6 1 INTRODUCTION 1.1 Develop your personal definition for the practice of surveying. Answers will vary by response. See Section 1.1 for book definitions. 1.2 Explain the difference between geodetic and plane surveys. From Section 1.4, In geodetic surveys the curved surface of the earth is considered by performing the computations on an ellipsoid (curve surface approximating the size and shape of the earth). In plane surveys, except for leveling, the reference base for fieldwork and computations is assumed to be a flat horizontal surface. The direction of a plumb line (and thus gravity) is considered parallel throughout the survey region, and all measured angles are presumed to be plane angles. 1.3 Describe some surveying applications in: (a) Construction In construction, surveying is used to locate the precise location of structures such as roads, buildings, bridges, and so forth. From the FIG definition of surveying, item 11: " The planning, measurement and management of construction works, including the estimation of costs. In application of the foregoing activities surveyors take into account the relevant legal, economic, environmental, and social aspects affecting each project." (b) Mining In mining, surveying is used to direct the locations of mining activities according to a systematic plan, to make sure mining occurs within the boundaries of the claim, to connect tunnels and shafts, and to provide legal records of mining activities. (c) Agriculture In agriculture, surveying is used to determine the acreage of fields, to locate lines of constant elevation for strip farming, to track harvesting machinery to enable the size of the harvest, and to track the position of the planting equipment to allow for precise applications of seeds and fertilizers. The field is known as high-precision agriculture. 1.4 List 10 uses for surveying other than property and construction surveying. Some items students may lists include" 1. Establishing control for use in other surveys. 2. Mapping the surface of the Earth and other celestial objects with photogrammetry, laser scanning, or remote sensing. 3. Mapping archeological artifacts. 7 4. Mapping the bottom of oceans and waterways. 5. Creating Geographic and Land Information Systems for public use. 6. Performing ordinance surveys for the military. 7. Creating topographic maps. 8. Optical tooling. 9. Mapping of statues and other forms of artwork using terrestrial photogrammetry or laser scanning. 10. Mapping of accident sites in forensic surveying. 1.5 Why is it important to make accurate surveys of underground utilities? To provide an accurate record of the locations of these utilities so they can be found if repairs or servicing is needed, and to prevent their accidental destruction during excavation for other projects. 1.6 Discuss the uses for topographic surveys. Topographic surveys are used whenever elevation data is required in the end product. Some examples include (1) creating maps for highway design; (2) creating maps for construction surveys; (3) creating maps for flood plain delineation; (4) creating maps for site location of buildings; and so on. 1.7 What are hydrographic surveys, and why are they important? From Section 1.6, hydrographic surveys define shorelines and depths of lakes, streams, oceans, reservoirs, and other bodies of water. Sea surveying is associated with port and offshore industries and the marine environment, including measurements and marine investigations made by ship borne personnel. 1.8 Name and briefly describe three different surveying instruments used by early Roman engineers. From Section 1.3: (1) gromma, (2) libella, and (3) chorobates. 