introduction 331
13.2 Overview of GPS 332
13.3 The GPS Signal 335
13.4 Reference Coordinate Systems 337
13.5 Fundamentals of Satellite Positioning 345
13.6 Errors in Observations 348
13.7 Differential Positioning 356
13.8 Kinematic Methods 358
13.9 Relative Positioning 359
13.10 Other Satellite Navigation Systems 362
13.11 The Future 364
Problems 365
Bibliography 366
14 • GLOBAL NAVIGATION SATELLITE SYSTEMS—STATIC SURVEYS 367
14.1 Introduction 367
14.2 Field Procedures in Satellite Surveys 369
14.3 Planning Satellite Surveys 372
14.4 Performing Static Surveys 384
14.5 Data Processing and Analysis 386
14.6 Sources of Errors in Satellite Surveys 393
14.7 Mistakes in Satellite Surveys 395
Problems 395
Bibliography 397
15 • GLOBAL NAVIGATION SATELLITE SYSTEMS—KINEMATIC SURVEYS 399
15.1 Introduction 399
15.2 Planning of Kinematic Surveys 400
15.3 Initialization 402
15.4 Equipment Used in Kinematic Surveys 403
15.5 Methods Used in Kinematic Surveys 405
15.6 Performing Post-Processed Kinematic Surveys 408
15.7 Communication in Real-Time Kinematic Surveys 411
15.8 Real-Time Networks 412
15.9 Performing Real-Time Kinematic Surveys 413
15.10 Machine Control 414
15.11 Errors in Kinematic Surveys 418
15.12 Mistakes in Kinematic Surveys 418
Problems 418
Bibliography 419
16 • ADJUSTMENTS BY LEAST SQUARES 421
16.1 Introduction 421
16.2 Fundamental Condition of Least Squares 423
16.3 Least-Squares Adjustment by the Observation Equation Method 424
16.4 Matrix Methods in Least-Squares Adjustment 428
16.5 Matrix Equations for Precisions of Adjusted Quantities 430
16.6 Least-Squares Adjustment of Leveling Circuits 432
16.7 Propagation of Errors 436
16.8 Least-Squares Adjustment of GNSS Baseline Vectors 437
16.9 Least-Squares Adjustment of Conventional Horizontal Plane Surveys 443
16.10 The Error Ellipse 452
16.11 Adjustment Procedures 457
16.12 Other Measures of Precision for Horizontal Stations 458
16.13 Software 460
16.14 Conclusions 460
Problems 461
Bibliography 466
17 • MAPPING SURVEYS 467
17.1 Introduction 467
17.2 Basic Methods for Performing Mapping Surveys 468
17.3 Map Scale 468
17.4 Control for Mapping Surveys 470
17.5 Contours 471
17.6 Characteristics of Contours 474
17.7 Direct and Indirect Methods of Locating Contours 474
17.8 Digital Elevation Models and Automated Contouring Systems 477
17.9 Basic Field Methods for Locating Topographic Details 479
17.10 Three-Dimensional Conformal Coordinate Transformation 488
17.11 Selection of Field Method 489
17.12 Working with Data Collectors and Field-to-Finish Software 490
17.13 Hydrographic Surveys 493
17.14 Sources of Error in Mapping Surveys 497
17.15 Mistakes in Mapping Surveys 498
Problems 498
Bibliography 500
18 • MAPPING 503
18.1 Introduction 503
18.2 Availability of Maps and Related Information 504
18.3 National Mapping Program 505
18.4 Accuracy Standards for Mapping 505
18.5 Manual and Computer-Aided Drafting Procedures 507
18.6 Map Design 508
18.7 Map Layout 510
18.8 Basic Map Plotting Procedures 512
18.9 Contour Interval 514
18.10 Plotting Contours 514
18.11 Lettering 515
18.12 Cartographic Map Elements 516
18.13 Drafting Materials 519
18.14 Automated Mapping and Computer-Aided Drafting Systems 519
18.15 Impacts of Modern Land and Geographic Information Systems on Mapping 525
18.16 Sources of Error in Mapping 526
18.17 Mistakes in Mapping 526
Problems 526
Bibliography 528
19 • CONTROL SURVEYS AND GEODETIC REDUCTIONS 529
19.1 Introduction 529
19.2 The Ellipsoid and Geoid 530
19.3 The Conventional Terrestrial Pole 532
19.4 Geodetic Position and Ellipsoidal Radii of Curvature 534
19.5 Geoid Undulation and Deflection of the Vertical 536
19.6 U.S. Reference Frames 538
19.7 Accuracy Standards and Specifications for Control Surveys 547
19.8 The National Spatial Reference System 550
19.9 Hierarchy of the National Horizontal Control Network 550
19.10 Hierarchy of the National Vertical Control Network 551
19.11 Control Point Descriptions 551
19.12 Field Procedures for Traditional Horizontal Control Surveys 554
19.13 Field Procedures for Vertical Control Surveys 559
19.14 Reduction of Field Observations to Their Geodetic Values 564
19.15 Geodetic Position Computations 577
19.16 The Local Geodetic Coordinate System 580
19.17 Three-Dimensional Coordinate Computations 581
19.18 Software 584
Problems 584
Bibliography 587
20 • STATE PLANE COORDINATES AND OTHER MAP PROJECTIONS 589
20.1 Introduction 589
20.2 Projections Used in State Plane Coordinate Systems 590
20.3 Lambert Conformal Conic Projection 593
20.4 Transverse Mercator Projection 594
20.5 State Plane Coordinates in NAD27 and NAD83 595
20.6 Computing SPCS83 Coordinates in the Lambert Conformal Conic System 596
20.7 Computing SPCS83 Coordinates in the Transverse Mercator System 601
20.8 Reduction of Distances and Angles to State Plane Coordinate Grids 608
20.9 Computing State Plane Coordinates of Traverse Stations 617
20.10 Surveys Extending from One Zone to Another 620
20.11 Conversions Between SPCS27 and SPCS83 621
20.12 The Universal Transverse Mercator Projection 622
20.13 Other Map Projections 623
20.14 Map Projection Software 627
Problems 628
Bibliography 631
21 • BOUNDARY SURVEYS 633
21.1 Introduction 633
21.2 Categories of Land Surveys 634
21.3 Historical Perspectives 635
21.4 Property Description by Metes and Bounds 636
21.5 Property Description by Block-and-Lot System 639
21.6 Property Description by Coordinates 641
21.7 Retracement Surveys 641
21.8 Subdivision Surveys 644
21.9 Partitioning Land 646
21.10 Registration of Title 647
21.11 Adverse Possession and Easements 648
21.12 Condominium Surveys 648
21.13 Geographic and Land Information Systems 655
21.14 Sources of Error in Boundary Surveys 655
21.15 Mistakes 655
Problems 656
Bibliography 658
22 • SURVEYS OF THE PUBLIC LANDS 659
22.1 Introduction 659
22.2 Instructions for Surveys of the Public Lands 660
22.3 Initial Point 663
22.4 Principal Meridian 664
22.5 Baseline 665
22.6 Standard Parallels (Correction Lines) 666
22.7 Guide Meridians 666
22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines 667
22.9 Designation of Townships 668
22.10 Subdivision of a Quadrangle into Townships 668
22.11 Subdivision of a Township into Sections 670
22.12 Subdivision of Sections 671
22.13 Fractional Sections 672
22.14 Notes 672
22.15 Outline of Subdivision Steps 672
22.16 Marking Corners 674
22.17 Witness Corners 674
22.18 Meander Corners 675
