1.1 SURVEYING 1.2 GEOMATICS Introduction Surveying has been with us for several thousand years, It is the science of determining the dimensions and contour (or three-dimensional characteristics) of the earth's surface by measure- ‘ment of distances, directions, and elevations. Surveying also includes staking out the lines and srades needed for the construction of buildings, roads, dams, and other structures, In addition 10 these field measurements, surveying includes the computation of areas, volumes, and other ‘quantities, as well as the preparation of necessary maps and diagrams, In the past few decades there have been almost unbelievable advances in the technology used for measuring, collecting, recording, and displaying information concerning the earth. For instance, ‘until recently, surveyors made their measurements with steel tapes, angle-measuring devices called transits and theodolites, and elevation equipment called levels. In addition, the measurements obtained were presented with laboriously prepared tables andl maps. "Today the surveyor predominantly uses electronic instruments to automatically measure, display, and record distances and positions of points, Computers are used to process the measured data and produce needed maps and tables with tremendous speed. “These developments have contributed to great progress in many other areas including geographic information systems (GIS), land information systems (LIS), the global positioning system (GPS), remote sensing, and others. As a result, many persons have long had a feeling that the word surveying, ‘was not adequate to represent all these new activities along with the traditional work of the surveyor. In 1988 the Canadian Association of Aerial Surveyors introduced the term geomaties to encompass the disciplines of surveying, mapping, remote sensing, and geographic information systems. ‘Surveying is considered to be a part of this new discipline. "There are quite a few definitions of geomatics floating around as might be expected, considering the term’s relative infancy. With each of the definitions, however, there is a common theme and that is “working with spatial data.” ‘The word spatial refers to space and the words “spatial data” refer to data that can be linked to specific locations in geographic space. In this text, geomatics is defined as being an integrated approach to the measurement, analysis, management, storage, and presentation of the descriptions and locations of spatial data. The term geomatics is rapidly being accepted in the English-speaking world, particularly in the colleges and universities of the United States, Canada, ‘Australia, and the United Kingdom. Some schools now offer degrees in geomatics. ‘Although this text is primarily concemed with surveying, the reader needs to understand that surveying is partof the very large, moder, and growing field of geomatics. As result, muchemphasis, is given herein to modem surveying equipment and methods for gathering and processing data. 1.3 FAMOUS SURVEYORS ‘Many famous persons in our history were engaged in surveying at some period in their lives Particularly notable among these are several presidents—Washington, Jefferson, and Lincoln,2 Chapter 1 Introduetion [Although the practice of surveying will not provide a sure road to the White House, many members of the profession like to think thatthe characteristics of the surveyor (honesty, perseverance, self- reliance, ete.) contributed to the development of these leaders. Today, surveying is an honored and. Widely respected profession. A knowledge of its principles and ethies is useful to a person whatever his or her future endeavors will be.' AA large number of surveyors, other than presidents, have served our country well. Included are persons such as Andrew Ellicott (who surveyed several of our state boundaries and designed the beautiful streets of Washington, D.C.), David Ritten-house (a far -yor, elockmaker, ‘and one of our earliest surveying instrument makers), and General Rufus Putman (an aide to General Washington during the Revolutionary War and the first Surveyor General of the United States). Surveying provided Henry David Thoreau (of Walden Pond fame) with his living for over a decade, ‘The highest mountain in the world is named fora surveyor, Colonel Sir George Everest. Everest was famous for his work as superintendent of the Great Trigonometrical Survey of India, It is not known whether or not George Everest ever saw the mountain that bears his name, but his ‘eiangulation network that was part of the Great Survey was extended and used to locate the summit by Andrew Waugh, Everest’s successor as Surveyor General in India. Waugh's admiration of Everest’s achievements led to the naming of “Peak XV" in the Himala Many other famous surveyors are mentioned throughout this book 14 EARLY HISTORY OF SURVEYING {tisimpossibl to determine when surveying was frst used, but in ts simplest form its surely as old a recorded civilization. As long as there has been property ownership, there have been means of ‘measuring the property or distinguishing one person's land from anokher. The Babylonians surely Practiced some type of surveying as early as 2500 B.C., because archaeologists have found Babylonian maps on tablets ofthat estimated age, Evidence has also been found in the historical Fecords of India and China that show that surveying was practiced in those countries in the same time period, ‘The early development of surveying cannot be separated from the development of aston- Om astrology, or mathematies because these disciplines were so closely interrelated. Infact the term geometry is derived from Greek words meaning earth measurements. The Greek historian Herodotus (‘the father of history”) says that surveying was used in Egypt as early as 1400 B.C. Men that country was divided into plots for taxation purposes. Apparently, geometty of Where as particularly necessary in the Nile valley to establish and control landmarks. hen the yearly loods of the Nile swept away many ofthe landmarks, surveyors were appointed they and seats These surveyors were called harpedonapata, ot “rope stretchers” becalse Hts ropes (with markers or Knots in them at certain designated intervals) for theit Dating this same period surve construction of itigation systems, apparently quite satisfactory, Forint only about 8 in for a 750-ft base 'Yors were certainly needed for assistance in the design and huge pyramids, public buildings, and so on, Their work was ane, the dimensions ofthe Great Pyramid of Gizeh are in ert0t lis i ; ; Pyramid bases with thee ropes and che Lene ete Ope stretchers Laid off the sides ofthe the almost level foundations of the ‘heeked squareness by measuring diagonals. In order to obi se great structures, the Egyptians probably either poured water ms radperson the oe of women inthe {Source htp/tawa suneyhison ors gere °C.M. Brova, W.G, RobillatandD. A Wi Joho Wiey Som nes BI gag NN iene ond Procedures for Benda Lecaton, 2a (New Yor everest htm accessed January, 2011ee 1.4 Early History of Surveying 3 Pram tine Sake Ancient leveling fame Figure 1-1 Ancient leveling frame. into long, narrow clay troughs (an excellent method) of used triangular frames with plum bobs or ‘other weights suspended from their apexes as shown in Figure 1-1.* ‘Each leveling frame apparently had a mark on its lower bar that showed where the plumb line should be when that bar was horizontal. These frames, which were probably used for leveling for many centuries, could easily be checked for proper adjustment by reversing them end for end. If the plumb lines returned to the same points, the instruments were in proper adjustment and the tops of the supporting stakes (see Figure 1-1) would be at the same elevation, “The practical-minded Romans introduced many advances in surveying by an amazing series of engineering projects constructed throughout their empire. They laid out projects such as cities military camps, and roads by using system of rectangular coordinates. They surveyed the principal routes used for military operations on the European continent, inthe British Isles, in northern Africa, ‘and even in parts of Asia. ‘Three instruments used by the Romans were the odometer, or measuring wheel, the groma, and the chorobate. The groma, from which the Roman surveyors received their name of gromatici, was ‘used for laying off right angles. It consisted of two cross-arms fastened together at right angles in the Shape of « horizontal cross, with plumb bobs hanging from each of the four ends (see Figure 1-2). ‘The groma, which was pivoted eccentrically on a vertical staff, would be leveled and sights taken along its cross-arms in line with the plumb-bob strings. "The chorobate (Figure 1-3) was an approximately 20-ft-long wooden straight edge with supporting legs. Ithad a groove of trough cut into its top to hold water so that it could be used as a level Figure 1-2 Groma, a Roman surveying device used for laying off right angles TAR Legault HM MeMaser and RR, Malet, Surveying (Englewood Cif, NJ: Prentice-Hall. Ine.4 Chapter 1 Se cin vhs wu pnd Wea bar eereieT ‘so water stood evenly t —| ve es brat) Powe ZZ Appa. 20f, J-——________ Amma igure 1-3. Chorobate, another Roman surveying device, From Roman times until the modem era there were few advances in the ar of surveying, but the last few centuries have seen the introduction of the telescope, vernier, theodolite, electronic . Ess respectively, the total probable error can be computed from the following equation: Euan = SVR + RHE Not coincidently, this equation reduces to Eiyai = +EV A when Ey=E>= . . Ey. Example 2.5 illustrates the application of this equation EXAMPLE 2. SOLUTION ‘The four approximately equal sides of a tract of land were measured. ‘These: measurements included the following probable errors: +£0.09 f, 10.013 ft, +0.18 ft, and +0.40 f, respectively. Determine the probable error for the total length or perimeter of the tract. Pats Eau ~ + (0.09) + (0.013) + (0.18)? + (040 — 20.458 The reader should carefully note the results of the preceding calculations, where the uncertainty in the total distance measured (0.45 1) isnot very different from the uncertainty ttiven for the measurement of the fourth side alone (0.40). 11 should be obvious that there is a litle advantage in making very careful measurements for some of a group of quantities and not for the others. 2.11 SIGNIFICANT FIGURES ‘This section might also be entitled “judgment” or “sense of proportion.” and its comprehension is a very necessary part of the training of anyone who takes and/or uses measured quantities of any kind. When measurements are made, the results can be precise only to the degree that the measuring instrument is precise. This means that numbers that represent measurements are all approxi values. For instance, a distance may be measured with a steel tape as being 465 ft, or more precisely 8 465.3 f, or with even more care as 465.32 ft, butan exact answer can never be obtained. The value ‘will always contain some error. ‘The number of significant figures that a measured quantity has is not (as is frequently thought) the mumber of decimal places. Instead, it is the nurnber of certain digits plus one digit that is estimated. For instance, in reading a steel tape a point may be between 34.2 and 34.3 ft (the scale being marked at the 1/10-ft points) and the value is estimated as being 34.26 ft. The answer has four significant figures. Other examples of significant figures follow: 36,00620 has seven significant figures. 