Elementary Surveying: An Introduction to Geomatics, 15th Edition Solution Manual

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TABLE OF CONTENTSPrefacevPart I:Solutions to Problems11Introduction22Units, Significant Figures, and Field Notes73Theory of Errors in Observations124Leveling Theory, Methods, and Equipment185Leveling — Field Procedures and Computations256Distance Measurement367Angles, Azimuths, and Bearings428Total Station Instruments; Angle Observations499Traversing5610Traverse Computations6111Coordinate Geometry in Surveying Calculations7312Area8013Global Navigation Satellite Systems—Introduction and Principles of Operation9014Global Navigation Satellite Systems—Static Surveys9515Global Navigation Satellite Systems—Kinematic Surveys10216Adjustment by Least Squares10717Mapping Surveys11918Mapping12519Control Surveys and Geodetic Reductions13020State Plane Coordinates and Other Map Projections13721Boundary Surveys15222Public Land Surveys16123Construction Surveying16524Horizontal Curves17325Vertical Curves19026Volumes20027Photogrammetry21028Introduction to Geographic Information Systems221Part II:Sample Introductory Course231Sample Syllabus232Sample Practical Exercises235Sample Quizzes239Quiz 1239Quiz 2239Quiz 3240Quiz 4240Quiz 5241Quiz 6242Sample Exams248

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PART I:SOLUTIONS TO PROBLEMS

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Solution Manual2Elementary Surveying: An Introduction to Geomatics1INTRODUCTIONNOTE:Answers for some of these problems, and some in later chapters, can be obtained byconsulting the bibliographies, later chapters, websites, or professional surveyors.1.1List 10 uses for surveying in areas other than boundary surveying.Answers may vary many are included in Section 1.6, which lists control, topographichydrographic, alignment, construction, as-built, mine, solar, optical tooling, ground,aerial, and satellite surveys. This list is not complete and could also include other types ofsurveys such as hydrographic surveys, for example.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 all measuredangles are presumed to be plane angles.1.3Describe some surveying applications in:(a)ArcheologyThere are many different uses of surveying in archeology. Some include using sonarto identify possible underground or underwater archeology sites, LiDAR to helpidentify possible ancient human settlements in unexplored forest and jungles, andtraditional surveying and laser scanning to help locate artifacts in site excavations.(b)Gas explorationThere are several stages of surveying in gas exploration, which include but are notlimited to determining anomalies in the gravity field, which identify possible gasdeposits, boundary surveys identifying properties that have mineral rights to the gasdeposits, alignment surveys for placement of pipelines to transport extracted gas.(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.

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1.4List some application of surveying in geology, forestry, and archeology.Applications in each are multiple. For some in geology and archeology see the answer toProblem 1.3 (a) and (b). Some uses of surveying in forestry identifying forest boundaries,locating spread of diseases and insects through remote sensing, using GIS to helpinventory and keep records on resources in forested regions.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 ifrepairsorservicingisneeded,andtopreventtheiraccidentaldestructionduringexcavation 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 surveying is associated with port andoffshore industries and the marine environment, including measurements and marineinvestigations made by ship borne personnel.1.8Print a view of your location using GoogleEarth.®Answers will vary but should be an image in your region.1.9BrieflyexplaintheprocedureusedbyEratosthenesindeterminingtheEarth’scircumference.From Section 1.3, paragraph 8 of text: His procedure, which occurred about 200 B.C., isillustratedinFigure1.3.EratostheneshadconcludedthattheEgyptiancitiesofAlexandria and Syene were located approximately on the same meridian, and he had alsoobserved 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 seenreflecting 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 couldmeasure the arc length between the two cities, and the angle it subtended at the earth'scenter,hecouldcomputetheearth'scircumference.Hedeterminedtheanglebymeasuring the length of the shadow cast at Alexandria from a tall vertical staff of knownlength. The arc length was found from multiplying the number of caravan days betweenSyene and Alexandria by the average daily distance traveled. From these measurements