22.19 Lost and Obliterated Corners 675
22.20 Accuracy of Public Lands Surveys 678
22.21 Descriptions by Township Section and Smaller Subdivision 678
22.22 BLM Land Information System 679
22.23 Sources of Error 680
22.24 Mistakes 680
Problems 681
Bibliography 683
23 • CONSTRUCTION SURVEYS 685
23.1 Introduction 685
23.2 Specialized Equipment for Construction Surveys 686
23.3 Horizontal and Vertical Control 689
23.4 Staking Out a Pipeline 691
23.5 Staking Pipeline Grades 692
23.6 Staking Out a Building 694
23.7 Staking Out Highways 698
23.8 Other Construction Surveys 703
23.9 Construction Surveys Using Total Station Instruments 704
23.10 Construction Surveys Using GNSS Equipment 706
23.11 Machine Guidance and Control 709
23.12 As-Built Surveys with Laser Scanning 710
23.13 Sources of Error in Construction Surveys 711
23.14 Mistakes 712
Problems 712
Bibliography 714
24 • HORIZONTAL CURVES 715
24.1 Introduction 715
24.2 Degree of Circular Curve 716
24.3 Definitions and Derivation of Circular Curve Formulas 718
24.4 Circular Curve Stationing 720
24.5 General Procedure of Circular Curve Layout by Deflection Angles 721
24.6 Computing Deflection Angles and Chords 723
24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords 725
24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords 726
24.9 Setups on Curve 727
24.10 Metric Circular Curves by Deflection Angles and Incremental Chords 728
24.11 Circular Curve Layout by Deflection Angles and Total Chords 730
24.12 Computation of Coordinates on a Circular Curve 731
24.13 Circular Curve Layout by Coordinates 733
24.14 Curve Stakeout Using GNSS Receivers and Robotic Total Stations 738
24.15 Circular Curve Layout by Offsets 739
24.16 Special Circular Curve Problems 742
24.17 Compound and Reverse Curves 743
24.18 Sight Distance on Horizontal Curves 743
24.19 Spirals 744
24.20 Computation of “As-Built” Circular Alignments 749
24.21 Sources of Error in Laying Out Circular Curves 752
24.22 Mistakes 752
Problems 753
Bibliography 755
25 • VERTICAL CURVES 757
25.1 Introduction 757
25.2 General Equation of a Vertical Parabolic Curve 758
25.3 Equation of an Equal Tangent Vertical Parabolic Curve 759
25.4 High or Low Point on a Vertical Curve 761
25.5 Vertical Curve Computations Using the Tangent Offset Equation 761
25.6 Equal Tangent Property of a Parabola 765
25.7 Curve Computations by Proportion 766
25.8 Staking a Vertical Parabolic Curve 766
25.9 Machine Control in Grading Operations 767
25.10 Computations for an Unequal Tangent Vertical Curve 767
25.11 Designing a Curve to Pass Through a Fixed Point 770
25.12 Sight Distance 771
25.13 Sources of Error in Laying Out Vertical Curves 773
25.14 Mistakes 774
Problems 774
Bibliography 776
26 • VOLUMES 777
26.1 Introduction 777
26.2 Methods of Volume Measurement 777
26.3 The Cross-Section Method 778
26.4 Types of Cross Sections 779
26.5 Average-End-Area Formula 780
26.6 Determining End Areas 781
26.7 Computing Slope Intercepts 784
26.8 Prismoidal Formula 786
26.9 Volume Computations 788
26.10 Unit-Area, or Borrow-Pit, Method 790
26.11 Contour-Area Method 791
26.12 Measuring Volumes of Water Discharge 793
26.13 Software 794
26.14 Sources of Error in Determining Volumes 795
26.15 Mistakes 795
Problems 795
Bibliography 798
27 • PHOTOGRAMMETRY 799
27.1 Introduction 799
27.2 Uses of Photogrammetry 800
27.3 Aerial Cameras 801
27.4 Types of Aerial Photographs 803
27.5 Vertical Aerial Photographs 804
27.6 Scale of a Vertical Photograph 806
27.7 Ground Coordinates from a Single Vertical Photograph 810
27.8 Relief Displacement on a Vertical Photograph 811
27.9 Flying Height of a Vertical Photograph 813
27.10 Stereoscopic Parallax 814
27.11 Stereoscopic Viewing 817
27.12 Stereoscopic Measurement of Parallax 819
27.13 Analytical Photogrammetry 820
27.14 Stereoscopic Plotting Instruments 821
27.15 Orthophotos 826
27.16 Ground Control for Photogrammetry 827
27.17 Flight Planning 828
27.18 Airborne Laser-Mapping Systems 830
27.19 Remote Sensing 831
27.20 Software 837
27.21 Sources of Error in Photogrammetry 838
27.22 Mistakes 838
Problems 839
Bibliography 842
28 • INTRODUCTION TO GEOGRAPHIC INFORMATION SYSTEMS 843
28.1 Introduction 843
28.2 Land Information Systems 846
28.3 GIS Data Sources and Classifications 846
28.4 Spatial Data 846
28.5 Nonspatial Data 852
28.6 Data Format Conversions 853
28.7 Creating GIS Databases 856
28.8 Metadata 862
28.9 GIS Analytical Functions 862
28.10 GIS Applications 867
28.11 Data Sources 867
Problems 869
Bibliography 871
APPENDIX A • DUMPY LEVELS, TRANSITS, AND THEODOLITES 873
APPENDIX B • EXAMPLE NOTEFORMS 888
APPENDIX C • ASTRONOMICAL OBSERVATIONS 895
APPENDIX D • USING THE WORKSHEETS FROM THE COMPANION WEBSITE 911
APPENDIX E • INTRODUCTION TO MATRICES 917
APPENDIX F • U.S. STATE PLANE COORDINATE SYSTEM DEFINING PARAMETERS 923
APPENDIX G • ANSWERS TO SELECTED PROBLEMS 927
INDEX 933
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Solution Manual for Elementary Surveying An Introduction to Geomatics 13th Edition by Ghilani
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Charles D. Ghilani
Hardcover: 984 pages
Publisher: Prentice Hall; 13 edition (January 8, 2011)
Language: English
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Table of Contents
1 • INTRODUCTION 1
1.1 Definition of Surveying 1
1.2 Geomatics 3
1.3 History of Surveying 4
1.4 Geodetic and Plane Surveys 9
1.5 Importance of Surveying 10
1.6 Specialized Types of Surveys 11
1.7 Surveying Safety 13
1.8 Land and Geographic Information Systems 14
1.9 Federal Surveying and Mapping Agencies 15
1.10 The Surveying Profession 16
1.11 Professional Surveying Organizations 17
1.12 Surveying on the Internet 18
1.13 Future Challenges in Surveying 19
Problems 20
Bibliography 21
2 • UNITS, SIGNIFICANT FIGURES, AND FIELD NOTES 23
PART I UNITS AND SIGNIFICANT FIGURES 23
2.1 Introduction 23
2.2 Units of Measurement 23
2.3 International System of Units (SI) 25
2.4 Significant Figures 27
2.5 Rounding Off Numbers 29
PART II FIELD NOTES 30
2.6 Field Notes 30
2.7 General Requirements of Handwritten Field Notes 31
2.8 Types of Field Books 32
2.9 Kinds of Notes 33
2.10 Arrangements of Notes 33
2.11 Suggestions for Recording Notes 35
2.12 Introduction to Data Collectors 36
2.13 Transfer of Files from Data Collectors 39
2.14 Digital Data File Management 41
2.15 Advantages and Disadvantages of Data Collectors 42
Problems 43
Bibliography 44