10.0 has three significant figures. (0.003042 has four significant figures, ‘The answer obtained by solving any problem can never be more accurate than the information, used. If this principle is not completely understood, results will be slovenly. Notice that it is not reasonable to add 23.2 cu yd of concrete to 31 cu yd and get $4.2 cu yd. One cannot properly express the total to the nearest tenth of a yard as 54.2 because one of the quantities was not computed to the nearest tenth and the correct total should be 54 cu yd. A few general rules regarding significant figures follow 1, Zeros between other significant figures are significant, as, for example, in the following numbers, each of which contains four significant figures: 23.07 and 3008,2.12 FIELD NOTES Binet Introduction to Measurements 2. For numbers less than unity, zeros immediately to the right of the decimal are not significant. They merely show the poston of the decimal, The number 0.0034 has two significant figures 3 Zeros placed atthe end of decimal numbers, such ss 243200, ae significant 4. When a number ends with one or more zr0s to the let ofthe decimal it is necessary to indicate the exact numberof significant figures, The number 35 2.000 could have three, four, five, or six significant figures. It could be written as 352,000, which has three Significant figures, or as 35 2,00, which has six significant figures. It is also possible to handle the problem by using scientific notation. The number 2.500 x 10° has four significant figures, andthe auraber 2.50 10° has thre. When numbers are multiplied or divided or both, the answer should not have more Siificant figures than hoe inthe factor, which has the lest number of significant figures, As an illustration, the folowing calculations should result in an answer having three significant igues, which is the number of significant gues in the term 3.25, 3.25 x 4.6962 8.1002 x 6.153 ~ 9306 33,842 361.3 81124 476.382 = 476.4 7. : a a ; E 3 : 5 2 BS : laryesicg ® to some length to emphasize this aspect of. Formost of surveying history feld data were h ‘ decades, however. this precedon faite 1nd printed in special field books. In the past few fer surveying matically changed as au with moxk ineents have coe aa Re et llestersineraed noses ill an mporan topic and wll png automatic dita collectors sncused nee Giscused in his section, The cos of keeping a surveying crew or pry n he lodging i may ran as high a $1,000 per cg a Held Confusing, mich ine and money 10 repeat some oral ofthe monk This absolutly essential for re evemeless, the use of hand printed 1 cea 30 fF Bond many more years. The use of HEX ection ofthis chapter while hand printed notes are212 Field Noes 25 Field books may be bound or loose-leaf, but bound books are usually used. Although it seems that the loose-leaf types have all the advantages (such as the capability of having their pages rearranged, fled, moved in with other sets of notes, shifted back and forth between the field and the office), the bound ones are more commonly used because of the possibility of losing some of the loose-leaf sheets. Long-life bound books capable of withstanding rough use and bad weather situations are the usual choice. ‘There are several kinds of field notebooks available, but the usual ones are 4 5/8 in. x 7 1/4 in... size that can easily be carried in a pocket. This characteristic is quite important because the surveyor needs his hands for other work. Examples of field-book notes are shown throughout the text, the first. ‘one being Figure 3-1 in the next chapter. A general rule is that measured quantities are shown on the left-hand pages, and sketches and miscellaneous notes are shown on the right-hand pages. In keeping notes the surveyor should bear in mind that on many occasions (particularly in large organizations) persons not familiar with the locality will make use of the notes. Some details may ‘appear so obvious to the surveyor that he or she does not include them, but they may not be obvious at all to someone back in the office. Therefore, considerable effort should be made to record all the information necessary for others to understand the survey clearly. With practice the information needed in the field notes will be learned. ‘An additional consideration is that surveying notes are often used for purposes other than the cone for which they were originally developed, and therefore they should be carefully preserved. To ‘maintain good field notes is not an easy task. Students are often embarrassed in their first attempts at ‘making accurate and neat notes, but with practice the ability can be developed. The following items are absolutely necessary for the successful recording of surveying information: 1. The name, address, and phone number of the surveyor should be printed in ink on the inside and outside of the field-book cover. 2. The title ofthe job, date, weather, and location should be recorded. When surveying notes are being used in the office, it may be helpful to know something of the weather conditions atthe time the measurements were taken. This information will often be useful in judging the accuracy of a particular survey, Was it 110°F or ~10°F? Was it raining? Were strong winds blowing? Was it foggy or dusty or snowing? 3. The names of the party members, together with their assignments as instrument man ( rodman (@), notekeeper (N), and So on should be recorded. As a minimum the first initial ‘and full last name of each person should be provided, Sometimes court cases require that, these persons be interviewed many years after a survey is done. 4. Field notes should be organized in a form appropriate tothe type of survey. Because other people may very well use these notes, generally standard forms are used for each of the different types of surveys. If each surveyor used his or her own individual forms for all, surveys, there would be much confusion back in the office. Of course, there are situations where the notekeeper will have to improvise with some style of nonstandard notes. Measurements must be recorded in the field when taken and not trusted t0 memory or written on scraps of paper to be recorded at a later date. Sometimes itis necessary to copy information from other field notes. In such cases the word “COPY” should be clearly marked on each page with a note giving the source. (6. Frequent sketches are used where needed for clarity, preferably drawing lines with a straightedge. Because field books are relatively inexpensive compared to the other costs of surveying, crowding of sketches or other data does not really save money. (The sketches need not always be drawn to scale, as distorted sketches may be better for clearing up questions.) 7. Field measurements must not be erased when incorrect entries are made. A line should be drawn through the incorrect number without destroying its legibility and the corrected value written above or below the old value, Erasures cause suspicion that there has been some dishonest alteration of values, but a crossed-out number is looked upon as an open26 Chapter? Introduction to Measurements ‘admission of a blunder. (Imagine a property case coming up for court litigation and a surveying notebook containing frequent erasures being presented for evidence.) It is a ‘200d idea to use a red pencil for making additions to the notes back in the office to distinguish them clearly from values obtained in the field. 8 Notes are printed with a sharp medium-hard (3H or 4H) pencil so that the records will be relatively permanent and will nt smear. Field books are generally used in damp and dirty situations and the use of hard pencils will preserve the notes A clipboard and acclear plastic sheet of acetate can minimize field weather problems, The lettering used on sketches is to be arranged so that it can be read from the bottom of the page or the right-hand side. 9 The type of instrument and its number should be recorded with each day's work. It may Inter be discovered thatthe measurements taken wit that instrument contained significant €rrors that could not be accounted for in any other way. With the instrument identified the Surveyor may be able to go back to the instrument and make satisfuctory corrections. 10. A fow other requirements include numbering of pages, inclusion of a table of contents, Grawing arrows on sketches indicating the general direction of north and clear separation ofeach day's work by tarng onaclean page cach day. Should a particular survey extend over several days, cross-references may be necessary between the various pages of the Traits essa that notes be checked before leaving the ste ofthe survey to make sure {hat al tequred information has been obtained and recoded, Many surveyors keep checklists in 2.13 ELECTRONICALLY RECORDED NOTES We aiscuss at various places in this book the availabilty and ‘measuring devices, total sa apability enables us to reduce th # blunders that might otherwise oceur in recording information and in transferring it 1 the ofhee, MT T tra time a you ‘avipment. measurements ate made much mare ray, ra maatic daa collciors ae used lest ime require for Processing and displaying Wage amount Of data is being collected. A needed information for a partic ‘Ther ae some penal probes wt Segenaan smtions For estancs it is ot yet ler wheter cog ene MES in ela fed books, wll accep ial len Eutiogeee ne a tion to legal ich readily aecept hand-prepared ‘are problems withthe potential of deliberate MLFigure 2-6 Electronic fleld book used ‘ith total station equipment which is discussed in Chapter 10, (Courtesy of ‘Sokkia Corporation.) altering of digital files or their possible inadvertent destruction by human mistakes or by other electronic equipment. 2.14 OFFICE WORK AND DIGITAL COMPUTERS 2.18 PLANNING Field surveying measurements provide the basis for large amounts of office work. Office work may include precision computations, preparation of property drawings called plats, calculations for and «drawings of topographic maps, and computation of earthwork volumes. A lange percentage of these items are commonly handled today with digital computers, thus, transferring field notes or data collector files to a personal computer may be required. There are several commercially available software programs to aid the surveyor. Some surveying software are standalone while others are integrated into a Computer Aided Design (CAD) program such as AutoCAD or Microstation, Surveying software automates all aspects of office work, including making calculations of land ‘areas and earthwork volumes, and production of plats and maps. Figure 2-7shows a property survey plat that was produced using a computer program. If we are to perform accurate surveys, we need to employ good equipment, good procedures, and good planning. Accurate surveys can be made with old and perhaps out-of-date equipment, but time and money can be saved with modern instruments. Good planning is the most important item necessary for achieving economy and is also very important for achieving accuracy Pethaps no topic in this book is of more importance than the few words presented in this chapter fon the subject of planning. Planning involves establishing project objectives and constraints, identifying work elements and selecting procedures, and organizing the parties and equipment to be28 CChapter2 Introduction to Measurements 1.76 Acres (spe Bt py Sl aso) "Spool Wheel Road = S-32-115 66’ R/W Adam J. Backman fi Kristy B. Backman eetled o» 0d Met faxs ~ ibet SC Legtn Camly ety ste at oe bt my nos oteen 4s pu FEuA food asence Rote Mey Haber 450550025 6 secte ‘oe sreperty show ere is lected in on uneroged Fone has Catered 1 be otc te ake SURVEY & | Mappinc Figure 27, Property Survey Plat produce using computer program. (Counesy of Dacor sean 1220 Pat Sng ead Services) ||| yAieaSeies Ron | (803) 796-8214 Dale C. Swygert, RLS.)Problems 29 used. In other words, if we want a survey to be conducted with a precision of 1/30,000, what procedures and equipment will we have to use and who will be involved? ‘A great deal of space in this book is devoted to the terms accuracy and precision. © thorough ‘understanding of these subjects will enable the surveyor to improve his or her work and reduce the costs involved by careful planning. “The planning of a survey for a particular project may also include a reconnaissance of the area for existing surveying monuments, selection of possible locations for surveying stations, a review of land records related to the property being surveyed, and so on. ‘The longer a construction project lasts, the more expensive it becomes. The owner's money is tied up longer, resulting in increases in interest costs and postponement of the time when business ‘operations can begin and produce some return on investment. Surveying, which is one of the many phases of a construction project, needs to be done as quickly as possible for the reasons mentioned above. The cost of accurate surveying is frequently 1% to 3% of the overall cost of the construction project—but if itis done poorly, the percentages may be many times these valu speed may be essential . Thus, carefulness in a survey must not be slighted, even though In general, surveyors would like to obtain precisions that are better than those required for the particular project at hand. However, economic limitations (ie., what the employer is willing to pay) will frequently limit those desires. PROBLEMS. 241 The sides of a closed figure have been measured and found to have a total length of 4826.55 f. Ifthe total error in the measurements is estimated to be equal to 0.27 ft, what is the precision of the work? (Ans.: 1/17,876) 2.2 Repeat Problem 2.1 if the total distance is 6432.81 ft and the estimated total error is 0.38 f. 2.3. What is a probable or 50% error? 24 What is the law of compensation relating to errors? 2.5 A quantity was measured 10 times with the following results: 3.462, 3.467, 3.465, 3.458, 3.463, 3.457, 3.468, 3.452, 3.464, and 3.456 f. Determine the following: fa, Most probable value of the measured quantity. b, Probable error of a single measurement. €. 90% error, 95% error. (Ans.: 3.461, 0.0035, +0.0086, and 0.0102) 2.6 The same questions apply as for Problem 2.5, but the following 12 quantities were measured: 154.70, 154.67, 154,68, 154,69, 154.62, 154.66, 154.60, 154.74, 154.55, 154.58, 154.65, and 154.63 ft 2.7 A distance is measured to be 916.45 ft with an estimated ‘Standard deviation of +0,21 ft. Determine the probable errors ‘and the estimated probable precision at 2 and at 3c. (Ans.: £0.14f, +0.42ft, 1/2182, 1/1454). 28 The following six independent length measurements ‘were made (in feet) for a line: 736.352, 736.363, 736.375, 736.324, 736.358, and 736,383. Determine: ‘a. The most probable value. 1b, The standard deviation of the measurements. ¢. The error at 3.290. For Problems 2.9 to 2.11, answer the same questions as for Problem 2.8 Problem 2.9 Problem 2.10 Problem 2.11 201.658 185.35, 61327 201.642 135.42 61324 201.660 155.30 61338 201.732 155.58, 613.29 201.649 155.47 61343 201.661 155.32 61322 201.730 155.61 61339 201.680 55.44 613.40 613.25 613.21 (2-9 Ans: 201.677, £0.035, 40.115) (2-11 Ans: 613.31, £0.07, £0.23) 2.12 Ifthe accidental errorisestimated tobe ++0.008 ftforeach of 32 separate measurements, what isthe total estimated error? 