1.9 Briefly explain the procedure used by Eratosthenes in determining the Earth’s circumference. From Section 1-3, paragraph 8 of text: His procedure, which occurred about 200 B.C., is illustrated in Figure 1-2. Eratosthenes had concluded that the Egyptian cities of Alexandria and Syene were located approximately on the same meridian, and he had also observed that at noon on the summer solstice, the sun was directly overhead at Syene. (This was apparent because at that time of that day, the image of the sun could be seen reflecting from the bottom of a deep vertical well there.) He reasoned that at that moment, the sun, Syene, and Alexandria were in a common meridian plane, and if he could measure the arc length between the two cities, and the angle it subtended at the earth's center, he could compute the earth's circumference. He determined the angle by measuring the length of the shadow cast at Alexandria from a tall vertical staff of known length. The arc length was found from multiplying the number of caravan days between Syene and Alexandria by the average daily distance traveled. From these measurements Eratosthenes calculated the earth's 8 circumference to be about 25,000 mi. Subsequent precise geodetic measurements using better instruments, but techniques similar geometrically to Eratosthenes', have shown his value, though slightly too large, to be amazingly close to the currently accepted one. 1.10 Describe the steps a land surveyor would need to do when performing a boundary survey. Briefly, the steps should include (1) preliminary walking of property with owner; (2) courthouse research to locate deed of property and adjoiners to determine ownership, possible easements, right-of-ways, conflicts of interest, and so on; (3) location survey of property noting any encroachments; conflicting elements; and so on; (4) resolution of conflicting elements between deed and survey; (5) delivery of surveying report to owner. 1.11 Do laws in your state specify the accuracy required for surveys made to lay out a subdivision? If so, what limits are set? Responses will vary 1.12 What organizations in your state will furnish maps and reference data to surveyors and engineers? Responses will vary but some common organizations are the (1) county surveyor, (2) register of deeds, (3) county engineer, (4) Department of Transportation, (5) Department of Natural Resources of its equivalent, and so on. 1.13 List the legal requirements for registration as a land surveyor in your state. Responses will vary. Contact with you licensing board can be found on the NCEES website at http://www.ncees.org/licensure/licensing_boards/. 1.14 Briefly describe the European Galileo system and discuss its similarities and differences with GPS. See Section 13.10.2. Students can look this information and much more with a web search. 1.15 List at least five nonsurveying uses for GPS. Responses may include (1) logistics in transportation; (2) hunting; (3) location of cell phone calls; (4) timing of telecommunications networks; (5) navigation in the boating industry; and so on. 9 1.16 Explain how aerial photographs and satellite images can be valuable in surveying. Photogrammetry presently has many applications in surveying. It is used, for example, in land surveying to compute coordinates of section corners, boundary corners, or point of evidence that help locate these corners. Large–scale maps are made by photogrammetric procedures for many uses, one being subdivision design. Photogrammetry is used to map shorelines, in hydrographic surveying, to determine precise ground coordinates of points in control surveying, and to develop maps and cross sections for route and engineering surveys. Photogrammetry is playing an important role in developing the necessary data for modern Land and Geographic Information Systems. 1.17 Search the Internet and define a VLBI station. Discuss why these stations are important to the surveying community. VLBI stands for Very Long Baseline Interferometry . Responses will vary. These stations provide extremely accurate locations on the surface of the Earth. The stations are used to develop world-wide reference frameworks such as ITRF00. They also may provide tracking information for satellites. 1.18 Describe how a GIS can be used in flood emergency planning. Responses will vary but may mention the capabilities of a GIS to overlay soil type and their permeability with slopes, soil saturation, and watershed regions. A GIS can also be used to provide a list of business and residences that will be affected by possible flooding for evacuation purposes. It can provide “best” routes out of a flooded region. 