3 • THEORY OF ERRORS IN OBSERVATIONS 45
3.1 Introduction 45
3.2 Direct and Indirect Observations 45
3.3 Errors in Measurements 46
3.4 Mistakes 46
3.5 Sources of Errors in Making Observations 47
3.6 Types of Errors 47
3.7 Precision and Accuracy 48
3.8 Eliminating Mistakes and Systematic Errors 49
3.9 Probability 49
3.10 Most Probable Value 50
3.11 Residuals 51
3.12 Occurrence of Random Errors 51
3.13 General Laws of Probability 55
3.14 Measures of Precision 55
3.15 Interpretation of Standard Deviation 58
3.16 The 50, 90, and 95 Percent Errors 58
3.17 Error Propagation 60
3.18 Applications 65
3.19 Conditional Adjustment of Observations 65
3.20 Weights of Observations 66
3.21 Least-Squares Adjustment 67
3.22 Using Software 68
Problems 69
Bibliography 71
4 • LEVELING–THEORY, METHODS, AND EQUIPMENT 73
PART I LEVELING–THEORY AND METHODS 73
4.1 Introduction 73
4.2 Definitions 73
4.3 North American Vertical Datum 75
4.4 Curvature and Refraction 76
4.5 Methods for Determining Differences in Elevation 78
PART II EQUIPMENT FOR DIFFERENTIAL LEVELING 85
4.6 Categories of Levels 85
4.7 Telescopes 86
4.8 Level Vials 87
4.9 Tilting Levels 89
4.10 Automatic Levels 90
4.11 Digital Levels 91
4.12 Tripods 93
4.13 Hand Level 93
4.14 Level Rods 94
4.15 Testing and Adjusting Levels 96
Problems 100
Bibliography 102
5 • LEVELING–FIELD PROCEDURES AND COMPUTATIONS 103
5.1 Introduction 103
5.2 Carrying and Setting Up a Level 103
5.3 Duties of a Rodperson 105
5.4 Differential Leveling 106
5.5 Precision 112
5.6 Adjustments of Simple Level Circuits 113
5.7 Reciprocal Leveling 114
5.8 Three-Wire Leveling 115
5.9 Profile Leveling 117
5.10 Grid, Cross-Section, or Borrow-Pit Leveling 121
5.11 Use of the Hand Level 122
5.12 Sources of Error in Leveling 122
5.13 Mistakes 124
5.14 Reducing Errors and Eliminating Mistakes 125
5.15 Using Software 125
Problems 127
Bibliography 129
6 • DISTANCE MEASUREMENT 131
PART I METHODS FOR MEASURING DISTANCES 131
6.1 Introduction 131
6.2 Summary of Methods for Making Linear Measurements 131
6.3 Pacing 132
6.4 Odometer Readings 132
6.5 Optical Rangefinders 133
6.6 Tacheometry 133
6.7 Subtense Bar 133
PART II DISTANCE MEASUREMENTS BY TAPING 133
6.8 Introduction to Taping 133
6.9 Taping Equipment and Accessories 134
6.10 Care of Taping Equipment 135
6.11 Taping on Level Ground 136
6.12 Horizontal Measurements on Sloping Ground 138
6.13 Slope Measurements 140
6.14 Sources of Error in Taping 141
6.15 Tape Problems 145
6.16 Combined Corrections in a Taping Problem 147
PART III ELECTRONIC DISTANCE MEASUREMENT 148
6.17 Introduction 148
6.18 Propagation of Electromagnetic Energy 149
6.19 Principles of Electronic Distance Measurement 152
6.20 Electro-Optical Instruments 153
6.21 Total Station Instruments 156
6.22 EDM Instruments Without Reflectors 157
6.23 Computing Horizontal Lengths from Slope Distances 158
6.24 Errors in Electronic Distance Measurement 160
6.25 Using Software 165
Problems 165
Bibliography 168
7 • ANGLES, AZIMUTHS, AND BEARINGS 169
7.1 Introduction 169
7.2 Units of Angle Measurement 169
7.3 Kinds of Horizontal Angles 170
7.4 Direction of a Line 171
7.5 Azimuths 172
7.6 Bearings 173
7.7 Comparison of Azimuths and Bearings 174
7.8 Computing Azimuths 175
7.9 Computing Bearings 177
7.10 The Compass and the Earth’s Magnetic Field 179
7.11 Magnetic Declination 180
7.12 Variations in Magnetic Declination 181
7.13 Software for Determining Magnetic Declination 183
7.14 Local Attraction 184
7.15 Typical Magnetic Declination Problems 185
7.16 Mistakes 187
Problems 187
Bibliography 189
8 • TOTAL STATION INSTRUMENTS; ANGLE OBSERVATIONS 191
PART I TOTAL STATION INSTRUMENTS 191
8.1 Introduction 191
8.2 Characteristics of Total Station Instruments 191
8.3 Functions Performed by Total Station Instruments 194
8.4 Parts of a Total Station Instrument 195
8.5 Handling and Setting Up a Total Station Instrument 199
8.6 Servo-Driven and Remotely Operated Total Station Instruments 201
PART II ANGLE OBSERVATIONS 203
8.7 Relationship of Angles and Distances 203
8.8 Observing Horizontal Angles with Total Station Instruments 204
8.9 Observing Horizontal Angles by the Direction Method 206
8.10 Closing the Horizon 207
8.11 Observing Deflection Angles 209
8.12 Observing Azimuths 211
8.13 Observing Vertical Angles 211
8.14 Sights and Marks 213
8.15 Prolonging a Straight Line 214
8.16 Balancing-In 216
8.17 Random Traverse 217
8.18 Total Stations for Determining Elevation Differences 218
8.19 Adjustment of Total Station Instruments and Their Accessories 219
8.20 Sources of Error in Total Station Work 222
8.21 Propagation of Random Errors in Angle Observations 228
8.22 Mistakes 228
Problems 229
Bibliography 230
9 • TRAVERSING 231
9.1 Introduction 231
9.2 Observation of Traverse Angles or Directions 233
9.3 Observation of Traverse Lengths 234
9.4 Selection of Traverse Stations 235
9.5 Referencing Traverse Stations 235
9.6 Traverse Field Notes 237
9.7 Angle Misclosure 238
9.8 Traversing with Total Station Instruments 239
9.9 Radial Traversing 240
9.10 Sources of Error in Traversing 241
9.11 Mistakes in Traversing 242
Problems 242
10 • TRAVERSE COMPUTATIONS 245
10.1 Introduction 245
10.2 Balancing Angles 246
10.3 Computation of Preliminary Azimuths or Bearings 248
10.4 Departures and Latitudes 249
10.5 Departure and Latitude Closure Conditions 251
10.6 Traverse Linear Misclosure and Relative Precision 251
10.7 Traverse Adjustment 252
10.8 Rectangular Coordinates 255
10.9 Alternative Methods for Making Traverse Computations 256
10.10 Inversing 260
10.11 Computing Final Adjusted Traverse Lengths and Directions 261
10.12 Coordinate Computations in Boundary Surveys 263
10.13 Use of Open Traverses 265
10.14 State Plane Coordinate Systems 268
10.15 Traverse Computations Using Computers 269
10.16 Locating Blunders in Traverse Observations 269
10.17 Mistakes in Traverse Computations 272
Problems 272
Bibliography 275
11 • COORDINATE GEOMETRY IN SURVEYING CALCULATIONS 277
11.1 Introduction 277
11.2 Coordinate Forms of Equations for Lines and Circles 278
11.3 Perpendicular Distance from a Point to a Line 280
11.4 Intersection of Two Lines, Both Having Known Directions 282
11.5 Intersection of a Line with a Circle 284
11.6 Intersection of Two Circles 287
11.7 Three-Point Resection 289
11.8 Two-Dimensional Conformal Coordinate Transformation 292
11.9 Inaccessible Point Problem 297
11.10 Three-Dimensional Two-Point Resection 299