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Solution Manual4Elementary Surveying: An Introduction to GeomaticsEratosthenes calculated the earth's circumference to be about 25,000 mi. Subsequentprecisegeodeticmeasurementsusingbetterinstruments,buttechniquessimilargeometrically to Eratosthenes', have shown his value, though slightly too large, to beamazingly 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.1.11What is the name of the state-level professional surveying organization in your state orregion?Answer will vary by location.1.12What organizations in your state 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 or county highway department (4) Department ofTransportation, (5) Department of 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 your licensing board can be found on the NCEESwebsite athttp://www.ncees.org/licensure/licensing_boards/.1.14Briefly describe an Earth-Centered, Earth-Fixed coordinate system.From Section 1.4 and 13.4.3, a ECEF coordinate system is an Earth-based three-dimensional coordinate system with its origin a the mass-center of the Earth, itZaxisaligned with the semi-minor (spin) axis of the Earth defined at some epoch, itXaxis inthe plane of the equator passing through mean Greenwich meridian, and itYaxis in theplane of the equator and creating a right-handed coordinate system. At this stage of theirintroduction to surveying it should be sufficient for students to simply know that it is anEarth-based three-dimensional coordinate system.1.15List the professional societies representing the geospatial industry in the(a)United States.There are several including AAGS, ASCE, ASPRS, GLIS, NSPS, and SaGES.(b)Canada.Canadian Institute of Geomatics (CIG)

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(c)International.International Federation of Surveyors (FIG)1.15Explain 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.1.16Search the Internet and define a Very Long Baseline Interferometry (VLBI) station.Discuss why these stations are important to the geospatial industry.VLBI stands for Very 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 ITRF08 and thus provide a worldwidecoordinate system that links continents. They also may provide tracking information forsatellites.1.17Describe 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.Visit one of the surveying websites 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 software1.19·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 otherGPS related links·National Society of Professional Surveyors – professional organization for boundaryand construction·American Association for Geodetic Surveying – professional organization for controlsurveying·Geographic and Land Information Society – professionalorganization for developersand users of geographic and land information systems

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Solution Manual6Elementary Surveying: An Introduction to Geomatics·AmericanSocietyforPhotogrammetryandRemoteSensing–professionalorganization for photogrammetry and remote sensing·The Pearson Prentice Hall publishers access to software and support materials thataccompany this book.·SaGES – An organization to advance surveying/geomatics education1.20Read one of the articles cited in the bibliography for this chapter, or another of yourchoosing, that describes an application where satellite surveying methods were used.Write a brief summary of the article.Answer will vary.1.21Same as Problem 1.20, except the article should be on safety as related to surveying.Answers will vary but should be related to safety issues in surveying.

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1.20Read one of the articles cited in the bibliography for this chapter, or another of yourchoosing, that describes an application where satellite surveying methods were used.Write a brief summary of the article.Answers will vary. Students should be told to look in trade journals for articles.1.21Same as Problem 1.20, except the article should be on safety as related to surveying.Answers will vary. Students should be told to look in trade journals for articles.

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Instructor’ Solution Manual7Elementary Surveying: An Introduction to Geomatics2UNITS, 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 international foot), 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, orradian)2.3The easting coordinate for a point is 725,316.911 m. What is the coordinate using the(a)Survey foot definition?(b)International foot definition?(c)Why was the survey foot definition maintained in the United States?(a)2,379,643.90 sft;725,316.911(39.3712)= 2,379,643.899 sft(b)2,379,648,66 ft;725,316.911/0.3048 = 2,379,648.658 ft(c)From Section 2.2: “Because of the vast number of surveys performed prior to 1959,it would have been extremely difficult and confusing to change all relateddocuments and maps that already existed. Thus the old standard, now called theU.S.survey foot, is still used.”2.4Convert the following distances given in meters to U.S. survey feet:*(a)4129.574 m13,548.44 sft(b)588.234 m1929.90 sft(c)102,302.103 m335,636.15 sft