1.19 Visit one of the surveying web sites listed in Table 1.1, and write a brief summary of its contents. Briefly explain the value of the available information to surveyors. Responses will vary with time, but below are brief responses to the question  NGS – control data sheets, CORS data, surveying software  USGS – maps, software  BLM – cadastral maps, software, ephemerides  U.S. Coast Guard Navigation Center - GPS information  U.S. Naval Observatory –Notice Advisory for NAVSTAR Users (NANU) and other GPS related links  American Congress on Surveying and Mapping (ACSM) – professional organization for surveying and mapping profession  American Society for Photogrammetry and Remote Sensing – professional organization for photogrammetry and remote sensing  The Pennsylvania State University Surveying Program – Access to latest software that accompanies this book. 10 1.20 Read one of the articles cited in the bibliography for this chapter, or another of your choosing, that describes an application where GPS was used. Write a brief summary of the article. Response will vary. 1.21 Same as Problem 1.20, except the article should be on safety as related to surveying. Responses will vary. 11 2 UNITS, SIGNIFICANT FIGURES, AND FIELD NOTES 2.1 List the five types of measurements that form the basis of traditional plane surveying. From Section 2.1, they are (1) horizontal angles, (2) horizontal distances, (3) vertical (altitude or zenith) angles, (4) vertical distances, and (5) slope (or slant) distances. 2.2 Give the basic units that are used in surveying for length, area, volume, and angles in (a) The English system of units. From Section 2.2: length (U.S. survey ft or in some states m), area (sq. ft. or acres), volume (cu. ft. or cu. yd.), angle (sexagesimal) (b) The SI system of units. From Section 2.3: length (m), area (sq. m. or hectare), volume (cu. m.), angle (sexagesimal, grad, or radian) 2.3 Why was the survey foot definition maintained in the United States? From Section 2.2: The survey foot definition was maintained in the United States because of the vast number of surveys performed prior to 1959. It would have been extremely difficult and confusing to change all related documents and maps that already existed. Thus the old standard, now call the U.S. survey foot, is still used today. 2.4 Convert the following distances given in meters to U.S. survey feet: *(a) 4129.574 m 13,548.44 ft (b) 738.296 m 2422.23 ft (c) 6048.083 m 19,842.75 ft 2.5 Convert the following distances given in feet to meters: *(a) 537.52 ft 163.836 m (b) 9364.87 ft 2854.418 m (c) 4806.98 ft 1465.170 m 2.6 Compute the lengths in feet corresponding to the following distances measured with a Gunter’s chain: *(a) 10 ch 13 lk 668.6 ft (b) 6 ch 12 lk 404 ft (c) 24 ch 8 lk 1589 ft 12 2.7 Express 95,748 ft 2 in: *(a) acres 2.1981 ac (b) hectares 0.88953 ha (c) square Gunter’s chains 21.981 sq. ch. 2.8 Convert 5.6874 ha to: (a) acres 14.054 ac (b) square Gunter’s chains 140.54 sq. ch 2.9 What are the lengths in feet and decimals for the following distances shown on a building blueprint: (a) 30 ft 9-3/4 in. 30.81 ft (b) 12 ft 6-1/32 in. 12.50 ft 2.10 What is the area in acres of a rectangular parcel of land measured with a Gunter’s chain if the recorded sides are as follows: *(a) 9.17 ch and 10.64 ch 9.76 ac (b) 12 ch 36 lk and 24 ch 28 lk 30.01 ac 2.11 Compute the area in acres of triangular lots shown on a plat having the following recorded right-angle sides: (a) 208.94 ft and 232.65 ft 0.55796 ac (b) 9 ch 25 lk and 6 ch 16 lk 2.85 ac 2.12 A distance is expressed as 125,845.64 U.S. survey feet. What is the length in *(a) international feet? 125,845.89 ft (b) meters? 38,357.828 m 2.13 What are the radian and degree-minute-second equivalents for the following angles given in grads: *(a) 136 .00 grads  122°24 (b) 89.5478 grads   80°35 35 (c) 68.1649 grads   61°20 54 2.14 Give answers to the following problems in the correct number of significant figures: *(a) sum of 23.15, 0.984, 124, and 12.5 160. (b) sum of 36.15, 0.806, 22.4, and 196.458 255.8 (c) product of 276.75 and 33.7 9330 (d) quotient of 4930.27 divided by 1.29 3820 2.15 Express the value or answer in powers of 10 to the correct number of significant figures: 13 (a) 11,432 1.1432 × 10 4 (b) 4520 4.52 × 10 3 (c) square of 11,293 1.2753 × 10 8 (d) sum of (11.275 + 0.5 + 146.12) divided by 7.2 2.2 × 10 1 2.16 Convert the adjusted angles of a triangle to radians and show a computational check: *(a) 39 41 54 , 91 30 16 , and 48 47 50          0.692867, 1.59705, and 0.851672 0.6928666 + 1.597054 + 0.8516721 = 3.14059 check (b) 82 17 43 , 29 05 54 , and 68 36 23          1.43632, 0.507862 , and 1.19741 1.436324 + 0. 