11.11 Software 302
Problems 303
Bibliography 307
12 • AREA 309
12.1 Introduction 309
12.2 Methods of Measuring Area 309
12.3 Area by Division Into Simple Figures 310
12.4 Area by Offsets from Straight Lines 311
12.5 Area by Coordinates 313
12.6 Area by Double-Meridian Distance Method 317
12.7 Area of Parcels with Circular Boundaries 320
12.8 Partitioning of Lands 321
12.9 Area by Measurements from Maps 325
12.10 Software 327
12.11 Sources of Error in Determining Areas 328
12.12 Mistakes in Determining Areas 328
Problems 328
Bibliography 330
13 • GLOBAL NAVIGATION SATELLITE SYSTEMS—INTRODUCTION AND PRINCIPLES OF OPERATION 331
13.1 Introduction 331
13.2 Overview of GPS 332
13.3 The GPS Signal 335
13.4 Reference Coordinate Systems 337
13.5 Fundamentals of Satellite Positioning 345
13.6 Errors in Observations 348
13.7 Differential Positioning 356
13.8 Kinematic Methods 358
13.9 Relative Positioning 359
13.10 Other Satellite Navigation Systems 362
13.11 The Future 364
Problems 365
Bibliography 366
14 • GLOBAL NAVIGATION SATELLITE SYSTEMS—STATIC SURVEYS 367
14.1 Introduction 367
14.2 Field Procedures in Satellite Surveys 369
14.3 Planning Satellite Surveys 372
14.4 Performing Static Surveys 384
14.5 Data Processing and Analysis 386
14.6 Sources of Errors in Satellite Surveys 393
14.7 Mistakes in Satellite Surveys 395
Problems 395
Bibliography 397
15 • GLOBAL NAVIGATION SATELLITE SYSTEMS—KINEMATIC SURVEYS 399
15.1 Introduction 399
15.2 Planning of Kinematic Surveys 400
15.3 Initialization 402
15.4 Equipment Used in Kinematic Surveys 403
15.5 Methods Used in Kinematic Surveys 405
15.6 Performing Post-Processed Kinematic Surveys 408
15.7 Communication in Real-Time Kinematic Surveys 411
15.8 Real-Time Networks 412
15.9 Performing Real-Time Kinematic Surveys 413
15.10 Machine Control 414
15.11 Errors in Kinematic Surveys 418
15.12 Mistakes in Kinematic Surveys 418
Problems 418
Bibliography 419
16 • ADJUSTMENTS BY LEAST SQUARES 421
16.1 Introduction 421
16.2 Fundamental Condition of Least Squares 423
16.3 Least-Squares Adjustment by the Observation Equation Method 424
16.4 Matrix Methods in Least-Squares Adjustment 428
16.5 Matrix Equations for Precisions of Adjusted Quantities 430
16.6 Least-Squares Adjustment of Leveling Circuits 432
16.7 Propagation of Errors 436
16.8 Least-Squares Adjustment of GNSS Baseline Vectors 437
16.9 Least-Squares Adjustment of Conventional Horizontal Plane Surveys 443
16.10 The Error Ellipse 452
16.11 Adjustment Procedures 457
16.12 Other Measures of Precision for Horizontal Stations 458
16.13 Software 460
16.14 Conclusions 460
Problems 461
Bibliography 466
17 • MAPPING SURVEYS 467
17.1 Introduction 467
17.2 Basic Methods for Performing Mapping Surveys 468
17.3 Map Scale 468
17.4 Control for Mapping Surveys 470
17.5 Contours 471
17.6 Characteristics of Contours 474
17.7 Direct and Indirect Methods of Locating Contours 474
17.8 Digital Elevation Models and Automated Contouring Systems 477
17.9 Basic Field Methods for Locating Topographic Details 479
17.10 Three-Dimensional Conformal Coordinate Transformation 488
17.11 Selection of Field Method 489
17.12 Working with Data Collectors and Field-to-Finish Software 490
17.13 Hydrographic Surveys 493
17.14 Sources of Error in Mapping Surveys 497
17.15 Mistakes in Mapping Surveys 498
Problems 498
Bibliography 500
18 • MAPPING 503
18.1 Introduction 503
18.2 Availability of Maps and Related Information 504
18.3 National Mapping Program 505
18.4 Accuracy Standards for Mapping 505
18.5 Manual and Computer-Aided Drafting Procedures 507
18.6 Map Design 508
18.7 Map Layout 510
18.8 Basic Map Plotting Procedures 512
18.9 Contour Interval 514
18.10 Plotting Contours 514
18.11 Lettering 515
18.12 Cartographic Map Elements 516
18.13 Drafting Materials 519
18.14 Automated Mapping and Computer-Aided Drafting Systems 519
18.15 Impacts of Modern Land and Geographic Information Systems on Mapping 525
18.16 Sources of Error in Mapping 526
18.17 Mistakes in Mapping 526
Problems 526
Bibliography 528
19 • CONTROL SURVEYS AND GEODETIC REDUCTIONS 529
19.1 Introduction 529
19.2 The Ellipsoid and Geoid 530
19.3 The Conventional Terrestrial Pole 532
19.4 Geodetic Position and Ellipsoidal Radii of Curvature 534
19.5 Geoid Undulation and Deflection of the Vertical 536
19.6 U.S. Reference Frames 538
19.7 Accuracy Standards and Specifications for Control Surveys 547
19.8 The National Spatial Reference System 550
19.9 Hierarchy of the National Horizontal Control Network 550
19.10 Hierarchy of the National Vertical Control Network 551
19.11 Control Point Descriptions 551
19.12 Field Procedures for Traditional Horizontal Control Surveys 554
19.13 Field Procedures for Vertical Control Surveys 559
19.14 Reduction of Field Observations to Their Geodetic Values 564
19.15 Geodetic Position Computations 577
19.16 The Local Geodetic Coordinate System 580
19.17 Three-Dimensional Coordinate Computations 581
19.18 Software 584
Problems 584
Bibliography 587
20 • STATE PLANE COORDINATES AND OTHER MAP PROJECTIONS 589
20.1 Introduction 589
20.2 Projections Used in State Plane Coordinate Systems 590
20.3 Lambert Conformal Conic Projection 593
20.4 Transverse Mercator Projection 594
20.5 State Plane Coordinates in NAD27 and NAD83 595
20.6 Computing SPCS83 Coordinates in the Lambert Conformal Conic System 596
20.7 Computing SPCS83 Coordinates in the Transverse Mercator System 601
20.8 Reduction of Distances and Angles to State Plane Coordinate Grids 608
20.9 Computing State Plane Coordinates of Traverse Stations 617
20.10 Surveys Extending from One Zone to Another 620
20.11 Conversions Between SPCS27 and SPCS83 621
20.12 The Universal Transverse Mercator Projection 622
20.13 Other Map Projections 623
20.14 Map Projection Software 627
Problems 628
Bibliography 631
21 • BOUNDARY SURVEYS 633
21.1 Introduction 633
21.2 Categories of Land Surveys 634
21.3 Historical Perspectives 635
21.4 Property Description by Metes and Bounds 636
21.5 Property Description by Block-and-Lot System 639
21.6 Property Description by Coordinates 641
21.7 Retracement Surveys 641
21.8 Subdivision Surveys 644
21.9 Partitioning Land 646
21.10 Registration of Title 647
21.11 Adverse Possession and Easements 648
21.12 Condominium Surveys 648
21.13 Geographic and Land Information Systems 655
21.14 Sources of Error in Boundary Surveys 655
21.15 Mistakes 655
Problems 656
Bibliography 658
22 • SURVEYS OF THE PUBLIC LANDS 659