2.13 A random or accidental error of +0.007 ft is estimated for each of the 24 length measurements. These measurements are to be added together to obtain the total length. ‘a, What is the estimated total error? (Ans.: 0.034 ft) 'b, What is the estimated total error if the random error is estimated to be +0.004 ft per length? (Ans.: +0.020f1)A ee rere ae | 30 Chapter 2 Introduction to Measurements 2.14 Itis assumed that the probable random error in taping 100 ft is +0.020 ft. Two distances are measured with this tape with the following results: 1527.44 and 1812.37 ft. Determine the probable total error in measuring each ofthe lines and then the total probable error for the two sides together. 2.18 _A series of elevations was determined. The accidental, error in taking each reading is estimated to be = 0,004ft What is the total estimated error if 25 readings were taken? (Ans.: + 0.020) 2.16 A surveying crew or party is capable of taping distances, with an estimated probable accidental error of + 0.008 m for each 30-m distance or tape length. What total estimated probable accidental eror should be expected if a total distance of 1,500 m is to be measured? 2.17 Two sides of a rectangle were measured as being 158.46ft + 0.03 ft and 212.71 = 0.04%. Determine the area ofthe figure and the probable errr of the area. Assume probable enor = AE} + BPE where A and B arc lengths of sides. (Ans: 33,706.03 sq ft = 8.99 sq ft) 218. Iv is desired to tape a distance of 2.200 with « total Sandard eror of not more than 0.20‘ 4 How accurately should each 100-f distance be measured so thatthe permissible vale is not exceeded?” . How accurately would each 100. distance have to be ‘measured so thatthe 95% error would not exceed 0.24 ft ina toa distance of 4000 f1? 219 Fora nine-sidd closed figure the sum of the interior Angles is exactly 1260". It is specitied for a survey of this figure that if these angles are measured inthe fel, their sum should not miss 1260° by more than +1. How accurately should each ange be measured? (Ans: + 20")Chapter 3 Distance Measurement 3.1 INTRODUCTION One of the most basic operations of surveying is the measurement of distance. In surveying, the distance between two points is understood to be a horizontal distance. The reason for this is that most of the surveyor’s work is plotted on a drawing as some type of map. A map, of course, is plotted on a flat plane and the distances shown thereon are horizontal projections. Land areas are computed on the basis of the same horizontal measurements. This means that if a person wants to obtain the largest amount of actual land surface area for each acre of land purchased, it should be purchased on the side of a very steep mountain. Early measurements were made in terms of the dimensions of parts of the human body such as cubits, fathoms, and feet. The cubit (the unit Noah used in building his boat) was defined as the distance from the tip of a man’s middle finger to the point of his elbow (about 18 in.);a fathom was the distance between the tip of a man’s middle fingers when his arms were outstretched (approximately 6 ft). Other ‘measurements were the foot the distance from the tip of aman’ sbig toe to the back of his heel) and the ppole or rod or perch (the length of the pole used for driving oxen, later set at 16.5 ft). In England the “rood” (rod or perch) was once defined as being equal to the sum of the lengths of te left feet of 16 men, whether they were short or tall, as they came out of church one Sunday moming." ‘Today all of the countries of the world except Burma, Liberia, and the United States use the metric system for their measurements, This system was developed in France in the 1790s. ‘The meter is approximately equal t0 1/10,000,000 of the distance from the equator to the North Pole along the surface of the Earth, Its application in the United States in the past has been limited almost entirely to geodetic surveys. In 1866 the U.S. Congress legalized the use ofthe metric system by which the meter was defined as being equal to 3.280833 ft (or 39.37 in.) and 1 inch was equal to 2.540005 centimeters, These values were based on the length at 0°C of an International Prototype Meter bar consisting of 90% platinum and 10% iridium that is kept in Sevres, France, near Paris. In accordance with the treaty of May 20, 1875, the National Prototype Meter 27, identical with the International Prototype Meter, was distributed to various countries. Two copies are kept by the U.S. Bureau of Standards at Gaithersburg, Maryland. Reference to the prototype bur was ended in 1959 and the meter was redefined as being equal to 1,650,763.73 wavelengths of orange-red krypton gas, equal 10 3.280840ft. In 1983 the meter definition was changed again to its present value: the distance traveled by light in 1/229,792,458 sec. Supposedly. its now possible to define the meter much more accurately. Furthermore, this enables us to use time (our most accurate basic measurement) to define length.” Based on these values, before 1959 the foot was equal to 1/3.280833 = 0.3048006m, whereas since that date it equals 1/3.280840 = 0,3048000 m. This very slight difference (about 0.0105 ft in | mile) is of no significance for plane surveys but does affect geodetic surveys, which often extend TEM Brown, W. G. Rohilland nd D, A. Wilwon, Evidence and Procedures for Boundary Location, 2nd ed (New York Jota Wiley & Sons, Ie, 1981), p 268 ® Source: CIA World Factbook, Appendix G, 2008. RC. Brinker and R. Minnick, es, The Surveying Handbook 2d ed. (New York: Van Nostrand Reinhold Company Inc 1995).7.43, 3eI ior 32 Chupter3 Distance Measurement for many miles. As a large number of our geodetic surveys were performed before 1959, the earlier value Gi, 1m =3.2808334) is wsed to define the US. survey foot. To the surveyor the most commonly used metic units are the meter (on) for linear measure the ‘square meter (m") for areas, the cubic meter (m*) for volumes, and the radian (rad) for plane angles {Im many countries the comma is usd to indicat decimal tus, to avoid confusion inthe metic system, spaces rather than commas are used. Fora umber having four or mor digits, the digits are separated into groups of threes, counting bah sight and left fom the decimal, For instance 44642,261 is weten as 4 642 261, and 340.32165 is writen as 340.321 65 There is curently no state or feral legislation tha requires surveys for projects to be conducted using metric unit. From 1988 to 1998, the Federal Highway Administration (FHWA) required the use of metric units inthe federal highway program: however, the 1998 Transpor, tation Equity Act forthe 21st Century mae the use of metic units optional anal states have since chosen to use customary U.S. units for all highway projects. To change surveying to metric units may scm at ft glance to be quite simp. In sense this is true in that if the surveyor ean measure distance witha It tape, he or she can do jst as well with 8 30-m tape using the same procedures. Funhetmore, alma! al electronic distance. measuring devices provide distances in feet or meters as desired, However, we have several hundred years of Jand descriptions recorded in the English system of units and stored in our various courthouses and ther archives. Future generations of surveyors will hereforeaever getaway completely fom the English system of units. As an illsration today’s surveyor sill equomty enecemtes oid end descriptions made in terms of so many chains efrence being mate ws te €e hha) here are several methods that an be used for messing distance, These include pacing, odometer ‘eadings Sadi, taping electronic distance measuring devices, andthe global positioning sytem. The Occasionally other units of length include the following: 1, The furlong is defined as the len, rile or 6608 or 40 rods, tho med of guar 10-scre eld and equals 1h of 3.2 PACING tape). Here the authors define the considered to equal two steps or3.3. Odometers and Measuring Wheels 33 a a Wars ie ee kegt Marseq PeLp cat Figure 3-1. Field notes for taking a traverse. when taking natural steps. Others like to try to take paces of certain lengths (e.g., 3ft), but this method is tiring for long distances and usually gives results of lower precision for short or long, distances. As horizontal distances are needed, some adjustments should be made when pacing on sloping ground. Paces tend to be shorter on uphill slopes and longer on downhill ones. Thus, the surveyor would do well to measure his or her pace on sloping ground as well as on level ground. With a little practice a person can pace distances with a precision of roughly 1/50 to 1/200, ‘depending on the ground conditions (slope, underbrush). For distances of more than a few hundred feet, a mechanical counter or pedometer can be used. Pedometers can be adjusted to the average pace of the user and automatically record the distance paced. ‘The notes shown in Figure 3-1 are presented as a pacing example for students. A five-sided figure was laid out and each of the corners marked with a stake driven into the ground. The average pace of the surveyor was determined by pacing a known distance of 400 ft, as shown atthe bottom of the left page of the field notes. Then the sides of the figure were paced and their lengths calculated. ‘This same figure or traverse is used in later chapters as an example for measuring distances with a steel tape, measuring angles with a total station, computing the precision of the latter measurements, and calculating the enclosed area of the figure. ‘A note should be added here regarding the placement of the stakes. It is good practice for the student to record field book information on the location of the stakes. The position of each stake should be determined in relation to atleast two prominent objects, such as trees, wall, sidewalks, so that there will be no difficulty in relocating them a week or a month later. This information can be shown on the sketch as illustrated in Figure 3-1. ‘You will note that a north arrow is shown in the igure. Every drawing of property should include such a direction arrow, as it will be of help (as to directions and positions) to anyone using the sketch, 3.3 ODOMETERS AND MEASURING WHEELS Distances can be roughly measured by rolling a wheel along the line in question and counting the ‘number of revolutions, An odometeris a device attached to the wheel (similar to the distance recorder used ina car), which does the counting and from the circumference ofthe wheel convertsthe number of34° Chapter3_ Distance Measurement revoainios tae Schade poise apoinay 1/20 eth ound {smooth alng a highway, bu est ae mh pos Wien he surface siege "The coreter maybe uel or pliinarysreys, perhaps when pacing would take to Tong. It is ecantonally ud for nal ue ovation survey and foe ick checks on other measure Innis A sini dvie isthe mesug whee wich iv wheel meunted on aod Itsuser can pesh the whet along the tin tobe measured sequently Wed fo curved ies. Some odometer are lable hacen eattached othe ear end of amovor eile nse while the vehicle is moving ta speed of several mils per hou (CHYMETRY ‘The term tachymetry or tacheometry, which means “swift measurements,” i derived from the Greek words takus, meaning “swift.” and metron, meaning “measurement.” Actually, any measurement made swiftly could be said tobe tacheometric, but the generally accepted practice isto list under this category only measurements made with subtense bars or by stadia. Thus, the extraordinarily fast electronic distance-measuring devices are not listed in this section. Subtense Bar (Obsolete) AAtachymetric method that was oecasionally used uni few decades ago for rural property surveys made use of the subtense bar (Figure 3-2). This obsolete device has been replaced by electronic distance-measuring devices. In Europe, where the method was most commonly used, & horizontal bar with sighting marks on it, usually located 2.m apart, was mounted on a tripod. ‘The tripod was centered over one end of te line tobe measured and the bar was leveled and tured so that it was made roughly perpendicular tothe line A theodblte was set up atthe oer end ofthe line and sighted onthe subiense har. It was used to align the bar precisely in position perpendicularo the line of sight by observing the sighting mark on the subtense bar. This mark could be seen clearly only when the bar was perpendicular tothe line of sight. The angle subtended between the marks onthe ba Was carclly measured (preferably witha theodolite ‘measuring tothe nearest second of ac) andibe stance between the endothe line was computed. The distance D from the dhecsdolite to the sabtense bar was computed fom the fllowing expresion Ue le Das SeotS orct$ sinces = 2m in which Sis the distance between the sighting values are showa in Figure 3-3, For reasonably short distances, say less than S00 errors to 1/5000 was ordinarily obtained. The subtense bat was across rivers, canyons, busy streets, and other difficult, 'g marks onthe bar and «isthe subtended angle. These ‘were small and a precision of 1/1000 Particularly useful for measuring distances ‘reas, Ithad an additional advantage in that Figure3.2 Digital image of a Sobtens Bar. (Courtesy of Malcolm Stewar,) fStadia 34 Tachymeny 35 a free Figure 3.3. Distance measurement with a subtense bat. the subtended angle was independent of the slope of the line of sight; thus the horizontal distance ‘was obtained directly and no slope correction had to be Although the subtense bar was occasionally used in the United States, the stadia method was far more common. Its development is generally credited to the Scotsman James Watt in 1771.