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8Solution ManualElementary Surveying: An Introduction to Geomatics2.5Convert the following distances given in survey feet to meters:*(a)537.52 sft163.836 m(b)2,405,687.82 sft733,255.114 m(c)5783.12 sft1762.699 m or 1762.70 m2.6Compute the lengths in survey feet corresponding to the following distances measuredwith a Gunter’s chain:*(a)10 ch 13 lk668.6 sft(b)56 ch 83 lk3750.8 sft(c)124 ch 35 lk8207.1 sft2.7Express5,377,700 sft2in:*(a)acres123.46 ac(b)hectares49.961 ha(c)square Gunter’s chains1234.6 sq. ch.2.8Convert 23.4587 ha to:(a)square survey feet2,525,070 sft2(b)acres57.9676 ac(b)square Gunter’s chains579.676 sq. ch2.9What are the lengths in feet and decimals for the following distances shown on abuilding blueprint:(a)12 ft 6-1/4 in.12.5 ft601/4/12(b)10 ft 6-1/2 in.10.5 ft253/2/122.10What 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)16 ch 78 lk and 52 ch 49 lk88.08 ac2.11Compute the area in acres of triangular lots shown on a plat having the followingrecorded right-angle sides:(a)335.36 ft and 804.02 ft3.0945 ac(b)93.064 m and 30.346 m0.69785 ac2.12A distance is expressed as 9756.12 sft. What is the length in*(a)international feet?9756.14 ft(b)meters?2973.67 m2.13What are the radian and degree-minute-second equivalents for the following anglesgiven in grads:

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Instructor’ Solution Manual9Elementary Surveying: An Introduction to Geomatics(a)*136.000 grads𝟏𝟐𝟐°𝟐𝟒′𝟎𝟎"; 2.13628 rad(b)115.089 grads𝟏𝟎𝟑°𝟑𝟒′𝟓𝟎″; 1.80781 rad(c)363.809 grads𝟑𝟐𝟕°𝟐𝟓′𝟒𝟎″; 5.71469 rad2.14Give answers to the following problems in the correct number of significant figures:*(a)sum of 23.15, 0.984, 124, and 12.5161(b)sum of 2.115, 23.04, 13.8, and 199.66238.6(c)product of 127.08 and 13.11660(d)quotient of 4466.83 divided by 35.61125.42.15Express the value or answer in powers of 10 to the correct number of significant figures:(a)4586.494.58679 × 103(b)24502.45 × 103(c)square of 199.993.9996 × 104(d)sum of (32.087 + 1.56 + 206.44) divided by 2.31.95 × 1012.16Convert the angles of a triangle to radians and show a computational check:*(a)39°41′54, 91°30'16", 48°47′50"0.692867, 1.59705,and0.8516720.6928666 + 1.597054 + 0.8516721 = 3.14159 check(b)96°23'18, 44°56′53", 38°39′49"1.68229, 0.784492, and0.6748071.682294 + 0.784492 + 0.674807 = 3.14159 check2.17Why should a ball point pen not be used in field notekeeping?From Section 2.7: "Books so prepared (with 3h or higher pencil) will withstand dampweather in the field (or even a soaking) and still be legible, whereas graphite from asoft pencil, or ink from a pen or ballpoint, leaves an undecipherable smudge undersuch 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 wouldraise the issue of what are you hiding, legibility since the numbers are often hard tointerpret when 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 thetime of the measurements to avoid loss of data.2.20Why should the field notes show the precision of the measurements?

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10Solution ManualElementary Surveying: An Introduction to GeomaticsField notes should show the precision of the measurements made to indicate theaccuracy of the measurements.2.21Explain the reason for item 7 in Section 2.11 when recording field notes.In general a sketch will show more than a table of numbers. As the saying goes, “Apicture is worth a thousand words.”2.22Explain the reason for item 13 in Section 2.11 when recording field notes.A standard set of symbols and signs improve the clarity of drawings.2.23Explain 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.2.24When 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 why data should always be backed up at regular intervals.From Section 2.13, paragraph 1: “At regular intervals, usually at lunchtime and at theend of a day’s work, or when a survey has been completed, the information stored infiles within a data collector is transferred to another device. This is a safety precautionto avoid accidentally losing substantial amounts of data.”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 students.