22.1 Introduction 659
22.2 Instructions for Surveys of the Public Lands 660
22.3 Initial Point 663
22.4 Principal Meridian 664
22.5 Baseline 665
22.6 Standard Parallels (Correction Lines) 666
22.7 Guide Meridians 666
22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines 667
22.9 Designation of Townships 668
22.10 Subdivision of a Quadrangle into Townships 668
22.11 Subdivision of a Township into Sections 670
22.12 Subdivision of Sections 671
22.13 Fractional Sections 672
22.14 Notes 672
22.15 Outline of Subdivision Steps 672
22.16 Marking Corners 674
22.17 Witness Corners 674
22.18 Meander Corners 675
22.19 Lost and Obliterated Corners 675
22.20 Accuracy of Public Lands Surveys 678
22.21 Descriptions by Township Section and Smaller Subdivision 678
22.22 BLM Land Information System 679
22.23 Sources of Error 680
22.24 Mistakes 680
Problems 681
Bibliography 683
23 • CONSTRUCTION SURVEYS 685
23.1 Introduction 685
23.2 Specialized Equipment for Construction Surveys 686
23.3 Horizontal and Vertical Control 689
23.4 Staking Out a Pipeline 691
23.5 Staking Pipeline Grades 692
23.6 Staking Out a Building 694
23.7 Staking Out Highways 698
23.8 Other Construction Surveys 703
23.9 Construction Surveys Using Total Station Instruments 704
23.10 Construction Surveys Using GNSS Equipment 706
23.11 Machine Guidance and Control 709
23.12 As-Built Surveys with Laser Scanning 710
23.13 Sources of Error in Construction Surveys 711
23.14 Mistakes 712
Problems 712
Bibliography 714
24 • HORIZONTAL CURVES 715
24.1 Introduction 715
24.2 Degree of Circular Curve 716
24.3 Definitions and Derivation of Circular Curve Formulas 718
24.4 Circular Curve Stationing 720
24.5 General Procedure of Circular Curve Layout by Deflection Angles 721
24.6 Computing Deflection Angles and Chords 723
24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords 725
24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords 726
24.9 Setups on Curve 727
24.10 Metric Circular Curves by Deflection Angles and Incremental Chords 728
24.11 Circular Curve Layout by Deflection Angles and Total Chords 730
24.12 Computation of Coordinates on a Circular Curve 731
24.13 Circular Curve Layout by Coordinates 733
24.14 Curve Stakeout Using GNSS Receivers and Robotic Total Stations 738
24.15 Circular Curve Layout by Offsets 739
24.16 Special Circular Curve Problems 742
24.17 Compound and Reverse Curves 743
24.18 Sight Distance on Horizontal Curves 743
24.19 Spirals 744
24.20 Computation of “As-Built” Circular Alignments 749
24.21 Sources of Error in Laying Out Circular Curves 752
24.22 Mistakes 752
Problems 753
Bibliography 755
25 • VERTICAL CURVES 757
25.1 Introduction 757
25.2 General Equation of a Vertical Parabolic Curve 758
25.3 Equation of an Equal Tangent Vertical Parabolic Curve 759
25.4 High or Low Point on a Vertical Curve 761
25.5 Vertical Curve Computations Using the Tangent Offset Equation 761
25.6 Equal Tangent Property of a Parabola 765
25.7 Curve Computations by Proportion 766
25.8 Staking a Vertical Parabolic Curve 766
25.9 Machine Control in Grading Operations 767
25.10 Computations for an Unequal Tangent Vertical Curve 767
25.11 Designing a Curve to Pass Through a Fixed Point 770
25.12 Sight Distance 771
25.13 Sources of Error in Laying Out Vertical Curves 773
25.14 Mistakes 774
Problems 774
Bibliography 776
26 • VOLUMES 777
26.1 Introduction 777
26.2 Methods of Volume Measurement 777
26.3 The Cross-Section Method 778
26.4 Types of Cross Sections 779
26.5 Average-End-Area Formula 780
26.6 Determining End Areas 781
26.7 Computing Slope Intercepts 784
26.8 Prismoidal Formula 786
26.9 Volume Computations 788
26.10 Unit-Area, or Borrow-Pit, Method 790
26.11 Contour-Area Method 791
26.12 Measuring Volumes of Water Discharge 793
26.13 Software 794
26.14 Sources of Error in Determining Volumes 795
26.15 Mistakes 795
Problems 795
Bibliography 798
27 • PHOTOGRAMMETRY 799
27.1 Introduction 799
27.2 Uses of Photogrammetry 800
27.3 Aerial Cameras 801
27.4 Types of Aerial Photographs 803
27.5 Vertical Aerial Photographs 804
27.6 Scale of a Vertical Photograph 806
27.7 Ground Coordinates from a Single Vertical Photograph 810
27.8 Relief Displacement on a Vertical Photograph 811
27.9 Flying Height of a Vertical Photograph 813
27.10 Stereoscopic Parallax 814
27.11 Stereoscopic Viewing 817
27.12 Stereoscopic Measurement of Parallax 819
27.13 Analytical Photogrammetry 820
27.14 Stereoscopic Plotting Instruments 821
27.15 Orthophotos 826
27.16 Ground Control for Photogrammetry 827
27.17 Flight Planning 828
27.18 Airborne Laser-Mapping Systems 830
27.19 Remote Sensing 831
27.20 Software 837
27.21 Sources of Error in Photogrammetry 838
27.22 Mistakes 838
Problems 839
Bibliography 842
28 • INTRODUCTION TO GEOGRAPHIC INFORMATION SYSTEMS 843
28.1 Introduction 843
28.2 Land Information Systems 846
28.3 GIS Data Sources and Classifications 846
28.4 Spatial Data 846
28.5 Nonspatial Data 852
28.6 Data Format Conversions 853
28.7 Creating GIS Databases 856
28.8 Metadata 862
28.9 GIS Analytical Functions 862
28.10 GIS Applications 867
28.11 Data Sources 867
Problems 869
Bibliography 871
APPENDIX A • DUMPY LEVELS, TRANSITS, AND THEODOLITES 873
APPENDIX B • EXAMPLE NOTEFORMS 888
APPENDIX C • ASTRONOMICAL OBSERVATIONS 895
APPENDIX D • USING THE WORKSHEETS FROM THE COMPANION WEBSITE 911
APPENDIX E • INTRODUCTION TO MATRICES 917
APPENDIX F • U.S. STATE PLANE COORDINATE SYSTEM DEFINING PARAMETERS 923
APPENDIX G • ANSWERS TO SELECTED PROBLEMS 927
INDEX 933
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Solution Manual for Elementary Surveying: An Introduction to Geomatics, 13th Edition Charles D. Ghilani
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Charles D. Ghilani
Hardcover: 984 pages
Publisher: Prentice Hall; 13 edition (January 8, 2011)
Language: English
ISBN-10: 0132554348
ISBN-13: 978-0132554343
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Table of Contents
1 • INTRODUCTION 1
1.1 Definition of Surveying 1
1.2 Geomatics 3
1.3 History of Surveying 4
1.4 Geodetic and Plane Surveys 9
1.5 Importance of Surveying 10
1.6 Specialized Types of Surveys 11
1.7 Surveying Safety 13
1.8 Land and Geographic Information Systems 14
1.9 Federal Surveying and Mapping Agencies 15
1.10 The Surveying Profession 16
1.11 Professional Surveying Organizations 17
1.12 Surveying on the Internet 18
1.13 Future Challenges in Surveying 19