* The word stadia is the plural of the Greek word stadium, which was the name given to a foot race track approximately 600 ft in length. “Many transit, theodolite, and leveling telescopes are equipped with three horizontal cross hairs that are mounted on the cross-hair ring. The top and bottom hairs are called stadia hairs. The surveyor sights through the telescope and takes readings where the stadia hairs intersect a scaled rod. ‘The difference between the two readings is called the rod intercept. The hairs are typically spaced so that at a distance of 100ft their intercept on a vertical rod is 1 ft; at 200 itis 2ft; and so on, as illustrated in Figure 3-4. To determine a particular distance, the telescope is sighted on the rod and the difference between the top and bottom cross-hair readings is multiplied by 100. When one is working on sloping ground, a vertical angle is measured and is used for computing the horizontal ‘component of the slope distance. These measurements can also be used to determine the vertical component of the slope distance or the difference in elevation between the two points. ‘When the stadia method was used in surveying practice it had its greatest value in locating details for maps. Sometimes it was also used for making rough surveys and for checking more precise ones. Precisions of the order of 1/250 to 1/1000 were obtained. Such precisions are not satisfactory for and surveys. Though the use ofthe stadia method is briefly described in Chapter 14 b= 1008 Figure3-4_ Stadia ewings 5A R Legal, HM. MeMaser and R. R. Maries. Surveying (Englewood Chiff, Ni Preotice Hall, In, 1956), p39.36 Chapter3 Distance Measurement set igg esta Figure 3§ Estimating the height of atree of this text i is seldom used by today’s surveyor because of the advent of total station instruments described in Chapters 10 and 14. ‘The same principle can be used to estimate the heights of buildings, trees, or other objects, as illustrated in Figure 3-5. A ruler is held upright ata given distance such as arm's length (about 2 ft for many people) in front of the observer's eye so that its top falls in line with the top of the tee. ‘Then the thumb is moved down so that it coincides withthe point where the line of sight strikes the ruler when the observer looks at the base of the tree. Finally, the distance to the hase of the tree is, measured by pacing or taping. By assuming the dimensions shown in Figure 3-5, the height of the tree shown can be estimated as follows: mit ce = (2) 6 Artillery students were formerly trained in a similar fashion o estimate distances by estimating the size of objects when they were viewed between the knuckles of their hands held at arm's length, 3.5 TAPING OR CHAINING For many centuries, surveyors measured distances with ropes, ines, or cons that were treated with wax and calibrated in eubits oF other ancient units, These devices are obsolete today, although precisely calibrated wires are sometimes used, Forte fis two-hitds ofthe twentieth century the 100-ft sel ribbon tape was the common device wed for measuring distances, Such measuring is often ealled chaining, a carryover name from the time when Gunter’s chain was introduced, The English mathematician Edmund Gunter (1581-1626) invented the surveyors chain (Figure 3-6) used up until that time, was available in several lengths, including 33 f,66ft, and 100ft The 66-ft length was the most common. (Gunter is also credited wit the introduction ofthe words ever aod Figure 346 Old 66-f. chain3.6 Electronic Distance Measurements 37 ‘cotangent to trigonometry, the discovery of magnetic variations [discussed in Chapter 9}, and other ‘outstanding scientific accomplishments.”) ‘The 66-ft chain, sometimes called the four-pole chain, consisted of 100 heavy wire links each 7.92in. in length, In studying old deeds and plats the surveyor will often find distances measured with the 66-ft chain, He or she might very well see a distance given as 11 ch, 20.21ks. or 11.202 ch. ‘The usual area measurement in the United States is the acre, which equals 10 square chains. This is equivalent 10 66 ft by 660 ft, or 1/80 mi by 1/8 mi. or 43,560 sq ft Many ofthe early two-lane roads in the United States and Canada were laid out to a width of one chain, resulting ina 66-ft right-of-way. Steel tapes came into general use around the beginning of the twentieth century. They are available in lengths from a few feet to 1,000 ft. For ordinary conditions, precisions of from 1/1000 to 1/5000 can be obtained, although much better work can be done by using procedures to be described late. ‘The general public, riding in their cars and seeing surveyors measuring distances with a steel tape, might think: “Anybody could do that. What could be simpler?” The truth is, however, that the ‘measurement of distance with a steel tape, though simple in theory, is probably the most difficult part of good surveying. The efficient use of today’s superbly manufactured surveying equipment for other surveying funetions such as the measurement of angles is quickly learned. But correspond- ingly precise distance measurement with a steel tape requires thought, care, and experience. Tn theory, itis simple, but in practice itis not so easy. Sections 3.9 to 3.11 are devoted to a detailed description of taping equipment and field measurements made with steel tapes, 3.6 ELECTRONIC DISTANCE MEASUREMENTS Sound waves have long been used for estimating distances, Nearly all ofus have counted the number of seconds elapsing between the flash of a bolt of lightning and the arrival of the sound of thunder and then multiplied the number of seconds by the speed of sound (about one-fifth of a mile per second). The speed of sound is 1129 fUsee at 70° Fand inereases by a little more than I {ysee for each degree Fahrenheit increase in temperature. For this reason alone, sound waves do not serve as a pructical means of precise distance measurement because temperatures along line being measured would have to be known to almost the nearest 0.01°F. In the same way some distances for hydrographic surveying were formerly estimated by firing a ‘gun and then measuring the time required for the sound to travel to another ship and be echoed back to the point of firing. Ocean depths are determined with depth finders that use echoes of sound from the ocean bottom, Sonar equipment makes use of supersonic signals echoed off the hulls of submarines to determine underwater distances. It has been discovered during the past few decades that the use of either light waves, electromagnetic waves, infrared, or even lasers offers much more precise methods of measuring distance. Although it is true that some of these waves are affected by changes in temperature, pressure, and humidity, the effects are small and can be accurately corrected. Under normal conditions the corrections amount 0 no mote than a few centimeters in several miles. Numerous. portable electronic devices making use of these wave phenomena have been developed that permit the measurement of distance with tremendous precision. “These devices have not completely replaced chaining or taping, but they are commonly used by ‘almost all surveyors and contractors. Their costs are ata point where the average surveyor must use them to remain economically competitive. For those who prefer to lease. arrangements may be made with various companies. Electronic distance-measuring instruments (EDMSs) have several important advantages over other methods of measurements, They ate very useful in measuring distances that are difficult to access, for ‘example, across lakes and rivers, busy highways, standing farm crops, canyons, and so on. For long, distances (say, several thousand feet or more), the time required is in minutes, not hours as would be © Updated Ref. “Edmund Gunier” Encyclopedia Britannica. Encyclopaedia Britannica Online. Encyclopaedia Britannica, 2011. Web acessed Jan, 2011, 1/1,000,000 Established to enable planes, ships, and other military groups to quickly determine their postions; inereasingly being used for locating important control points and in ‘many other phases of surveying including construction 3.9 EQUIPMENT REQUIRED FOR TAPING Steel Tapes AA brief discussion of the various types of equipment normally used for taping is presented in this. section, and the next two sections are devoted to the actual use of the tapes. (Many surveyors still, refer to the steel tape as a “chain” and the less precise rollup or woven tape as a tape.) A taping or chaining party should have at least one 100-ft stce! tape, two range poles, a set of 11 chaining pins, a 50-ft woven tape, two plumb bobs, and a hand level. These items are discussed briefly in the following paragraphs. Until recently, most surveying distance measurements requiring high precision were done with tee} tapes. Although electronic distance measurement is now preferred because ofits accuracy and convenience, ste! tapes are sill used for short distance measurements (e.g. afew hundred feet or tess), The most common are lightweight stee! tapes that are nylon coated. Lightweight steel tapes come in various lengths the most common being 100 ft long. They are continuously graduated thoughout in fet and hundredths of feet, Metric lightweight steel tapes are typically 30 meters long and are graduated in meters and millimeters Highly precise heavy steel tapes (also known as highway tapes or drag tapes) are most commonly 100 long, 1/410 /16 in. wide, 0.016 100.025 in. thick, and weigh or3 Ib. They areeither carried ona, reel (Figure 3-8) or done up in 5-tloops to forma figure 8, These tapes are quite strong as Tong as they are ep straight, but if they are tightened when they have Toops or kinks in them, they will break very easly. Ifa tape gets wet, it should be wiped witha dry cloth and then again with an oily cloth, Heavy steel tapes are usually very close to the correct length when they are continuously supported and subjected to a tension of usually 10 0 12 1b and a temperature of 68°F. Heavy steel tapes are sometimes chrome clad with end that are made with heavy brass loops that provide a place to attach leather thongs orension handles, enabling the user to tighten or tension them firmly. (UF the leather thong is missing or breaks, and if a tension handle is not available, one of the chaining pins can be inserted through the loop and used as handle for tightening the tape) Heavy stel tapes are not graduated continuously with their smallest interval. Rather, they are marked atthe I-ft points from 0 to 100Ff. Older tapes have the last foot at each end divided into tenths of afoot, bu the newer tapes have an extra foct beyond 0, which is subdivided. Tapes with the40 Chapter’3 Distance Measurement Fiberglass Tapes Range Poles Figure 38 Stee! ape. (Courtesy of Robert Bosch Tool Corporation) extra foot are called add tapes; those without the extra foot are called cu tapes (see Figure 3-12) Several variations are availabe: for example, tapes divided into feet, tenths, and hundredths for their entire lengths; tapes wit the O- and 100cf points about 1/2 from the ends, and so on. Needless to say, the surveyor must be completely familiar with the divisions of the tape and its 0- and 100-f ‘marks before he or she does any measuring. Cut tapes were used for many decades by a large numberof surveyors but a large percentage of those surveyors did not like them because their use frequently led to arithmetic mistakes. For ‘example, it was rather easy to add the end reading instead of subtracting it Mistakes seem to be less frequent when add tapes are used, and as a consequence, add tapes have become the common type manufactured. Tapescanbe obtainedin variouslengts other than 100 ft. The 300-and 500-8 lengths are probably the most popular. The longer tapes, which usually consist of 1/8 n-wide wire bands, are divided only at the 5-ftpoins to redace costs, They are quite useful for rapid, precise measurements af long distances onlevel ground. Theuse oflong apes permitsa considerable eduction in the ime required for marking at ape ends, and it also virwaly eliminates the accidental rors that oecue while marking, For very precise taping the Invartpe, made with 65% nickel and 35% see, was fomnerly used Although this type of tape had avery low coeticientof thermal expansion (pethapsI/30thr tom of the values for standard steel tapes) it was rather sot easily broken, and cost about ten tines sec as regular steel tapes. Inva tapes were atone time used for precise peodetic work and wee cencdard for checking the lengths of regula steel tapes. The Lovar tape had propetics and coats somewhere in between those ofthe regular steel tapes and Invar tapes. Some tapes were made witha gaioed thermometer scale that corresponded to temperature expansions and contractions, Wil ciffeeay temperatures the surveyor could use a different terminal mark on the tape, thus automatically correcting forthe temperature change In recent years, fiberglass tapes made of thousands of, have been introduced on the market. These lessen co en ep wae Ne eee eyo ae convenient because it can easily be transported from one job to anethe * PTPAPS the39 Equipment Required for Taping 41 ‘Taping Pins (also referred to as Chaining Pins or Taping Arrows) Plumb Bobs Woven Tapes ‘Taping pins are