Solution Manual For Elementary Surveying: An Introduction To Geomatics, 13th Edition

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61INTRODUCTION1.1Develop your personal definition for the practice of surveying.Answers will vary by response. See Section 1.1 for book definitions.1.2Explain the difference between geodetic and plane surveys.From Section 1.4,In geodetic surveys the curved surface of the earth is considered by performing thecomputations on an ellipsoid (curve surface approximating the size and shape of theearth). In plane surveys, except for leveling, the reference base for fieldwork andcomputations 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 allmeasured angles are presumed to be plane angles.1.3Describe some surveying applications in:(a)ConstructionIn construction, surveying is used to locate the precise location of structures such asroads, 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 relevantlegal, economic, environmental, and social aspects affecting each project."(b)MiningIn mining, surveying is used to direct the locations of mining activities according to asystematic plan, to make sure mining occurs within the boundaries of the claim, toconnect tunnels and shafts, and to provide legal records of mining activities.(c)AgricultureIn agriculture, surveying is used to determine the acreage of fields, to locate lines ofconstant elevation for strip farming, to track harvesting machinery to enable the sizeof the harvest, and to track the position of the planting equipment to allow for preciseapplications of seeds and fertilizers. The field is known as high-precision agriculture.1.4List 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.

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74.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 photogrammetryor laser scanning.10.Mapping of accident sites in forensic surveying.1.5Why 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 ifrepairs or servicing is needed, and to prevent their accidental destruction duringexcavation for other projects.1.6Discuss 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 forconstruction surveys; (3) creating maps for flood plain delineation; (4) creating maps forsite location of buildings; and so on.1.7What 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 surveyingis associated with port andoffshore industries and the marine environment, including measurements and marineinvestigations made by ship borne personnel.1.8Name and briefly describe three different surveying instruments used by early Romanengineers.From Section 1.3: (1) gromma, (2) libella, and (3) chorobates.1.9BrieflyexplaintheprocedureusedbyEratosthenesindeterminingtheEarth’scircumference.From Section 1-3, paragraph 8 of text: His procedure, which occurred about 200 B.C., isillustrated in Figure 1-2. Eratosthenes had concluded that the Egyptian cities of Alexandriaand Syene were located approximately on the same meridian, and he had also observed thatat noon on the summer solstice, the sun was directly overhead at Syene. (This was apparentbecause at that time of that day, the image of the sun could be seen reflecting from thebottom of a deep vertical well there.) He reasoned that at that moment, the sun, Syene, andAlexandria were in a common meridian plane, and if he could measure the arc lengthbetween the two cities, and the angle it subtended at the earth's center, he could computethe earth's circumference. He determined the angle by measuring the length of the shadowcast at Alexandria from a tall vertical staff of known length. The arc length was found frommultiplying the number of caravan days between Syene and Alexandria by the averagedaily distance traveled. From these measurements Eratosthenes calculated the earth's

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8circumference to be about 25,000 mi. Subsequent precise geodetic measurements usingbetter instruments, but techniques similar geometrically to Eratosthenes', have shown hisvalue, though slightly too large, to be amazingly close to the currently accepted one.1.10Describe 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 ofproperty noting any encroachments; conflicting elements; and so on; (4) resolution ofconflicting elements between deed and survey; (5) delivery of surveying report to owner.1.11Do laws in your state specify the accuracy required for surveys made to lay out asubdivision? If so, what limits are set?Responses will vary1.12What organizations in your state will furnish maps and reference data to surveyors andengineers?Responses will vary but some common organizations are the (1) county surveyor, (2)register of deeds, (3) county engineer, (4) Department of Transportation, (5) Departmentof Natural Resources of its equivalent, and so on.1.13List 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 NCEESwebsite at http://www.ncees.org/licensure/licensing_boards/.1.14Briefly describe the European Galileo system and discuss its similarities and differenceswith GPS.See Section 13.10.2. Students can look this information and much more with a websearch.1.15List at least five nonsurveying uses for GPS.Responses may include (1) logistics in transportation; (2) hunting; (3) location of cellphone calls; (4) timing of telecommunications networks; (5) navigation in the boatingindustry; and so on.