Problems 20
Bibliography 21
2 • UNITS, SIGNIFICANT FIGURES, AND FIELD NOTES 23
PART I UNITS AND SIGNIFICANT FIGURES 23
2.1 Introduction 23
2.2 Units of Measurement 23
2.3 International System of Units (SI) 25
2.4 Significant Figures 27
2.5 Rounding Off Numbers 29
PART II FIELD NOTES 30
2.6 Field Notes 30
2.7 General Requirements of Handwritten Field Notes 31
2.8 Types of Field Books 32
2.9 Kinds of Notes 33
2.10 Arrangements of Notes 33
2.11 Suggestions for Recording Notes 35
2.12 Introduction to Data Collectors 36
2.13 Transfer of Files from Data Collectors 39
2.14 Digital Data File Management 41
2.15 Advantages and Disadvantages of Data Collectors 42
Problems 43
Bibliography 44
3 • THEORY OF ERRORS IN OBSERVATIONS 45
3.1 Introduction 45
3.2 Direct and Indirect Observations 45
3.3 Errors in Measurements 46
3.4 Mistakes 46
3.5 Sources of Errors in Making Observations 47
3.6 Types of Errors 47
3.7 Precision and Accuracy 48
3.8 Eliminating Mistakes and Systematic Errors 49
3.9 Probability 49
3.10 Most Probable Value 50
3.11 Residuals 51
3.12 Occurrence of Random Errors 51
3.13 General Laws of Probability 55
3.14 Measures of Precision 55
3.15 Interpretation of Standard Deviation 58
3.16 The 50, 90, and 95 Percent Errors 58
3.17 Error Propagation 60
3.18 Applications 65
3.19 Conditional Adjustment of Observations 65
3.20 Weights of Observations 66
3.21 Least-Squares Adjustment 67
3.22 Using Software 68
Problems 69
Bibliography 71
4 • LEVELING–THEORY, METHODS, AND EQUIPMENT 73
PART I LEVELING–THEORY AND METHODS 73
4.1 Introduction 73
4.2 Definitions 73
4.3 North American Vertical Datum 75
4.4 Curvature and Refraction 76
4.5 Methods for Determining Differences in Elevation 78
PART II EQUIPMENT FOR DIFFERENTIAL LEVELING 85
4.6 Categories of Levels 85
4.7 Telescopes 86
4.8 Level Vials 87
4.9 Tilting Levels 89
4.10 Automatic Levels 90
4.11 Digital Levels 91
4.12 Tripods 93
4.13 Hand Level 93
4.14 Level Rods 94
4.15 Testing and Adjusting Levels 96
Problems 100
Bibliography 102
5 • LEVELING–FIELD PROCEDURES AND COMPUTATIONS 103
5.1 Introduction 103
5.2 Carrying and Setting Up a Level 103
5.3 Duties of a Rodperson 105
5.4 Differential Leveling 106
5.5 Precision 112
5.6 Adjustments of Simple Level Circuits 113
5.7 Reciprocal Leveling 114
5.8 Three-Wire Leveling 115
5.9 Profile Leveling 117
5.10 Grid, Cross-Section, or Borrow-Pit Leveling 121
5.11 Use of the Hand Level 122
5.12 Sources of Error in Leveling 122
5.13 Mistakes 124
5.14 Reducing Errors and Eliminating Mistakes 125
5.15 Using Software 125
Problems 127
Bibliography 129
6 • DISTANCE MEASUREMENT 131
PART I METHODS FOR MEASURING DISTANCES 131
6.1 Introduction 131
6.2 Summary of Methods for Making Linear Measurements 131
6.3 Pacing 132
6.4 Odometer Readings 132
6.5 Optical Rangefinders 133
6.6 Tacheometry 133
6.7 Subtense Bar 133
PART II DISTANCE MEASUREMENTS BY TAPING 133
6.8 Introduction to Taping 133
6.9 Taping Equipment and Accessories 134
6.10 Care of Taping Equipment 135
6.11 Taping on Level Ground 136
6.12 Horizontal Measurements on Sloping Ground 138
6.13 Slope Measurements 140
6.14 Sources of Error in Taping 141
6.15 Tape Problems 145
6.16 Combined Corrections in a Taping Problem 147
PART III ELECTRONIC DISTANCE MEASUREMENT 148
6.17 Introduction 148
6.18 Propagation of Electromagnetic Energy 149
6.19 Principles of Electronic Distance Measurement 152
6.20 Electro-Optical Instruments 153
6.21 Total Station Instruments 156
6.22 EDM Instruments Without Reflectors 157
6.23 Computing Horizontal Lengths from Slope Distances 158
6.24 Errors in Electronic Distance Measurement 160
6.25 Using Software 165
Problems 165
Bibliography 168
7 • ANGLES, AZIMUTHS, AND BEARINGS 169
7.1 Introduction 169
7.2 Units of Angle Measurement 169
7.3 Kinds of Horizontal Angles 170
7.4 Direction of a Line 171
7.5 Azimuths 172
7.6 Bearings 173
7.7 Comparison of Azimuths and Bearings 174
7.8 Computing Azimuths 175
7.9 Computing Bearings 177
7.10 The Compass and the Earth’s Magnetic Field 179
7.11 Magnetic Declination 180
7.12 Variations in Magnetic Declination 181
7.13 Software for Determining Magnetic Declination 183
7.14 Local Attraction 184
7.15 Typical Magnetic Declination Problems 185
7.16 Mistakes 187
Problems 187
Bibliography 189
8 • TOTAL STATION INSTRUMENTS; ANGLE OBSERVATIONS 191
PART I TOTAL STATION INSTRUMENTS 191
8.1 Introduction 191
8.2 Characteristics of Total Station Instruments 191
8.3 Functions Performed by Total Station Instruments 194
8.4 Parts of a Total Station Instrument 195
8.5 Handling and Setting Up a Total Station Instrument 199
8.6 Servo-Driven and Remotely Operated Total Station Instruments 201
PART II ANGLE OBSERVATIONS 203
8.7 Relationship of Angles and Distances 203
8.8 Observing Horizontal Angles with Total Station Instruments 204
8.9 Observing Horizontal Angles by the Direction Method 206
8.10 Closing the Horizon 207
8.11 Observing Deflection Angles 209
8.12 Observing Azimuths 211
8.13 Observing Vertical Angles 211
8.14 Sights and Marks 213
8.15 Prolonging a Straight Line 214
8.16 Balancing-In 216
8.17 Random Traverse 217
8.18 Total Stations for Determining Elevation Differences 218
8.19 Adjustment of Total Station Instruments and Their Accessories 219
8.20 Sources of Error in Total Station Work 222
8.21 Propagation of Random Errors in Angle Observations 228
8.22 Mistakes 228
Problems 229
Bibliography 230
9 • TRAVERSING 231
9.1 Introduction 231
9.2 Observation of Traverse Angles or Directions 233
9.3 Observation of Traverse Lengths 234
9.4 Selection of Traverse Stations 235
9.5 Referencing Traverse Stations 235
9.6 Traverse Field Notes 237
9.7 Angle Misclosure 238
9.8 Traversing with Total Station Instruments 239
9.9 Radial Traversing 240
9.10 Sources of Error in Traversing 241
9.11 Mistakes in Traversing 242
Problems 242
10 • TRAVERSE COMPUTATIONS 245
10.1 Introduction 245
10.2 Balancing Angles 246
10.3 Computation of Preliminary Azimuths or Bearings 248
10.4 Departures and Latitudes 249
10.5 Departure and Latitude Closure Conditions 251
10.6 Traverse Linear Misclosure and Relative Precision 251
10.7 Traverse Adjustment 252
10.8 Rectangular Coordinates 255
10.9 Alternative Methods for Making Traverse Computations 256
10.10 Inversing 260
10.11 Computing Final Adjusted Traverse Lengths and Directions 261
10.12 Coordinate Computations in Boundary Surveys 263
10.13 Use of Open Traverses 265
10.14 State Plane Coordinate Systems 268