used for marking the ends of tapes or intermediate points while taping. They are ‘easy 10 lose and are generally painted with alternating red and white bands. Ifthe paint wears off, they ean be repainted any bright color or they can have strips of eloth tied to them which can readily be seen. The pins are cartied on a wire loop which can conveniently be carried by a tapeman, perhaps by placing the loop around his or her belt. ‘A plumb bob is a pear-shaped or globular weight which is suspended on a string or wire and used to establish a vertical line (Figure 3-9a). Plumb bobs for surveying were formerly made of brass to limit possible interference with the compasses that were used on old surveying equipment. (Iron or steel plumb ‘bobs could cause errors in compass readings.) Plumb bobs usually weigh from 6 to 18 oz and have sharp replaceable points and a device atthe top to which plumb-bob strings may be tied. Very commonly. plumb bobs ate fastened toa ganmon reel (Figure 3-9). Thisis.adevice that providescasy up-and-down, ‘adjustment of the plumb bob, instant rewinding of the plumb-bob string, and a sighting target, Woven tapes (Figure 3-10) are most commonly 50ft in length with graduation marks at 0.25-in intervals. They can be either nonmetallic or metallic. Nonmetallic tapes are woven with very strong synthetic yams and are covered with a specific plastic coating that is not affected by water. Metalic tapes are made with a water-repellent fabri into which fine brass, bronze, or copper wires are placed in the lengthwise direction. These wires strengthen the tapes and provide considerable resistance to stretching, (Because of the metallic wires, they should not be used near electrical units. For such situations ‘nonmetallic woven or fiberglass tapes should be used.) Nevertheless, since all woven tapes are subject to cc) o Figure 3-9 (a) Plumb bob; (b) Gammon rel. (Courtesy of Robes Bosch Tool Corporation.)42° Chapter Distance Measurement Hand Levels Spring Balances (Clamping Handles Figure 310 Wow ape, some stretching and shrinkage, they re not suitable for precise measurement. Despite this disadvantage, woven tapes are often useful and should be a part ofa surveying part's standard equipment. They are ‘commonly used for finding existing points, locating details for maps, and measuring in situations where steel tapes might easly be broken (as along highways) or when small errors in distance are not too important. Their lengths should be checked periodically or standardized with steel tapes, ‘The hand levelisa device thats very useful tothe surveyor for helping hold tapes horizontally while ‘making measurements t also may be used forthe rough determination of elevation. It consicte of ‘etal sighting tube on whichis mounted a bubble tube (Figure 3-11), Ifthe bubble is centered while sighting through the tue, the line of sights horizontal, Actually, te bubble tube is located ontop of the instrument and its image is reflected by means of a4S* minror or prism inside the tube so that its user can see both the bubble and the terrain When a steel tape is tightened, it will stretch. The resulting With the formula presented in Section 4.6. For average taping the tension arp d sion applied can be estimate sufficiently to obtain desired precsions, but for very precise taping a spring balance or tension Aardle is necessary. ‘The usual spring balance can be read up t 30h in /2-b inerements or up (0 1S kg in 1/4-k ig increase in length may be determined Figure S11. Hand levels. (Courtesy f SECO)3.10 Taping Over Level Ground 43 desired values. When only partial lengths of tapes are used, itis somewhat difficult to pull the tape tightly, For such cases clamping handles are available. These have a scissors-type grip that enables ‘one to hold the tape tightly without damaging it. 3.10 TAPING OVER LEVEL GROUND Ideally, a steel tape should be supported for its full length on level ground or pavement Unfortunately, such convenient conditions are usually not available because the terrain being surveyed may be sloping and/or covered with underbrush. If taping is done on fairly smooth and level ground where there is litle underbrush, the tape can rest on the ground. The taping party consist of the head tapeman and the rea tapeman. The head tapeman leaves one taping pin with the rear tapeman for counting purposes and pechaps to mark the staring point. The head tapeman takes the zero end of the tape and walks down the line toward the other end. ‘When the 100-ft end of the tape reaches the rear tapeman, the rear tapemn calls “tape” or ‘chain’ to stop the head tapeman. The rear tapeman holds the 100-ft mark atthe starting point and aligns the head tapeman (using hand and perhaps voice signals) on the range pole that has been set behind the ending point, Ordinarily, this “eyeball” alignment ofthe tape is satisfactory, but use of a telescope is beter and will esult in improved precision. Sometimes there are places along a ine where the tapeman cannot see the end point and there may be positions where they cannot sce the signals ofthe instrumentman, For such eases its necessary to set intermediate ine points using the telescope hefore the taping can be stated. Itis necessary to pull the tape firmly (See Sections 4.6 and 4.7). This can be done by wrapping the leather thong a the end ofthe tape around the hand, by holding a taping pin that has been slipped through the eye at the end of the tape, or by using a clamp. When the rear tapeman has the 100-f ‘mark at the starting point and has satisfactorily aligned the head tapeman, he or she calls “ll right” or some other such signal. The head tapeman pulls the tape tightly and sticks a taping pin inthe ground at right angles to the tape and sloping at 20° to 30° from the vertical. Ifthe measurement is done on pavement, a scratch can be made atthe proper point a taping pin can be taped down to the pavement, or the point may be marked with a colored lumber crayon, called keel “The rear tapeman picks up his taping pin and the head tapeman pulls the tape down the line, and the process is repeated forthe next 100. It will be noticed thatthe number of hundreds of feet that have been measured at any time equal the numberof taping pins that the rear tapeman has in his or her possession, After 1,000 ft has been measured, the head tapeman will have used his eleventh pin, and he cals “tally” or some equivalent word so thatthe rear tapeman will return the taping pins and they can start on the next 1,000. This discussion of counting taping pins is of litle significance because almost any distance over 100 or 200 will today be measured with an EDM, as will a large percentage of distances of 100 oF 20011 or less. This topic is discussed in Chapter 5. ‘When the end ofthe line is reached, the distance from the last taping pin tothe end point will ‘normally be fractional part ofthe tape. For older tapes, the first foot ofthe tape (from Oto tt) is usvally divided into tenths, as shown in Figure 3-12. The head tapeman holds this part of the tape ‘over the end point while the rear tapeman moves the tape backward or forward until he has full foot mark atthe taping pin. The rear tapeman reads and calls out the foot mark, say 72 feet, and the head tapeman reads from the tape end the numberof tenths and perhaps estimates tothe nearest hundredth, say 0.46, and calls this out. This value is subtracted from 72 to give 71.54 ft and the number of hundreds of feet measured before is added, These numbers and the subtraction should be called out so that the math can be checked by each tapeman. For the steel tapes with the extra divided foot, the procedure is almost identical except that the rear tapeman would, forthe example just described, hold the 71-ft mark atthe taping pin in the ground, He or she would call out 71 and the head tapeman would read and call out plus 54 hundredths, giving the same total of 71.54 ft In review the rear tapeman reads the whole foot mark while the head tapeman reads the decimal value. Then the two readings are combined to establish the total distance.44 Chapter3 Distance Measurement “sau quot ape ila BHT Lisi Rear apeman en Re oot pealng 72-4 = 7154 seg act ope a penn sour eatg 71-084 71548 Figure 3:12 Readings of eut and add 1 Unga ae pes ‘A comment seems warranted here about practical significant figures as they apply to taping. If ordinary taping is being done and the total distance obtained for this line is 2771.54 f, the 4 at the end is ridiculous and the distance should be recorded as 2771.5 or even 2.772 t because the work is Just not done that precisely, 11 TAPING ALONG SLOPING GROUND OR OVER UNDERBRUSH ‘Should the ground be sloping there are three taping methods that canbe used. The tape (1) may be held horizontally with one or both of the tapemen using plumb bobs as shown in Figures 3-13 and 3-14; or (2) it may be eld along the slope, the slope determined, and a correction made to obtain the horizontal distance; or (3) the sloping distance may be taped, a vertical angle measured for each slope, and the horizontal distance later computed, This latter method is sometimes referred to as ‘dynamic taping. Descriptions of each of these methods of measucing slope distances with a tape follow. Holding the Tape Horizontally deal, the tape should be supported for its full len such convenient conditions are often not available and covered with underbrush, For sloping, unev handled in a similar mann Nieaeta! both tapemen must use a plumb bob, as shown in Figure 3.13, if If taping is being done downhill, the rear ground while the head tapeman uses a plumb ‘apeman may be able to hold his or her end on the bob [Figure 3-14(a).Ifthey are moving uphill the rear Figure 3-13 Holding the tape horizontally3.11 Taping Along Sloping Ground or Over Underbrush 45 Direcon of messrement (2) Head ugeman punbiog Rear tpem pumas (©) Beth apemes plumbing Figure 3-14 Holding the tape horizontally tapeman will have to hold his or her plumb bob over the last point, while the head tapeman may be able tohold his or her end on the ground [Figure 3-14(b)]. The head tapeman will always hold the so- called “smart” end or divided end of the tape. Normally, this is the zero end. Taping downbill is ‘easier than taping uphill because the rear tapeman can hold the tape end on the ground at the last point instead of having to hold a plumb bob over the point while the head tapeman is pulling against hhim or her, as would be the case in taping uphill. If the measurement is over uneven ground or ‘ground where there is considerable underbrush, both tapemen may have to use plumb bobs as they hold their respective ends of the tape above the ground (Figure 3-14(c)] Considerable practice is required for a person to be able to do precise taping in rolling or hilly ‘country. Although for many surveys the tapemen may estimate what is horizontal by eye. it pays to uuse a hand level for this purpose. Where there are steep slopes, itis difficult to estimate by eye when, the tape is horizontal because the common tendency is for the downhill person to hold his or her end. ‘much too low, causing significant error. Ifa precision of better than approximately 1/2500 or 1/3000 is desired in rolling country, holding the tape horizontally by estimation will not be sufficient. ‘Another problem in hoiding the tape above the ground is the error caused by sagging of the tape (see Section 4.6). Note that both of these errors (tape not horizontal and sag) will cause the surveyor to get too much distance. In other words, either ittakes more tape lengths tocovera certain distance or the surveyor does not move forward a full 100ft horizontally each time that he or she uses the tape. If the slope is less than approximately 5 ft per 100, (a height above the ground at which the average tapeman can comfortably hold the tape), the tapemen can measure a ull 100-f tape length ata time. Ifthey are taping downhill the head tapeman holds the plumb-bob string atthe O-end of the tape ‘with the plumb bob a few inches above the ground, When the rear tapeman is ready at their end, the head tapeman is lined up on the distant point, and when the tape is horizontal and pulled to the desired. tension, the head tapeman lets the plumb bob fall to the ground and sefs a taping pin at that point. In Figure 3-15 we see various methods of using a hand level. In pats (a) and (b) of the igure the tapeman on the left with the hand level bubble centered moves his head up or down until the line of sight through the hand level telescope hits the ground at the other tapeman’s feet. Ths is the height at which he needs to hold his tape end (the other end being held on the ground) for the tape to be horizontal. In part) the tapeman with the hand level stands with normal posture and sights (bubble centered) ‘on the other tapeman. From the position where the line of sight strikes the other tapeman he can tell the height to which he needs to hold his tape end. For instance, ifthe line of sight hits the other tapeman’s knee and they are both approximately the same height, the tapernan on the lefts lower by the distance from his eye to his knee: that is, the difference in elevation shown in part (c) of the figure. For slopes greater than approximately Sft per 100ft, the tapeman will be able to hold horizontally only parts of the tape at a time. Holding the tape more than Sit above the ground is difficult, and wind can make it more so Ifthe tape is held at heights