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Instructor’ Solution Manual11Elementary Surveying: An Introduction to Geomatics2.29Why do many survey controllers contain digital cameras?From Section 2.15: “Many modern survey controllers also contain digital cameras thatallow field personnel to capture a digital image of the survey.”2.30What are the dangers involved in using a survey controller?From Section 2.15: “Although survey controllers have many advantages, they alsopresent some dangers and problems. There is the slight chance, for example, the filescould be accidentally erased through carelessness or lost because of malfunction ordamage to the unit.”2.31Describe what is meant by the phrase “field-to-finish.”From Section 2.15, "The field codes can instruct the drafting software to draw a mapof the data complete with lines, curves and mapping symbols. The process ofcollecting field data with field codes that can be interpreted later by software is knownas 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 sketchesare simply to provide readers of the notes an approximate visual reference to themeasurements.

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12Solution ManualElementary Surveying: An Introduction to Geomatics3THEORY OF ERRORS IN OBSERVATIONS3.1Discuss the difference between an error and a residual.From Section 3.3, an error is the difference between the observation and its true value,or𝐸 = 𝑋 − 𝑋̅whereas a residual, which is defined in Section 3.11 is the differencebetween the mean of a set of observations and the observation or𝑣 = 𝑀̅ − 𝑀3.2Give two examples of(a)direct and(b)indirect measurements.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.3.3Define the termsystematic error, and give two surveying examples of a systematic error.See Section 3.63.4Define the termrandom error, and give two surveying examples of a random error.See Section 3.63.5Discuss the difference between accuracy and precision.From Section 3.7, accuracy is the nearness of the observed quantities to the true value,which is never known. Precision is the degree of refinement or consistency of a groupof observations and is evaluated on the basis of discrepancy size.3.6The observations of 124.53, 124.55, 142.51, and 124.52 are obtained when taping thelength of a line. What should the observer consider doing before a mean length isdetermined from the set of observations?It appears that the observation 142.51 is an outlier and a possible mistake in the dataset. The observer should collect another tape observation of the line and discard theoffending observation(s).A distanceABis observed repeatedly using the same equipment and procedures, and the results,in meters, are listed in Problems 3.7 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.*3.765.401, 65.400, 65.402, 65.396, 65.406, 65.401, 65.396, 65.401, 65.405, and 65.404(a)65.401∑654.012

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Solution Manual13Elementary Surveying: An Introduction to Geomatics(b)±0.003∑ν2= 0.000091(c)±0.0013.8Same as Problem 3.7 but discard only one 65.396 observation.(a)65.402∑588.616(b)±0.003∑ν2= 0.000064(c)±0.00093.9Same as Problem 3.7, but discard both 65.396 observations.(a)65.402∑523.220(b)±0.002∑ν2= 0.000030(c)±0.00073.10Same as Problem 3.7, but include two additional observations, 65.402 and 65.405.(a)65.402∑784.819(b)±0.003∑ν2= 0.000115(c)±0.0009In Problems 3.11 through 3.14, determine the range within which observations shouldfall (a) 90% of the time and (b) 95% of the time. List the percentage of values that actually fallwithin these ranges.3.11For the data of Problem 3.7.*(a)65.4012±0.0052(65.3960, 65.4064), 100%(b)65.4012±0.0062(65.3950, 65.4074), 100%3.12For the data of Problem 3.8.(a)65.4018±0.0046(65.3971, 65.4064), 90%, 65.396 outside of range(b)65.4018±0.0055(65.3963, 65.4073), 90%, 65.396 outside of range3.13For the data of Problem 3.9.(a)65.4025±0.0034(65.3991, 65.4059), 90%, 65.406 outside of range(b)65.4025±0.0040(65.3985, 65.4065), 100%3.14For the data of Problem 3.10.(a)65.4016±0.0053(65.3963, 65.4069), 83.3%, both 65.396 outside of range(b)65.4016±0.0063(65.3952, 65.4079), 100%

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