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91.16Explain how aerial photographs and satellite images can be valuable in surveying.Photogrammetry presently has many applications in surveying. It is used, for example, inland surveying to compute coordinates of section corners, boundary corners, or point ofevidence that help locate these corners. Large–scale maps are made by photogrammetricprocedures for many uses, one being subdivision design. Photogrammetry is used to mapshorelines, in hydrographic surveying, to determine precise ground coordinates of pointsin control surveying, and to develop maps and cross sections for route and engineeringsurveys. Photogrammetry is playing an important role in developing the necessary datafor modern Land and Geographic Information Systems.1.17Search the Internet and define a VLBI station. Discuss why these stations are importantto the surveying community.VLBI stands forVery Long Baseline Interferometry. Responses will vary. These stationsprovide extremely accurate locations on the surface of the Earth. The stations are used todevelop world-wide reference frameworks such as ITRF00. They also may providetracking information for satellites.1.18Describe 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 andtheir permeability with slopes, soil saturation, and watershed regions. A GIS can also beused to provide a list of business and residences that will be affected by possible floodingfor evacuation purposes. It can provide “best” routes out of a flooded region.1.19Visit one of the surveying web sites listed in Table 1.1, and write a brief summary of itscontents. 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) andother GPS related linksAmericanCongressonSurveyingandMapping(ACSM)–professionalorganization for surveying and mapping professionAmericanSocietyforPhotogrammetryandRemoteSensing–professionalorganization for photogrammetry and remote sensingThe Pennsylvania State University Surveying Program – Access to latest softwarethat accompanies this book.

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101.20Read one of the articles cited in the bibliography for this chapter, or another of yourchoosing, that describes an application where GPS was used. Write a brief summary ofthe article.Response will vary.1.21Same as Problem 1.20, except the article should be on safety as related to surveying.Responses will vary.

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112UNITS, SIGNIFICANT FIGURES, AND FIELD NOTES2.1List 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.2.2Give 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)2.3Why 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 vastnumber of surveys performed prior to 1959. It would have been extremely difficult andconfusing to change all related documents and maps that already existed. Thus the oldstandard, now call the U.S. survey foot, is still used today.2.4Convert the following distances given in meters to U.S. survey feet:*(a)4129.574 m13,548.44 ft(b)738.296m2422.23 ft(c)6048.083m19,842.75 ft2.5Convert the following distances given in feet to meters:*(a)537.52 ft163.836 m(b)9364.87ft2854.418 m(c)4806.98ft1465.170 m2.6Compute the lengths in feet corresponding to the following distances measured with aGunter’s chain:*(a)10 ch 13 lk668.6 ft(b)6ch 12 lk404 ft(c)24ch 8 lk1589 ft

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122.7Express 95,748 ft2in:*(a)acres2.1981 ac(b)hectares0.88953 ha(c)square Gunter’s chains21.981 sq. ch.2.8Convert 5.6874 ha to:(a)acres14.054 ac(b)square Gunter’s chains140.54 sq. ch2.9What are the lengths in feet and decimals for the following distances shown on abuilding blueprint:(a)30ft 9-3/4 in.30.81 ft(b)12ft 6-1/32 in.12.50 ft2.10What is the area in acres of a rectangular parcel of land measured with a Gunter’s chainif the recorded sides are as follows:*(a)9.17 ch and 10.64 ch9.76 ac(b)12ch 36 lk and 24 ch 28 lk30.01 ac2.11Compute the area in acres of triangular lots shown on a plat having the followingrecorded right-angle sides:(a)208.94ft and 232.65 ft0.55796 ac(b)9ch 25 lk and 6 ch 16 lk2.85 ac2.12A 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 m2.13What are the radian and degree-minute-second equivalents for the following anglesgiven in grads:*(a)136.00 grads122°24(b)89.5478grads80°35 35(c)68.1649grads61°20 542.14Give answers to the following problems in the correct number of significant figures:*(a)sum of 23.15, 0.984, 124, and 12.5160.(b)sum of 36.15, 0.806, 22.4, and 196.458255.8(c)product of 276.75 and 33.79330(d)quotient of 4930.27 divided by 1.2938202.15Express the value or answer in powers of 10 to the correct number of significantfigures:

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13(a)11,4321.1432 × 104(b)45204.52 × 103(c)square of 11,2931.2753 × 108(d)sum of (11.275 + 0.5 + 146.12) divided by 7.22.2 × 1012.16Convert 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,and0.8516720.6928666 + 1.597054 + 0.8516721 = 3.14059 check(b)82 17 43 , 29 05 54 , and 68 36 231.43632, 0.507862, and1.197411.436324 + 0. 5078617 + 1.197407 = 3.14159 check2.17Why should a pen not be used in field notekeeping?From Section 2.7: " Books so prepared will withstand damp weather in the field (oreven a soaking) and still be legible, whereas graphite from a soft pencil, or ink from apen or ballpoint, leaves an undecipherable smudge under such circumstances."2.18Explain why one number should not be superimposed over another or the lines ofsketches.From Section 2.7: This can be explained with the need for integrity since it would raisethe issue of what are you hiding, legibility since the numbers are often hard to interpretwhen so written, or by clarity since the notes are being crowded.*2.19Explain why data should always be entered directly into the field book at the timemeasurements are made, rather than on scrap paper for neat transfer to the field booklater.From Section 2.7: Data should always be entered into the field book directly at the timeof the measurements to avoid loss of data.2.20Why 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 wasaccomplished each day and to document an changes in the field crew, weather,instrumentation, and so on.2.21Explain 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.2.22Explain 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 thework to find the notes for a specific project, even if some notes come from previouswork.2.23Explain the reason for item 12 in Section 2.11 when recording field notes.