of 5 ft or less above the ground bboth forearms can be braced against the body and the tape can easily be pulled firmly without swaying and jerking.46 Chapter 3 Distance Measurement (6) Standing eret-tine of sgh of hand eet is ground a feet of ter srveyor, (Bending down uti ine of sgh his ground eto ober sirveyor ay use prada rod omens eight of had evel above ground), (©) Stain erect of siht is hab of oer sanyo ‘Thos differen in elevation been wo pains (fsuveye sane height) shown sone Figure 315 Using hand level3.11 Taping Along Sloping Ground or Over Underbrush 47 100-f mark o 65.Atmark we ape Plumb ne 30-8 mark f Plumb line ‘on tape has a ao Pent mn Figure 3-16 “Breaking tape” slong a stop. the rear tapeman with the foot mark that he has been holding. This careful procedure is followed because it is so easy for the head tapeman to forget which foot he was holding if he drops it and walks ahead. The tapemen repeat this process for as much more of the tape as they can hold horizontally until they reach the O-end of the tape. This process is illustrated in Figure 3-16, This process of measuring with sections of the tape is referred to as breaking tape or breaking chain. If the head tapeman follows the customary procedure of leaving a taping pin at each of the positions that he occupies when breaking tape, counting the number of hundreds of feet taped (as represented by the number of pins in the possession of the rear tapeman) would be confusing. ‘Therefore, at each of the intermediate points the head tapeman sets a pin in the ground and then takes ‘one pin from the rear tapeman, Instead of breaking tape, some surveyors find it convenient to ‘measure the partial tape lengths and record those values in their field notes. Its probably wise for a beginning surveyor to measure a few distances on slopes of different percentages holding the tape horizontal and then again with the tape along the slopes with no corrections made. These measurements should give him or her a feeling for the magnitude of slope errors. ‘Taping on Slopes and Making Slope Corrections ‘Occasionally, it may be more convenient or more efficient o tape along sloping ground withthe tape held ‘inclined along the slope. This procedure has long been common for underground mine surveys but to a ‘much lesser extent for surface surveys. Slope taping is quicker than horizontal taping and is considerably more precise because it eliminates plumbing with ts consequent accidental errors. Taping along slopes is sometimes useful when the surveyor is working along fairly constant, smooth slopes or when he wants to improve precision. Nevertheless, the method is generally not used because of the problem of correcting slope distances to horizontal values. This is particularly true in rough terrain where slopes are constantly varying and the problem of determining the magnitude of the slopes is difficult In some cases it may be impossible to hold the entire tape (or even a small part of it) horizontally, This may occur when taping is being done across a ravine (see Figure 3-17) or some Tape th Figure 3:17 Taping on slopeOc eee in sae Te he 48 Chapter’ Distance Measurement ion re S18 Grades }9 Hand level and clinometer. (Counesy of Robert Bosch Tool Corporation.) ‘obstacle where one tapemun is much lower than the other one and where itis not feasible to “break tape.” Here it may be practical to hold both ends of the tape onthe ground. Slopes are often expressed in terms of grade, that is, the number of feet of vertical chan; clevation per 100 feet of horizontal distance. Grade is expressed asa percentage and may be piven Plus sign for uphill slopes and a negative sign for downhill slopes. Examples are shown in Ligue 3-18 ‘When a persons measuring distance with tape held alonga slope it wil benecessary for him ‘rer to determine the difference in elevation between the ends ofthe tape for each position ofthe {ape or to measure the vertical angle involved. Once this is done, the horizontal distance for each measurement can be computed by trigonometry, the quadratic equation, approximate formula which is developed for that purpose in Section 45 An almost obsolete handheld instrument called the eli Yertical angles and grades, With this instrument, which is ilustated in Figure 319, itis posible Imeasire vertical angles to approximately the nearest 10" and o determine grades rughly In elfet the clinometer is a hand level to which a protractor is attached (or more easily by the inometer can be used for measuring Dynamic Taping With dyn: measured. taping, which is very similar to the sk lope taping method, slope distances are Then the vertical angle is measured and the horizontal distance computed 3.12 REVIEW OF SOME 'RIGONOMETRY In surveying there are innumerable occasions where i i measure certain distances and/or angles doe to obta s0.on. Frequently, the use of simple tigonometrc compute those needed values without the necesity caanple {sane tht asuneior's working witha ig nage Ike wade the tlangle and one of the angles (not the 90° one) have bec measured the vac eee lengths and the missing angle can be quickly computed with wigonometie frat ® quite difficult and time consuming to les, weather conditions, time constraints, and ‘uations will enable us to quickly and easily of having. to measure them in the field. As an3.12 Review of Some Trigonometry 49 "Aljacear side Figure 3-20 A right wiangle, “The most common use of trigonometry in surveying involves the use of right triangle relations. ‘Such a triangle is shown in Figure 3-20. Initially the angle « at comer A will be considered. In the figure the hyporenuse (L.pis the sloping side while the adjacent side (L-4p)is the side between the angle a and the right or 9° angle. The opposite side (Lux) isthe side which is opposite to or across from the angle. It can be proved that the relationships listed exist for right triangles with reference here being made to Figure 3-18 and angle a, These ratios are called the functions of the angles. The trigonometric terms sine, cosine, efc., are usually abbreviated as shown, opposite side _ Lac hypotenuse — Lac a= cosa — wiincent side _ Las cosine = cosa = = Ine opposite side Adjacent side — sinea = sin tangenta = wna adjacent side _ Lay ‘opposite side Lac __ hypotenuse _ Lac adjacent side ~ Las hypotenuse _ Lac opposite side ~ Lac cotangenta = cota = secant = sect cosecanta = esca = ‘To commit these equations to memory is not difficult as one only has to memorize the first three ‘and then realize that the cotangent is the invert ofthe tangent, the secant the invert of the cosine, and the cosecant the invert of the sine. ‘When the reader leams the names of the triangle sides as described here (hypotenuse, adjacent side, and opposite side), he or she will be able to easily apply the trigonometric relations to right triangles whatever their position (that is with the 90° angle on the left side or the right side or up on. top of the triangle). If we are considering the angle at comer C in Figure 3-21, the opposite side is Lan while the adjacent side is Lge: ‘The values of the trigonometric functions for various angle sizes are commonly available with pocket calculators, As a result the author does not include tables for their values in this book. Wher Tooking up the values of trigonometric functions with the usual calculator, the angles must first be converted to decimal form. For example, the sine of 3°18" becomes the sine of 3.3°. In working with angles itis necessary for the student to realize that our angles are usually designated as being in degrees, minutes, and seconds, such as 54°24'38". Then we must realize that to obtain the value of a trig function for a particular angle with the usual pocket calculator, itNN ETS TET eee eT ET TTTPTTTTTTTTTTTTTTTTTTTTTTTT Tr ee 50 Chapter’ Distance Measurement will be necessary to convert that angle toa decimal value. A sample calculation of this conversion follows: 54°24'38" 28 + (2) -se 24.6333) ‘ wes SE) uate Several example problems (3.1 to 3.5) make use of the right triangle relations. It should be ‘noted that some of the information obtained in these problems using trigonometric functions could have been obtained just as well with the pythagorean theorem. EXAMPLE 31 With reference othe wiangl n Figure 3-19 he length of side BC and ty dado te angle w | comer A have been measured. Determine the length of side AC using tigonometic equations opposite side length = $0.00 dace We a Figure 323 SOLUTION sina = sin 40° = 0.64278761 with calculator = opposite side sina = SPROSE SE hypotenuse 50.000 064278761 = 20.00 Tae Lac = 77.7868 EXAMPLE 3.2 PPetermine the values of angles o and inthe righ Bangle ot FAQS ADIL ¢ use = 632 wl ypore 46 83.12 Review of Some Trigonometry SI SOLUTION Lex _ 60.000 sn Te 626 p= 71.5638" =71°33.8 a = 180° — 90° — 71°33.8! = 18°26.2" = 0,948676596 ALTERNATE Lax _ 20,000 ‘SOLUTION since = 7s = Ganges = 0316228532 a = 18.4348" = 18°26.1' EXAMPLES A 14.4 ft long ladder is leaned against a wall so that its base i 3.2 ft from the wall. (See Figure 3-23.) How far will the ladder reach verically up the wall? | xr iF aan 2 Figure 3.23 SOLUTION gre PEL 32 dopo : Tye | Yaa 97222222 = 12.83958841° Las cos 12.83958841° iad Lan = 14.0480 | | ALTERNATE | SOLUTION USING PYTHAGOREAN THEOREM EXAMPLE 3.4 ‘With modem electronic surveying equipment a distance has been measured from point Ato point ‘Band found to be 646.34 ft. The two points are not atthe same elevation and the angle between horizontal line and the sloping Tine has been measured and found to be 3°10. Determine the horizontal distance between the tvo points and the difference in elevation between them (neglec- ting the effec of earth's curvature)52 Chapter Distance Measurement SOLUTION i opposite side sin 37101 = sin3.16667° = Pr ‘opposite side 0.055240626 = Diff.in elevation 66.34 Diffin elevation = (6446 34)(0.085240626) = 35.70 adjacent side _ Horiz.distance cos 3°10 Hypotenuse hypotenuse Horia distance Wipes a 99847307) — SOLUTION ‘A surveyor needs to determine the distance Between points A and B shown in Figure 3-24 Unfortunately, this surveyor’ electronic distance-measuring equipment is being repaired. There- fore, this surveyor lays off the 90° angle shown in the figure, sets point C 300 ft up the river as shown and measures the angle at Cand finds it be 54°18 Caleta the distance AB. bl igor 3.24 tan 54718’ = QPbesie side Adjacent side ~ Te so La 3 eee 1391647258 — Lay = 17 49480 Surveying caleutations pemain not only to ight tiangles but also to oblique ut also to oblique triangles, other polygons highway and railroad curves, and soon. Paticolrly common are oblique riarcles (hoe that do notcontain a 90° angle). Detaled t'gonometic formulas for eaeulting the andes cod lengths for these triangles are provided in Table 2 of Appendix € of tis bean 1 Table 1 of Appendix Cthe trigonometric functions forrght angles fo al sorts of situations are given In this table two other trgonometic tam ae enconered, These valun, ohagy v linesaslas desstadinChoper 220 ists iehoedbwaticralaraione eee ce svete yer ino yesine db extemal ea kn sea og ea OTSPROBLEMS 3 Name six methods of measuring distances and list advantages and disadvantages of each. 3.2. List two situations where each ofthe following methods or instruments can be used advantageously for measuring distance: a) pacing: b) odometer) stadia: d) taping; e) EDM. 33 A surveyor counted the number of paces required to cover a 250-ft distance. The results were as follows: 95, 93, 97, 98, and 92 paces. Then an unknown distance was stepped off four times, requiring 115, 118, 116, and 117 paces Determine the average pace length and the length of the second line. (Ans: 2.63211, 307) 34 A surveyor paces a 400-ft length four times with the following results: 140, 143, 141, and 142 paces. How many paces will be necessary for this surveyor to lay out a distance of 525 35. Convert the following distances given in meters to feet "using the latest meter definition that is based on the speed of light. a. 632.18m (Ans: 2074.08 £0) b. 895.49 m, (Ans.: 2937.96 10) e. 1254,30m (Ans: 4115.16f) 36 Convert the following angles to decimal values: a. 24°19'12" b, 59°44'37” . 123°10'09" 3.7 Convert the following angles written in decimal form to degrees, minutes, and seconds: a. 99.4871" (Ans.: 99°29'14") b. 51,9543" (Ans: 51°57'12") . 148.6736" (Ans: 148°40'25") 3.8 A 2-m subtense bar was set up at one end of a line, and a theodolite was setup atthe other end. What was the horizontal length ofthe line ifthe following angle readings were taken on the bar: 0°44'20", 0°48", 0°44'21", and O°44"19" 39 A.100-ft “cur” stel tape (zero end forward) was used to ‘measure the distance between two stakes. Ifthe rear tapeman is holding the 83-f point and the head tapeman cuts 0.48 f, ‘hat is the measured distance? (Ans: 82.5211) 340 A 100-fi steel tape is 1/40;n, thick and 5/16 in. wide, If eel weighs 4901", how much does this tape weigh? 