5078617 + 1.197407 = 3.14159 check 2.17 Why should a pen not be used in field notekeeping? From Section 2.7: " Books so prepared will withstand damp weather in the field (or even a soaking) and still be legible, whereas graphite from a soft pencil, or ink from a pen or ballpoint, leaves an undecipherable smudge under such circumstances." 2.18 Explain why one number should not be superimposed over another or the lines of sketches. From Section 2.7: This can be explained with the need for integrity since it would raise the issue of what are you hiding, legibility since the numbers are often hard to interpret when so written, or by clarity since the notes are being crowded. *2.19 Explain why data should always be entered directly into the field book at the time measurements are made, rather than on scrap paper for neat transfer to the field book later. From Section 2.7: Data should always be entered into the field book directly at the time of the measurements to avoid loss of data. 2.20 Why should a new day’s work begin on a new page? A new day's work should begin on a new page to provide a record of what work was accomplished each day and to document an changes in the field crew, weather, instrumentation, and so on. 2.21 Explain the reason for item 18 in Section 2.11 when recording field notes. A zero should be placed before a decimal point for the sake of clarity. 2.22 Explain the reason for item 24 in Section 2.11 when recording field notes. The need for a title, index, and cross-reference is to provide a clear path of where the work to find the notes for a specific project, even if some notes come from previous work. 2.23 Explain the reason for item 12 in Section 2.11 when recording field notes. 14 Explanatory notes are essential to provide office personnel with an explanation for something unusual and to provide a reminder in later reference to the project. 2.24 When should sketches be made instead of just recording data? Sketches should be made instead of recording data anytime observations need to be clarified so that the personnel interpreting the notes can have a clear understanding of the field conditions. This also serves as a reminder of the work performed and any unusual conditions in later references to the project. 2.25 Justify the requirement to list in a field book the makes and serial numbers of all instruments used on a survey. Listing the makes and serial numbers of the instruments used in the survey may help isolate instrumental errors later when reviewing the project. 2.26 Discuss the advantages of survey controllers that can communicate with several different types of instruments. The ability of survey controllers to communicate with several different types of instruments allows the surveyor to match the specific conditions of the project with the instrument that this is ideally suited for the job. Thus total station, digital levels, and GNSS receivers can all be used in a single project. 2.27 Discuss the advantages of survey controllers. From Section 2.15: " The major advantages of automatic data collection systems are that ( 1 ) mistakes in reading and manually recording observations in the field are precluded, and ( 2 ) the time to process, display, and archive the field notes in the office is reduced significantly. Systems that incorporate computers can execute some programs in the field, which adds a significant advantage. As an example, the data for a survey can be corrected for systematic errors and misclosures computed, so verification that a survey meets closure requirements is made before the crew leaves a site." 2.28 Search the Internet and find at least two sites related to (a) Manufacturers of survey controllers. (b) Manufacturers of total stations. (c) Manufacturers of global navigation satellite system (GNSS) receivers. Answers should vary with student. 