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14Explanatory notes are essential to provide office personnel with an explanation forsomething unusual and to provide a reminder in later reference to the project.2.24When should sketches be made instead of just recording data?Sketches should be made instead of recording data anytime observations need to beclarified so that the personnel interpreting the notes can have a clear understanding ofthe field conditions. This also serves as a reminder of the work performed and anyunusual conditions in later references to the project.2.25Justify the requirement to list in a field book the makes and serial numbers of allinstruments used on a survey.Listing the makes and serial numbers of the instruments used in the survey may helpisolate instrumental errors later when reviewing the project.2.26Discuss the advantages of survey controllers that can communicate with severaldifferent types of instruments.The ability of survey controllers to communicate with several different types ofinstruments allows the surveyor to match the specific conditions of the project with theinstrument that this is ideally suited for the job. Thus total station, digital levels, andGNSS receivers can all be used in a single project.2.27Discuss the advantages of survey controllers.From Section 2.15: " The major advantages of automatic data collection systems arethat (1) mistakes in reading and manually recording observations in the field areprecluded, and (2) the time to process, display, and archive the field notes in the officeis reduced significantly. Systems that incorporate computers can execute someprograms in the field, which adds a significant advantage. As an example, the data for asurvey can be corrected for systematic errors and misclosures computed, so verificationthat a survey meets closure requirements is made before the crew leaves a site."2.28Search 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.2.29What advantages are offered to field personnel if the survey controller provides a mapof the survey?This allows field personnel to view what has been accomplished and look for areas ofthe map that need more attention.

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152.30Prepare a brief summary of an article from a professional journal related to the subjectmatter of this chapter.Answer should vary by student.2.31Describe what is meant by the phrase “field-to-finish.”From Section 2.15, " These field codes can instruct the drafting software to draw a mapof the data complete with lines, curves and mapping symbols. The process of collectingfield data with field codes that can be interpreted later by software is known as afield-to-finishsurvey. This greatly reduces the time needed to complete a project."2.32Why are sketches in field books not usually drawn to scale?This is true since this would require an overwhelming amount of time. The sketches aresimply to provide readers of the notes an approximate visual reference to themeasurements.2.33Create a computational program that solves Problem 2.16.Answers to this problem should vary with students.

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163THEORY OF ERRORS IN OBSERVATIONS3.1Explain the difference betweendirectandindirectobservationsin surveying. Give twoexamples of each.From Section 3.2: A direct observation is made by applying a measurement instrumentdirectly to a quantity to be measured and an indirect observation is made by computinga quantity from direct observations.Examples should vary by student response.3.2Define the termsystematic error, and give two surveying examples of a systematic error.See Section 3.63.3Define the termrandom error, and give two surveying examples of a random error.See Section 3.63.4Explain the difference between accuracy and precision.See Section 3.73.5Discuss what is meant by the precision of an observation.See Section 3.7A distanceABis observed repeatedly using the same equipment and procedures, and theresults, in meters, are listed in Problems 3.6 through 3.10. Calculate(a)the line’s most probablelength,(b)the standard deviation and(c)the standard deviation of the mean for each set of results.*3.665.401, 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∑ν2= 0.000104(c)±0.0013.7Same as Problem 3.6, but discard one observation, 65.396.(a)65.402∑588.616(b)±0.003∑ν2= 0.000072(c)±0.001

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173.8Same as Problem 3.6, but discard two observations, 65.396 and 65.406.(a)65.402∑523.210(b)±0.003∑ν2= 0.00007168(c)±0.0013.9Same as Problem 3.6, but include two additional observations, 65.398 and 65.408.(a)65.401∑784.818(b)±0.004∑ν2= 0.000157(c)±0.0013.10Same as Problem 3.6, but include three additional observations, 65.398, 65.408, and65.406.(a)65.402∑850.224(b)±0.004∑ν2= 0.0001757(c)±0.001In 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 withinthese ranges.(a) E90= 1.6449σ(3.7)(b) E95= 1.9599σ(3.8)3.11For 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%3.12For 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%3.13For 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%3.14For 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%