41 Repeat Problem 3.10 if the tape is 0.030in, thick and Bin, wide (Ans. 3.83 Ibs) 32 A surveyor has determined that side AB of the right triangle shown has a length of 415.77 and thatthe interior angle at comer A is 26°18. Determine the lengths ofthe other sides of the triangle Problems 53 — 4187 343 The hypotenuse ofa righ triangle is 126.42 long and one of the other sides has a length equal to 82.83 ft. Find the angle opposite to the 82.83 ft side. (Ans40°56.1') 3d The three sides of a triangle are 120, 160, and 200. Determine the magnitudes of the interior angles. BAS A sloping earth dam rises 4.2ft for every 10ft of horizontal distance. What angle does the dam make with the horizontal? (Ans.22°46.93) 316 A surveyor measures an inclined distance and finds itto be 17524641. In addition, the angle between the horizontal and the line is measured and found to be 4°14'S2". Determine the horizontal distance measured and the difference in ele- vation between the two ends of the line 37 The angles at the comers ofa triangular field are 24°, 66°, and 90° and the hypotenuse is 751,92%t. How many feet of fencing will be needed to enclose this field? (Ans:1744 66 ft) 38 Itis desired to determine the height of a church steeple. ‘Assuming that the ground is level, a 350.00-ft length is measured out from the base of the steeple and a 40°15" vertical angle is vetermined from that point on the ground to the top of the steeple. How tall isthe steeple? 3.419 Repeat Problem 3.18 ifforan instrument set up 850.0 from a tower with its telescope center 5.500 ft above the ground. The telescope is sighted horizontally to a point 5.500 ft from the bottom of the steeple and then the angle to the top of the steeple is measured. I's 28°20. How tal is the tower? (Ans:287.16 1) 3.20. A section of a road with a constant 4% slope or grade (ie., ft vertically foreach 100 ft hoxizontally) is to be paved. If the road is 32.000 ft wide and its total horizontal length is 1,200 f, compute the road area to be paved. 321 Repeat Problem 3.20 if instead of having a 4% grade the road makes a 3° angle with the horizontal. (Ans 38.453 1°) 322 A surveyor needs to measure the height of the tower shown in the accompanying illustration, A horizontal distance has been measured out from the building as shown and the two vertical angles have been determined. How tall is the tower? Note thatit is unnecessary in this case to measure the height of the instrument telescope above the ground.54° Chapter’3_ Distance Measurement Cltptone - 3.23. Repeat Problem 3.22 if the horizontal distance is tower 400.00, the upper angle is 4°26'08”, and the lower angle is 201931" (Ans.: 187.19 ft) 3.24 Repeat Problem 3.22 if the height of the instrument is 5.50 ft above the ground and the lope distance From the center ‘ofthe instrument tothe base ofthe tower is 491.89 ft. Assume the vertical angle from the telescope to the top of the tower remains 8°19' and that the base of the tower is at the same elevation as the base of the instrument. The bottom angle is, ‘not measured, He horizontal distance = 73680 8Distance Corrections INTRODUCTION To the reader it may seem that the authors have far too much to say about taping when almost all distance measurements are today made with electronic distance-measuring instruments alone or as part of total stations. This feeling may be even stronger after you study the discussions pertaining to the corrections of taping measurements for temperature or sag or other items and after you struggle through the detailed information presented concerning errors and mistakes, The authors, however, feel very strongly that if you learn this information concerning tapes, you will understand much better the entire measuring process, regardless of the surveying operation involved or the equip ‘ment used. ‘The surveyor of today and tomorrow should become proficient with the steel ape, even though it is highly possible that he or she will eventually use the tape very little. Otherwise, the chance of making blunders and large errors will be magnified when the tape is used. 4.2 TYPES OF CORRECTIONS ‘The five major areas in which the surveyor may need to apply corrections either in measuring or in laying out lines with a tape are as follows: 1. Incorrect tape length or standardization error 2. Temperature variations 3. Slope 4, Sag, 5, Incorrect tension Once the appropriate errors are determined, the corrected distance for a measured line can be {determined by substituting into the following equation. The application of this equation will always be correct, provided the correct algebraic sign is used for each correction, Comtected distance ~ Measured distance + JT comections ‘The next few sections of this chapter are devoted to a discussion of the first three of these corrections. To save space, only a few remarks are made concerning corrections for tape sag and tension, 4.3 INCORRECT TAPE LENGTH OR STANDARDIZATION ERROR ‘An important topic in surveying is the standardization of equipment, or the comparison of the equipment (whether itis a tape, an electronic distance-measuring instrument, or whatever) against standard. In other words, has the equipment been damaged or shaken out of adjustment, have repairs ‘or weather changes affected it, and so on? If so, the surveyor will need to adjust the equipment or make mathematical corrections to compensate for the resulting errors.56 Chapter4 Distance Corrections {is said that in ancient Egypt the workers onthe pyramids were required to compare their cubit, sticks against the standard or royal cubit stick each fll moon. Those failing to do so were subject to death. Such a practice undoubtedly brought forth the bet efforts from their personnel in the area of standardization, Although steel tapes are manufactured to very precise lengths, with use they become kinked, worn, and imperfectly repaired after breaks. The net result is that tapes may vary by quite a few hundredths of a foot from their desired lengths. Therefore, itis wise to check them Periodically against a standard. There are several ways in which this might be done. For instance, some surveying offices used to keep one standardized tape (perhaps an Invar type, previously described in Section 3.9) that was used only for checking the lengths of their other {apes Some companies took a tape that had been standardized at 100.00 ft and used it to place {These Practices were advisable for surveyors who hed extensive practices and they yielded very Safatectory results for surveys where ordinary precision was desired, but they were probably not “ufficient for extremely precise work. For such work, tapes can be maled tothe National Ineuge of Standards and Technology in Gaithersburg, Maryland, For arather large fee, they will detornave the (Grate for speci tension and support conditions, A NIST srl umber willbe engraved ‘on each calibrated tape for identification purposes, Here ial governments aound the United Stats, various state agencies, and a good Natignal Coateaa gu andardize tapes, very often free as a service to the publi. In addition the NGS base lines were measured wih Ivar tapes andlor elena with accuracies approaching 1/1,000,000. The locations of these base lr website at htp//www.ngs.n0aa gov. If a tape proves to be in appreciable error from the sa measurement y the required amount. shouldbe cata oF negative, as explained inthe following x aul ae eae ore in ‘grasp in making corrections is that the tape “says zero ft at one end wae Te sae Sa hh CREM lena is 9.9818, 100.10, or some other he as measured a trees ee abe's Bue lebgt) ses his tape 10 arteries that he has measured a distance of 1 BH Su eee eee So nee of LO00E, but has really measured 10 times the acta tape tn measuring 4 given distance with tape s 00 long, the surveyor will not obtai large enough eissot te measurement and il hiveto make Rone, Be a asbontaely fos sees it il ke vee engtso meant acre: her wed for a shorter, correct-length tape. Fora tape that Mace iikegpe ree (his rue: Tape too long, add; tape fance-measuring equipment ines is available on the NGS dard, the surveyor must correct the ‘oted whether a correction is positive readers, reared ih Pe gt stu length 99.95 tn thi cere f Forward and back), and an average value was i ait St obained efor the wrong-length tape covtecion43 Incorrect Tape Length or Standardization Error 57 EXAMPLE 4.1 A distance is measured with a 100-ft ste tape and is found to be 896.24 ft. Later the tape is standardized and is found to have an actual length of 100,04 ft. What is the correct distance measured? SOLUTION ‘The tape is too long and a + correction of 0.04 must be made for each tape length as follows: Measured value = 896.24 ft Total correction = +(0.04)(8.9624) = _+0.36f Corrected distances = 896.60 ft ALTERNATI Obviously, the distance measured equals the number of tape lengths times the actual length of the SOLUTION tape. In this case, it took 8,9624 tape lengths to cover the distance and each tape length was 100.048. Distance measured = (8.9624)(100.04) = 896,60 f EXAMPLE 4.2 A distance is measured with @ 100-ft steel tape and is found to be 2320.30 ft. Later the tape is standardized and is found to have an actual length of 99.97 ft, What is the actual distance? SOLUTION The tape is too short. Therefore, the correction is minus. Measured value = 2320.30 219.601 ALTERNATIVE Using the tape length approach, dividing the measured value by the stated tape length gives SOLUTION 23.2030 tape lengths. Next, multiply the number of tape lengths by the actual length of tape to determine the actual distance, Distance measured = (23.2030)(99.97) = 2319.60 EXAMPLE 4.3 I is desired to lay off a dimension of 1200.00 ft with a 100-f steel tape that has an actual length ‘of 99.95 ft. What field measurement should be made with this tape so that the correct distance is obtained? SOLUTION This problem is stated exactly opposite to the ones of Examples 4.1 and 4.2. Itis obvious that if the tape is used 12 times, the distance measured (12 x 99.95) is less than the 1,200 ft desired, and correction of the number of tape lengths times the error per tape length must be added. 12 tape lengths = 12 x 100,00 = 1200.00 +12 0.05 = 40.604 Field measurement = 1200.60 ft ALTERNATE Dividing the actual distance to be measured by the actual tape length will give the number of SOLUTION tape lengths to use. Next, multiply the number of tape lengths by 100 to determine the field ‘measurement Number of tape lengths = 1200.00/99.95 = 12,006 lengths Field Distance measured = (12.006)(100) = 1200.6458 Chapter Distance Corrections CHECK The answer can be checked by considering the problem in reverse. Here a distance has been measured as being, 1200.60 witha tape 99.95 ft long. What actual distance was measured? The solution is as follows: Measured value = 1200.60 Total correction + ~(0.05)(12.006) = _—0.60ft Corrected distance = 1200.00ft rari * Jenveae ee |) eee CHATPOGA [ARI lear Mara $5 ©. Ket Teaena| Knight €c4, Fwd: [Back [Avg [eere [Bist be [iateo 10a [0.08 TS cay ania [0.07 1 flo ia asm ey Figure 4-1 Taping field nots, 4.4 TEMPERATURE VARIATIONS linea expansion for see tapes is 0.000006: lenprteaael ngene on tng Otte en Te ENS fo Fe ‘As described in Section 4.3, the standardized length ofaisge ne js 100.000 ft long atthe standard temperature wil. tay (0,0000065),100) = 100.021 f. The correction of adage made as described previously for wrong-length tapes {tape is determined at 68°F. A tape that Phave a length of 100,00 + (100 ~ 68) © measured at 100°F with this tape can be ‘The correction of a tape for temperature45 Slope Corrections 59 changes can be expressed with this formula noting that it may be either plus or minus C; = 0.0000065(7 — T;)(L) In this formula, C; is the change in length of the tape due to temperature change, T is the estimated temperature of the tape atthe time of measurement, 7, is the standardized temperature, and L is the tape length. IF ST units are being used, the coeicient of linear expansion is 0.000 011 6 per degree Celsius CC). The correction in length ofa metric tape for temperature changes can be expressed by the formula, C= (0.000 011 6)(7 ~7,)(E) where T, is the standardized temperature of the tape at manufacture (usually 20°C), T is the temperature of the tape at the time of measurement, and 1. isthe tape length Tr will be remembered that the expressions for temperature conversion are as follows: $6 C=5(F—32) °F Oui (°C) +32 Itis clear thata steel tape used on a hot summer day in the bright sunshine will have a much higher temperature than will the surrounding air. Actually, though, partly cloudy summer days will cause the ‘most troublesome variations in length, Fora few minutes the sun shines brightly and then itis covered, for awhile by clouds, causing the tape to coo! quickly. perhaps by as much as 20°F ot 30°F. Accurate corrections for tape temperature variations are difficultto make because the tape temperature may vary along its length with sun, shade, dampness (in grass, on ground), and so on. It has been shown that the variation of a few degrees may make an appreciable variation in the measurement of distance. For the best precision itis desirable to tape on cloudy days, early in the mornings, or late in the afternoons to minimize temperature variations. Furthermore, the very expensive Invar tapes, with their very small coefficients of expansion (0.000001 to 0.000002) are very helpful for precise work, but such measurement has been made obsolete by electronic distance-measuring equipment. For very precise surveying, tape measurements are recorded and the proper corrections made. On cloudy, hazy days an ordinary thermometer may be used for measuring the air temperature, but ‘on bright sunny days the temperature of the tape itself should be determined. For this purpose, plastic thermometers attached to the tapes near the ends (So that their weights do not appreciably affect sag) should be used. (As mentioned previously some tapes have different end marks to be used, depending on the temperature.) Regular steel tapes have not been used for geodetic work for quite a few decades because of their rather large coefficients of expansion and because of the impossibility of accurately determining their temperature during daytime operations. Until electronic distance-measuring. devices were introduced, almost all ofthe base-line measurements of the National Geodetic Survey during the twentieth century were done with Invar tapes. Today, almost all of their length ‘measurements are made with EDMSs although GPS is being used mote each year for this purpose. 