2.29 What advantages are offered to field personnel if the survey controller provides a map of the survey? This allows field personnel to view what has been accomplished and look for areas of the map that need more attention. 15 2.30 Prepare a brief summary of an article from a professional journal related to the subject matter of this chapter. Answer should vary by student. 2.31 Describe what is meant by the phrase “field-to-finish.” From Section 2.15, " These field codes can instruct the drafting software to draw a map of the data complete with lines, curves and mapping symbols. The process of collecting field data with field codes that can be interpreted later by software is known as a field- to-finish survey. This greatly reduces the time needed to complete a project." 2.32 Why are sketches in field books not usually drawn to scale? This is true since this would require an overwhelming amount of time. The sketches are simply to provide readers of the notes an approximate visual reference to the measurements. 2.33 Create a computational program that solves Problem 2.16. Answers to this problem should vary with students. 16 3 THEORY OF ERRORS IN OBSERVATIONS 3.1 Explain the difference between direct and indirect observations in surveying. Give two examples of each. From Section 3.2: A direct observation is made by applying a measurement instrument directly to a quantity to be measured and an indirect observation is made by computing a quantity from direct observations. Examples should vary by student response. 3.2 Define the term systematic error , and give two surveying examples of a systematic error. See Section 3.6 3.3 Define the term random error , and give two surveying examples of a random error. See Section 3.6 3.4 Explain the difference between accuracy and precision. See Section 3.7 3.5 Discuss what is meant by the precision of an observation. See Section 3.7 A distance AB is observed repeatedly using the same equipment and procedures, and the results, in meters, are listed in Problems 3.6 through 3.10. Calculate (a) the line’s most probable length, (b) the standard deviation and (c) the standard deviation of the mean for each set of results. *3.6 65.401, 65.400, 65.402, 65.396, 65.406, 65.401, 65.396, 65.401, 65.405, and 65.404 (a) 65.401 ∑ 654.012 (b) ±0.003 ∑ν 2 = 0.000104 (c) ±0.001 3.7 Same as Problem 3.6, but discard one observation, 65.396. (a) 65.402 ∑ 588.616 (b) ±0.003 ∑ν 2 = 0.000072 (c) ±0.001 17 3.8 Same as Problem 3.6, but discard two observations, 65.396 and 65.406. (a) 65.402 ∑ 523.210 (b) ±0.003 ∑ν 2 = 0.00007168 (c) ±0.001 3.9 Same as Problem 3.6, but include two additional observations, 65.398 and 65.408. (a) 65.401 ∑ 784.818 (b) ±0.004 ∑ν 2 = 0.000157 (c) ±0.001 3.10 Same as Problem 3.6, but include three additional observations, 65.398, 65.408, and 65.406. (a) 65.402 ∑ 850.224 (b) ±0.004 ∑ν 2 = 0.0001757 (c) ±0.001 In Problems 3.10 through 3.14, determine the range within which observations should fall (a) 90% of the time and (b) 95% of the time. List the percentage of values that actually fall within these ranges. (a) E 90 = 1.6449 σ (3.7) (b) E 95 = 1.9599 σ (3.8) 3.11 For the data of Problem 3.6. *(a) 65.4012±0.0055 (65.3957, 65.4067), 100% (b) 65.4012±0.0066 (65.3946, 65.4078), 100% 3.12 For the data of Problem 3.7. (a) 65.4018±0.0049 (65.3968, 65.4067), 88.9% (b) 65.4018±0.00059 (65.6959, 65.4076), 100% 3.13 For the data of Problem 3.8. (a) 65.4012±0.0045 (65.3968, 65.4057), 87.5% (b) 65.4012±0.0053 (65.3959, 65.4066), 100% 3.14 For the data of Problem 3.9. (a) 65.4012±0.0062 (65.3968, 65.4077), 91.6% (b) 65.4012±0.0074 (65.3940, 65.4089), 100% 18 In Problems 3.15 through 3.17, an angle is observed repeatedly using the same equipment and procedures. Calculate (a) the angle’s most probable value, (b) the standard deviation, and ( c ) the standard deviation of the mean. *3.15 23°30 00 , 23°29 40 , 23°30 15 ,       and 23 29 50    . (a) 23°29 ′ 56 ″ (b) ±14.9 ″ (c) ±7.5 ″ 3.16 Same as Problem 3.15, but with three additional observations, 23 29 55 , 23 30 05 ,       and 23 30 20 .    (a) 23°30 ′ 01 ″ (b) ±14.0 ″ (c) ±5.3 ″ 3.17 Same as Problem 3.16, but with two additional observations, 23 30 05    and 23 29 55    . (a) 23°30 ′ 56 ″ (b) ±12.4 ″ (c) ±4.1 ″ *3.18 A field party is capable of making taping observations with a standard deviation of 0.010 ft  per 100-ft tape length. What standard deviation would be expected in a distance of 200 ft taped by this party? By Equation (3.12): ±0.014 ft 0.010 2  3.19 Repeat Problem 3.18, except that the standard deviation per 30-m tape length is 0.003 m  and a distance of 120 m is taped. What is the expected 95% error in 120 m? By Equation (3.12): ±0.006 m = 0.003 4; By Equation (3.8): ±0.018   1.9559 0.006  3.20 A distance of 200 ft must be taped in a manner to ensure a standard deviation smaller than 0.04ft  . What must be the standard deviation per 100 ft tape length to achieve the desired precision? ±0.028 ft = 0.04 2  by Equation (3.12) rearranged. 3.21 Lines of levels were run requiring n instrument setups. If the rod reading for each backsight and foresight has a standard deviation  , what is the standard deviation in each of the following level lines? (a) 26, 0.010 ft n     By Equation (3.12): ±0.051 ft = 0.010 26 19 (b) 36, 3 mm n     By Equation (3.12): ±18 m = 3 36 3.22 A line AC was observed in 2 sections AB and BC , with lengths and standard deviations listed below. What is the total length AC , and its standard deviation? *(a) 60.00 0.015ft; 86.13 0.018 ft AB BC     ; 146.13±0.023 ft by Equation (3.11) (b) 60.000 0.008 m; 35.413 0.005 m AB    ; 95.413±0.0094 m by Equation (3.11) 3.23 Line AD is observed in three sections, AB, BC , and CD , with lengths and standard deviations as listed below. What is the total length AD and its standard deviation? (a) 572.12 0.02 ft; 1074.38 0.03 ft; 1542.78 0.05 ft AB BC CD       3189.28 ± 0.062 ft by Equation (3.11) (b) 932.965 0.009 m; 945.030 m 0.010 m; 652.250 m 0.008 m AB BC CD       2530.245 ± 0.016 m by Equation (3.11) 3.24 A distance AB was observed four times as 236.39, 236.40, 236.36 and 236.38 ft. The observations were given weights of 2, 1, 3 and 2, respectively, by the observer. * (a) Calculate the weighted mean for distance AB . ( b ) What difference results if later judgment revises the weights to 2, 1, 2, and 3, respectively? By Equation (3.17): *(a) 236.3775 ft (b) 236.3850 ft 3.25 Determine the weighted mean for the following angles: By Equation (3.17): (a) 89 42 45 , wt 2; 89 42 42 , wt 1; 89 42 44 , wt 3          89°42 ′ 44 ″ (b) 36 58 32 3 ; 36 58 28 2 ; 36 58 26 3 ; 36 58 30 1                     36°58 ′ 29.5 ″ 3.26 Specifications for observing angles of an n -sided polygon limit the total angular misclosure to E . How accurately must each angle be observed for the following values of n and E ? By rearranged Equation (3.12): (a) 10, 8 n E    ±2.5 ″ (b) 6, 14 n E    ±5.7 ″ 3.27 What is the area of a rectangular field and its estimated error for the following recorded values: By Equation (3.13): *(a) 243.89 0.05 ft, by 208.65 0.04 ft   50,887 ± 14 ft 2 or 1.1682 ± 0.0003 ac 20 (b) 725.33 0.08 ft by 664.21 0.06 ft   481,770 ± 70 ft 2 or 11.060 ± 0.002 ac (c) 128.526 0.005 m, by 180.403 0.007 m   23,186.5 ± 1.3 m 2 or 20.1865 ± 0.0001 ha 3.28 Adjust the angles of triangle ABC for the following angular values and weights: By Equation (3.17): *(a) 49 24 22 , wt 2; 39 02 16 , wt 1; 91 33 00 , wt 3 A B C             Misclosure = − 22 ″ Obs. Ang. Wt Corr. Num. Cor. Rnd. Cor. Adj. Ang. A 49°24 ′ 22 ″ 2 3x 6 ″ 6 ″ 49°24 ′ 28 ″ B 39°02 ′ 16 ″ 1 6x 12 ″ 12 ″ 39°02 ′ 28 ″ C 91°33 ′ 00 ″ 3 2x 4 ″ 4 ″ 91°33 ′ 04 ″ 179°59 ′ 38 ″ 6 11x 11x = 22 ″ x = 2 ″ (b) 80 14 04 , wt 2; 38 37 47 , wt 1; 61 07 58 , wt 3 A B C             Misclosure = − 11 ″ Obs. Ang. Wt Corr. Num. Cor. Rnd. Cor. Adj. Ang. A 80°14 ′ 04 ″ 2 3x 3 ″ 3 ″ 80°14 ′ 07 ″ B 38°37 ′ 47 ″ 1 6x 6 ″ 6 ″ 38°37 ′ 53 ″ C 61°07 ′ 58 ″ 3 2x 2 ″ 2 ″ 61°08 ′ 00 ″ 179°59 ′ 49 ″ 6 11x 11x =11 ″ x = 1 ″ 3.29 Determine relative weights and perform a weighted adjustment (to the nearest second) for angles A, B , and C of a plane triangle, given the following four observations for each angle: Angle A Angle B Angle C 38 47 58    71 22 26    69 50 04    38 47 44    71 22 22    69 50 16    38 48 12    71 22 12    69 50 30    38 48 02    71 22 12    69 50 10   