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18In Problems 3.15 through 3.17, an angle is observed repeatedly using the same equipmentand procedures. Calculate(a)the angle’s most probable value,(b)the standard deviation, and(c)the standard deviation of the mean.*3.1523°30 00 , 23°29 40 , 23°30 15 ,and23 29 50.(a) 23°29′56″(b) ±14.9″(c) ±7.5″3.16Same as Problem 3.15, but with three additional observations, 23 29 55 , 23 30 05 ,and23 30 20 .(a) 23°30′01″(b) ±14.0″(c) ±5.3″3.17Same as Problem 3.16, but with two additional observations,23 30 05and23 29 55.(a) 23°30′56″(b) ±12.4″(c) ±4.1″*3.18A field party is capable of making taping observations with a standard deviation of0.010 ftper 100-ft tape length. What standard deviation would be expected in adistance of 200 ft taped by this party?By Equation (3.12):±0.014 ft0.01023.19Repeat Problem 3.18, except that the standard deviation per 30-m tape length is0.003 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= 0.0034;By Equation (3.8):±0.0181.9559 0.0063.20A distance of 200 ft must be taped in a manner to ensure a standard deviation smallerthan0.04ft. What must be the standard deviation per 100 ft tape length to achieve thedesired precision?±0.028 ft=0.042by Equation (3.12) rearranged.3.21Lines of levels were run requiringninstrument setups. If the rod reading for eachbacksight and foresight has a standard deviation,what is the standard deviation ineach of the following level lines?(a)26,0.010 ftn  By Equation (3.12):±0.051 ft=0.01026

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19(b)36,3 mmn  By Equation (3.12):±18 m=3363.22A lineACwas observed in 2 sectionsABandBC, with lengths and standard deviationslisted below. What is the total lengthAC, and its standard deviation?*(a)60.000.015ft;86.130.018 ftABBC;146.13±0.023 ftby Equation (3.11)(b)60.0000.008 m; 35.4130.005 mAB;95.413±0.0094 mby Equation (3.11)3.23LineADis observed in three sections,AB,BC, andCD, with lengths and standarddeviations as listed below. What is the total lengthADand its standard deviation?(a)572.120.02 ft;1074.380.03 ft;1542.780.05 ftABBCCD3189.28 ± 0.062 ftby Equation (3.11)(b)932.9650.009 m;945.030 m0.010 m;652.250 m0.008 mABBCCD2530.245 ± 0.016 mby Equation (3.11)3.24A distanceABwas observed four times as 236.39, 236.40, 236.36 and 236.38 ft. Theobservations were given weights of 2, 1, 3 and 2, respectively, by the observer. *(a)Calculate the weighted mean for distanceAB. (b) What difference results if laterjudgment revises the weights to 2, 1, 2, and 3, respectively?By Equation (3.17):*(a)236.3775 ft(b)236.3850 ft3.25Determine 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 58 323 ; 36 58 282 ; 36 58 263 ; 36 58 30136°58′29.5″3.26Specifications for observing angles of ann-sided polygon limit the total angularmisclosure toE. How accurately must each angle be observed for the following valuesofnandE?By rearranged Equation (3.12):(a)10,8nE±2.5″(b)6,14nE±5.7″3.27What is the area of a rectangular field and its estimated error for the following recordedvalues:By Equation (3.13):*(a)243.890.05 ft, by 208.650.04 ft50,887 ± 14 ft2or1.1682 ± 0.0003 ac

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20(b)725.330.08 ft by 664.210.06 ft481,770 ± 70 ft2or11.060 ± 0.002 ac(c)128.5260.005 m, by 180.4030.007 m23,186.5 ± 1.3 m2or20.1865 ± 0.0001 ha3.28Adjust the angles of triangleABCfor 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 3ABCMisclosure =−22″Obs. Ang.WtCorr.Num. Cor.Rnd. Cor.Adj. Ang.A49°24′22″23x6″6″49°24′28″B39°02′16″16x12″12″39°02′28″C91°33′00″32x4″4″91°33′04″179°59′38″611x11x = 22″x = 2″(b)80 14 04 , wt 2;38 37 47 , wt 1;61 07 58 , wt 3ABCMisclosure =−11″Obs. Ang.WtCorr.Num. Cor.Rnd. Cor.Adj. Ang.A80°14′04″23x3″3″80°14′07″B38°37′47″16x6″6″38°37′53″C61°07′58″32x2″2″61°08′00″179°59′49″611x11x =11″x = 1″3.29Determine relative weights and perform a weighted adjustment (to the nearest second)for anglesA, B, andCof a plane triangle, given the following four observations for eachangle:AngleAAngleBAngleC38 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

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