10.15 Traverse Computations Using Computers 269
10.16 Locating Blunders in Traverse Observations 269
10.17 Mistakes in Traverse Computations 272
Problems 272
Bibliography 275
11 • COORDINATE GEOMETRY IN SURVEYING CALCULATIONS 277
11.1 Introduction 277
11.2 Coordinate Forms of Equations for Lines and Circles 278
11.3 Perpendicular Distance from a Point to a Line 280
11.4 Intersection of Two Lines, Both Having Known Directions 282
11.5 Intersection of a Line with a Circle 284
11.6 Intersection of Two Circles 287
11.7 Three-Point Resection 289
11.8 Two-Dimensional Conformal Coordinate Transformation 292
11.9 Inaccessible Point Problem 297
11.10 Three-Dimensional Two-Point Resection 299
11.11 Software 302
Problems 303
Bibliography 307
12 • AREA 309
12.1 Introduction 309
12.2 Methods of Measuring Area 309
12.3 Area by Division Into Simple Figures 310
12.4 Area by Offsets from Straight Lines 311
12.5 Area by Coordinates 313
12.6 Area by Double-Meridian Distance Method 317
12.7 Area of Parcels with Circular Boundaries 320
12.8 Partitioning of Lands 321
12.9 Area by Measurements from Maps 325
12.10 Software 327
12.11 Sources of Error in Determining Areas 328
12.12 Mistakes in Determining Areas 328
Problems 328
Bibliography 330
13 • GLOBAL NAVIGATION SATELLITE SYSTEMS—INTRODUCTION AND PRINCIPLES OF OPERATION 331
13.1 Introduction 331
13.2 Overview of GPS 332
13.3 The GPS Signal 335
13.4 Reference Coordinate Systems 337
13.5 Fundamentals of Satellite Positioning 345
13.6 Errors in Observations 348
13.7 Differential Positioning 356
13.8 Kinematic Methods 358
13.9 Relative Positioning 359
13.10 Other Satellite Navigation Systems 362
13.11 The Future 364
Problems 365
Bibliography 366
14 • GLOBAL NAVIGATION SATELLITE SYSTEMS—STATIC SURVEYS 367
14.1 Introduction 367
14.2 Field Procedures in Satellite Surveys 369
14.3 Planning Satellite Surveys 372
14.4 Performing Static Surveys 384
14.5 Data Processing and Analysis 386
14.6 Sources of Errors in Satellite Surveys 393
14.7 Mistakes in Satellite Surveys 395
Problems 395
Bibliography 397
15 • GLOBAL NAVIGATION SATELLITE SYSTEMS—KINEMATIC SURVEYS 399
15.1 Introduction 399
15.2 Planning of Kinematic Surveys 400
15.3 Initialization 402
15.4 Equipment Used in Kinematic Surveys 403
15.5 Methods Used in Kinematic Surveys 405
15.6 Performing Post-Processed Kinematic Surveys 408
15.7 Communication in Real-Time Kinematic Surveys 411
15.8 Real-Time Networks 412
15.9 Performing Real-Time Kinematic Surveys 413
15.10 Machine Control 414
15.11 Errors in Kinematic Surveys 418
15.12 Mistakes in Kinematic Surveys 418
Problems 418
Bibliography 419
16 • ADJUSTMENTS BY LEAST SQUARES 421
16.1 Introduction 421
16.2 Fundamental Condition of Least Squares 423
16.3 Least-Squares Adjustment by the Observation Equation Method 424
16.4 Matrix Methods in Least-Squares Adjustment 428
16.5 Matrix Equations for Precisions of Adjusted Quantities 430
16.6 Least-Squares Adjustment of Leveling Circuits 432
16.7 Propagation of Errors 436
16.8 Least-Squares Adjustment of GNSS Baseline Vectors 437
16.9 Least-Squares Adjustment of Conventional Horizontal Plane Surveys 443
16.10 The Error Ellipse 452
16.11 Adjustment Procedures 457
16.12 Other Measures of Precision for Horizontal Stations 458
16.13 Software 460
16.14 Conclusions 460
Problems 461
Bibliography 466
17 • MAPPING SURVEYS 467
17.1 Introduction 467
17.2 Basic Methods for Performing Mapping Surveys 468
17.3 Map Scale 468
17.4 Control for Mapping Surveys 470
17.5 Contours 471
17.6 Characteristics of Contours 474
17.7 Direct and Indirect Methods of Locating Contours 474
17.8 Digital Elevation Models and Automated Contouring Systems 477
17.9 Basic Field Methods for Locating Topographic Details 479
17.10 Three-Dimensional Conformal Coordinate Transformation 488
17.11 Selection of Field Method 489
17.12 Working with Data Collectors and Field-to-Finish Software 490
17.13 Hydrographic Surveys 493
17.14 Sources of Error in Mapping Surveys 497
17.15 Mistakes in Mapping Surveys 498
Problems 498
Bibliography 500
18 • MAPPING 503
18.1 Introduction 503
18.2 Availability of Maps and Related Information 504
18.3 National Mapping Program 505
18.4 Accuracy Standards for Mapping 505
18.5 Manual and Computer-Aided Drafting Procedures 507
18.6 Map Design 508
18.7 Map Layout 510
18.8 Basic Map Plotting Procedures 512
18.9 Contour Interval 514
18.10 Plotting Contours 514
18.11 Lettering 515
18.12 Cartographic Map Elements 516
18.13 Drafting Materials 519
18.14 Automated Mapping and Computer-Aided Drafting Systems 519
18.15 Impacts of Modern Land and Geographic Information Systems on Mapping 525
18.16 Sources of Error in Mapping 526
18.17 Mistakes in Mapping 526
Problems 526
Bibliography 528
19 • CONTROL SURVEYS AND GEODETIC REDUCTIONS 529
19.1 Introduction 529
19.2 The Ellipsoid and Geoid 530
19.3 The Conventional Terrestrial Pole 532
19.4 Geodetic Position and Ellipsoidal Radii of Curvature 534
19.5 Geoid Undulation and Deflection of the Vertical 536
19.6 U.S. Reference Frames 538
19.7 Accuracy Standards and Specifications for Control Surveys 547
19.8 The National Spatial Reference System 550
19.9 Hierarchy of the National Horizontal Control Network 550
19.10 Hierarchy of the National Vertical Control Network 551
19.11 Control Point Descriptions 551
19.12 Field Procedures for Traditional Horizontal Control Surveys 554
19.13 Field Procedures for Vertical Control Surveys 559
19.14 Reduction of Field Observations to Their Geodetic Values 564
19.15 Geodetic Position Computations 577
19.16 The Local Geodetic Coordinate System 580
19.17 Three-Dimensional Coordinate Computations 581
19.18 Software 584
Problems 584
Bibliography 587
20 • STATE PLANE COORDINATES AND OTHER MAP PROJECTIONS 589
20.1 Introduction 589
20.2 Projections Used in State Plane Coordinate Systems 590
20.3 Lambert Conformal Conic Projection 593
20.4 Transverse Mercator Projection 594
20.5 State Plane Coordinates in NAD27 and NAD83 595
20.6 Computing SPCS83 Coordinates in the Lambert Conformal Conic System 596
20.7 Computing SPCS83 Coordinates in the Transverse Mercator System 601
20.8 Reduction of Distances and Angles to State Plane Coordinate Grids 608
20.9 Computing State Plane Coordinates of Traverse Stations 617
20.10 Surveys Extending from One Zone to Another 620
20.11 Conversions Between SPCS27 and SPCS83 621
20.12 The Universal Transverse Mercator Projection 622
20.13 Other Map Projections 623
20.14 Map Projection Software 627
Problems 628
Bibliography 631
21 • BOUNDARY SURVEYS 633
21.1 Introduction 633
21.2 Categories of Land Surveys 634
21.3 Historical Perspectives 635
21.4 Property Description by Metes and Bounds 636
21.5 Property Description by Block-and-Lot System 639
21.6 Property Description by Coordinates 641
21.7 Retracement Surveys 641
21.8 Subdivision Surveys 644
21.9 Partitioning Land 646
21.10 Registration of Title 647
21.11 Adverse Possession and Easements 648
21.12 Condominium Surveys 648
21.13 Geographic and Land Information Systems 655
21.14 Sources of Error in Boundary Surveys 655
21.15 Mistakes 655
Problems 656
Bibliography 658
22 • SURVEYS OF THE PUBLIC LANDS 659
22.1 Introduction 659
22.2 Instructions for Surveys of the Public Lands 660
22.3 Initial Point 663
22.4 Principal Meridian 664
22.5 Baseline 665
22.6 Standard Parallels (Correction Lines) 666
22.7 Guide Meridians 666
22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines 667
22.9 Designation of Townships 668
22.10 Subdivision of a Quadrangle into Townships 668
22.11 Subdivision of a Township into Sections 670
22.12 Subdivision of Sections 671
22.13 Fractional Sections 672
22.14 Notes 672
22.15 Outline of Subdivision Steps 672
22.16 Marking Corners 674
22.17 Witness Corners 674
22.18 Meander Corners 675
22.19 Lost and Obliterated Corners 675
22.20 Accuracy of Public Lands Surveys 678
22.21 Descriptions by Township Section and Smaller Subdivision 678
22.22 BLM Land Information System 679
22.23 Sources of Error 680
22.24 Mistakes 680
Problems 681
Bibliography 683
23 • CONSTRUCTION SURVEYS 685
23.1 Introduction 685
23.2 Specialized Equipment for Construction Surveys 686
23.3 Horizontal and Vertical Control 689
23.4 Staking Out a Pipeline 691
23.5 Staking Pipeline Grades 692
23.6 Staking Out a Building 694
23.7 Staking Out Highways 698
23.8 Other Construction Surveys 703
23.9 Construction Surveys Using Total Station Instruments 704
23.10 Construction Surveys Using GNSS Equipment 706
23.11 Machine Guidance and Control 709
23.12 As-Built Surveys with Laser Scanning 710
23.13 Sources of Error in Construction Surveys 711
23.14 Mistakes 712
Problems 712
Bibliography 714
24 • HORIZONTAL CURVES 715
24.1 Introduction 715
24.2 Degree of Circular Curve 716
24.3 Definitions and Derivation of Circular Curve Formulas 718
24.4 Circular Curve Stationing 720
24.5 General Procedure of Circular Curve Layout by Deflection Angles 721
24.6 Computing Deflection Angles and Chords 723
24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords 725
24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords 726
24.9 Setups on Curve 727
24.10 Metric Circular Curves by Deflection Angles and Incremental Chords 728
24.11 Circular Curve Layout by Deflection Angles and Total Chords 730
24.12 Computation of Coordinates on a Circular Curve 731
24.13 Circular Curve Layout by Coordinates 733
24.14 Curve Stakeout Using GNSS Receivers and Robotic Total Stations 738
24.15 Circular Curve Layout by Offsets 739
24.16 Special Circular Curve Problems 742
24.17 Compound and Reverse Curves 743
24.18 Sight Distance on Horizontal Curves 743
24.19 Spirals 744
24.20 Computation of “As-Built” Circular Alignments 749
24.21 Sources of Error in Laying Out Circular Curves 752
24.22 Mistakes 752
Problems 753
Bibliography 755
25 • VERTICAL CURVES 757
25.1 Introduction 757
25.2 General Equation of a Vertical Parabolic Curve 758
25.3 Equation of an Equal Tangent Vertical Parabolic Curve 759
25.4 High or Low Point on a Vertical Curve 761
25.5 Vertical Curve Computations Using the Tangent Offset Equation 761
25.6 Equal Tangent Property of a Parabola 765
25.7 Curve Computations by Proportion 766
25.8 Staking a Vertical Parabolic Curve 766
25.9 Machine Control in Grading Operations 767
25.10 Computations for an Unequal Tangent Vertical Curve 767
25.11 Designing a Curve to Pass Through a Fixed Point 770
25.12 Sight Distance 771
25.13 Sources of Error in Laying Out Vertical Curves 773
25.14 Mistakes 774
Problems 774
Bibliography 776
26 • VOLUMES 777
26.1 Introduction 777
26.2 Methods of Volume Measurement 777
26.3 The Cross-Section Method 778
26.4 Types of Cross Sections 779
26.5 Average-End-Area Formula 780
26.6 Determining End Areas 781
26.7 Computing Slope Intercepts 784
26.8 Prismoidal Formula 786
26.9 Volume Computations 788
26.10 Unit-Area, or Borrow-Pit, Method 790
26.11 Contour-Area Method 791
26.12 Measuring Volumes of Water Discharge 793
26.13 Software 794
26.14 Sources of Error in Determining Volumes 795
26.15 Mistakes 795
Problems 795
Bibliography 798
27 • PHOTOGRAMMETRY 799
27.1 Introduction 799
27.2 Uses of Photogrammetry 800
27.3 Aerial Cameras 801
27.4 Types of Aerial Photographs 803
27.5 Vertical Aerial Photographs 804
27.6 Scale of a Vertical Photograph 806
27.7 Ground Coordinates from a Single Vertical Photograph 810
27.8 Relief Displacement on a Vertical Photograph 811
27.9 Flying Height of a Vertical Photograph 813
27.10 Stereoscopic Parallax 814
27.11 Stereoscopic Viewing 817
27.12 Stereoscopic Measurement of Parallax 819
27.13 Analytical Photogrammetry 820
27.14 Stereoscopic Plotting Instruments 821
27.15 Orthophotos 826
27.16 Ground Control for Photogrammetry 827
27.17 Flight Planning 828
27.18 Airborne Laser-Mapping Systems 830
27.19 Remote Sensing 831
27.20 Software 837
27.21 Sources of Error in Photogrammetry 838
27.22 Mistakes 838
Problems 839
Bibliography 842
28 • INTRODUCTION TO GEOGRAPHIC INFORMATION SYSTEMS 843
28.1 Introduction 843
28.2 Land Information Systems 846
28.3 GIS Data Sources and Classifications 846
28.4 Spatial Data 846
28.5 Nonspatial Data 852
28.6 Data Format Conversions 853
28.7 Creating GIS Databases 856
28.8 Metadata 862
28.9 GIS Analytical Functions 862
28.10 GIS Applications 867
28.11 Data Sources 867
Problems 869
Bibliography 871
APPENDIX A • DUMPY LEVELS, TRANSITS, AND THEODOLITES 873
APPENDIX B • EXAMPLE NOTEFORMS 888
APPENDIX C • ASTRONOMICAL OBSERVATIONS 895
APPENDIX D • USING THE WORKSHEETS FROM THE COMPANION WEBSITE 911
APPENDIX E • INTRODUCTION TO MATRICES 917
APPENDIX F • U.S. STATE PLANE COORDINATE SYSTEM DEFINING PARAMETERS 923
APPENDIX G • ANSWERS TO SELECTED PROBLEMS 927
INDEX 933
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Solution Manual for Elementary Surveying: An Introduction to Geomatics, 13th Edition Charles D. Ghilani
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