4.5 SLOPE CORRECTIONS Most tape measurements are made with tapes held horizontally, thus, avoiding the necessity for ‘making corrections for slope. In this section, however, measurements are assumed to be made on slopes. (You should realize that the correction formula developed inthis section i applicable to plan or alignment measurements as well as to profile or Slope measurements.) In Figure 4-2 a tape of length sis stretched along a slope and itis desired to determine the horizontal distance that has been measured. tis easy for tapemen to apply an approximate correction formula for most slopes. The expression, derived inthis section, is satisfactory for most ‘measurements, but for slopes of greater than approximately 10% to 15%, an exact trigonometric function othe Pythagorean theorem should be used. When a 100-t slope distance is measured, the tase of this approximate expression will cause an error of 0.0013 ft for a 10% slope and a 0.0064- enor for a 15% slope.60 Chapter 4 Distance Corections Figure 4-2. Taping along a slope. Its very helpful to write an expression forthe conection C shown in Figure 4-2. This value, ‘which equals sh in the figure, is written in a more practical form by using the Pythagorean theorem as follows: Sah ee wae from which Pa (s—h)(s+h) 2 sh and since Cash thus, This correction always has @ negative sgn, ‘or the typical 100-f tape, s equals 100ft and i varies fro Practical purposes, therefore, h can alto be assumed to equal long Cyc value: Foe nal 100ft when the slope correctio expression is applied. I is writen for 100 tapes nthe rg NPe® Me slope comecton Sometimes fora Jong constant slope the apes bias huhu men ew asters Secon me ‘hat the correction formula was derived for asingleage ridsncifusenedpabepactee length, the otal conection wll equal he numba ae sth Fot distance of orc dec, one tape “#0: lengths times the correction per tape length4.6 Sag and Tension Corrections 61 EXAMPLE 4.4 ‘A distance was measured on an 8% slope and found to be 2620.30t. What is the horizontal distance measured? | sotuTion | Conestion per tape length = ~ 5 ogy = 0-324 Total correction = (26.2030)(~0.32) = -8.38f Horizontal distance = 2620.30 + (~8.38) = 2611.92 ft If the slope distance 5 is measured with a tape and an instrument is used to measure the vertical angle a from the horizontal to the slope, the horizontal distance can be obtained from the following equation: H = scos. a EXAMPLE 4.5 A slope distance is measured with a steel tape and found to be 1240.32t Ifthe vertical angle is ‘measured with a theodolite and found to be 3° 27', what is the horizontal distance? SOLUTION H = (1240.32)(cos3°27') = 1238.07 ft EXAMPLE 46 It is desired to lay off a horizontal distance with a steel tape along a constant 4° 18" slope. What should the slope distance be so that the resulting horizontal distance is 840.00ft? SOLUTION H _ 8400 _ go 57m cosa” cos 418" 4,6 SAG AND TENSION CORRECTIONS Sag When a steel tape is supported only at its ends, it will sag into a curved shape known asthe catenary: ‘The obvious result is that the horizontal distance between its ends is less than when the tape is supported for its entire length. ‘To determine the difference in the length measured with a fully supported tape and one supported only at its ends or at certain intervals, the following approximate expression may be used. we OUP; where C,= correction in feet and is always negative weight of tape in pounds per foot unsupported length of tape in feet P, = total tension in pounds applied to the tape ‘This expression, although approximate, is sufficiently accurate for many surveying purposes. It is applicable to horizontal taping or to tapes held along slopes of not more than approximately 10°. ‘To minimize sag errors, itis possible to use this formula and apply the appropriate corrections tothe observed distance. Another and more practical procedure for ordinary surveying isto increase the pull or tension on the tape in order to compensate for the effect of sag. For very precise work, theat | 62 Chapter 4 Distance Corrections tape is either supported at sufficient imtervals to make sag effects negligible or it is standardized for the pull and manner of support to be used in the field ‘Variations in Tension ‘A steel tape stretches when it is pulled, and if the pull is greater than that for which it was standardized, the tape will be too long. If less tension is applied, the tape will be too short. A 100-f steel tape will change in length by approximately 0.01 ft for a15-Ib change in pull, Since variations in pull of this magnitude are improbable, erors caused by tension variations are negligible forall except the most precise chaining. Furthermore these errors are accidental and tend to some degree tocancel. Forprecise taping, spring balances are used so that certain prescribed tensile forces can be applied to the tapes. With such balances iti not difficult to apply tensions within 1/2 Ib or closer to desired values, As with all measuring devices, its necessary periodically to check or standardize the tension apparatus against a known standard, Despite the minor significance of tension errors, a general understanding of them is important to the surveyor and will serve to improve the quality ofthe work. The actual elongation of a tape in tension equals the tensile stress in psi over the modulus of elasticity ofthe steel (the modulus of elasticity of a material isthe ratio of stress to stain and equals 29,000,000 psi or 2.050 000 kg/em? for steel times the length ofthe tape. In the following expression, the clongation of the tape in feet is represented by Cy P) is the pull on the tape, isthe erass-sectional area in square inches, is the length in feet, and & is the modulus of elasticity of the stel in PUA, _ Pil EAE twill be noted that the tape has been standardized ata certain pull P, and therefore, in length from the standardized situation is desired and the expression is written 2c the change Normal Tension ) evince with the marked points on the ional tension. Its value may be | clongation of the tpe caused by tension tothe expression py = 0200 AE VPP4.8 Common Mistakes Made in Taping 63 , occurs on both sides of the equation, but its value for a particular tape may be determined by trial-and-error method, For a normal-weight 100-£ tape, this value will probably be in the range of 201b. As described in detail in Section 4.7, most distance measurements are too large because of the ‘cumulative errors of sag, poor alignment, slope, and so on. As. result, overpulling the tape is @ good idea for ordinary surveying because it tends to reduce some of these errors and improve the precision. ‘of the work, For such surveys, an estimated pull of approximately 30 Ibis often recommended. For very precise surveying, the normal tension is applied to the tape by using accurate spring balances. 4.7 COMBINED TAPING CORRECTIONS If corrections must be made for several factors at the same time (e.g., wrong-length tape, slope, temperature), the individual corrections per tape length may be computed separately and added together (taking into account their signs) in order to obtain a combined correction for all. Since each. correction will be relatively small, itis assumed that they do not appreciably affect each other and ‘each can be computed independently. Furthermore, the nominal tape length (100 ft) may be used for the calculation. This means that although the tape may be 99.92 ft long at 68°F and a temperature ‘correction is to be made for a 40°F increase in temperature, the increase in tape length can be figured 1s (40)(0.0000065)(100) without having to use (40)(0.0000065)(99.92). Example 4.7 illustrates the application of several corrections to a single distance measurement EXAMPLE 4.7 SOLUTION ‘A distance was measured on a uniform slope of 8% and was found to be 1665.2 ft. No field slope corrections were made. The tape temperature at the time of measurement was 18°F. What is the correct horizontal distance measured if the tape is 100.06 ft long at 68°F? ‘The corrections per tape length are computed, added together, and then multiplied by the number of tape lengths. Sipe saneco/tps eng = — 30 =-o3200n Temp comsson tape length ~ 60) (0000065) (10) = -00N258 Standanizaton ence length = +000008 Total correction/tape length 0.2925 ft Ganecton for entre dvance ~(16.65)(-02928) = 4878 Abb asated 2 Meuund dome} 5 conestine = 1665.2 + (-4.87) = 1660.3 ft 4.8, COMMON MISTAKES MADE IN TAPING. ‘Some of the most common mistakes made in taping are described in this section, and a method of eliminating each is suggested, Reading Tape Wrong {A frequent mistake made by tapemen is reading the wrong number on the tape, for example, reading. 6 instead of a 9 ora 9 instead of a 6. As tapes become older these mistakes become more frequent because the numbers on the tape become wom. These blunders can be eliminated if tapemen develop the simple habit of looking at the adjacent numbers on the tape when readings are taken,64 Chapter 4 Distance Comections Recording Numbers out to him or her. To Occasionally, the recorder will misunderstand 1 measurement that is called out to hi prevent this kind of mistake, the recorder can repeat the values aloud, including the decimals, as he or she records them, Missing a Tape Length It is not very difficult to lose or gain a tape length in measuring long distances. The careful use of ‘taping pins, described in Section 3.10, should prevent this mistake. In addition, the surveyor can often eliminate such mistakes by cultivating the habit of estimating distances by eye, pacing, o better yet, by taking stadia readings whenever possible. Mistaking End Point of Tape ‘Some tapes are manufactured with 0- and 100-f points atthe very ends of the tapes. Other tapes place them at a little distance from the ends. Tapemen can avoid mistaking the end point of tapes by ‘making sure that they take the time to examine the tape before they begin to take measurements, Making 1-Foot Mistakes ‘When a fractional part of the tape is being used! atthe end ofa line, itis possible to make a I-ft mistake. Mistakes like these can be prevented by carefully following the procedure described for such measurements in Section 3.10. Also helpfal are the habits of calling out the numbers and checking the adjacent numbers on the tape 4.9 ERRORS IN TAPING Accidental Taping Errors Because of human imperfections, taperen cannot read cannot set taping pins perfectly. ‘They will pl ie Baie fammo Bun pstcty. and lace the pins a bitke (a9 far forward or 4 little too far49 Brrorsin Taping 65 back. These errors are accidental in nature and will tend to cancel each other somewhat. Generally. errors caused by setting pins and reading the tapes are minor, but errors caused by plumbing may be ‘very important. Their magnitudes can be reduced by increasing the care with which the work is done or by taping along slopes and applying slope corrections to avoid plumbing. ‘Tape Not Horizontal If tapes are not held in the horizontal position, an error results that causes the surveyor to obtain distances that are too large. These errors are cumulative and can be quite large when surveying is done in hilly country. Here the surveyor must be very careful Ifa surveyor deliberately holds the tape along a slope, he or she can correct the measurement with the slope correction formula which was presented in Section 4.5. It might be noticed that if one end of a 100-ft tape is 1.414 ft above or below the other end, an error of is made, From this expression it can be seen that the error varies as the square of the elevation, difference, If the elevation difference is doubled, the error quadruples. For a 2.828-ft elevation difference, the error made is (2.828) o.08 Incorrect Tape Length ‘These important errors were discussed in Section 4.3 and must be given careful attention if good ‘work is to be done, For a given tape of incorrect length, the errors are cumulative and can add up to sizable values. ‘Temperature Variations Corrections for variations in tape temperature were discussed in Section 4.4. Errors in taping caused by temperature changes are usually thought of as being cumulative for a single day. They may, however, be accidental under unusual circumstances with changing temperatures during the day and also with different temperatures at the same time in different parts ofthe tape. Itis probably wiser to limit tape variations instead of trying to correct for them no matter how large they may be. Taping on cloudy days, early in the morning, or late in the afternoon or using Invar tapes are effective means of limiting length changes caused by temperature variations. Sag Sag effects (discussed in Section 4,6) cause the surveyor to obtain excessive distances. Most ‘surveyors attempt to reduce these errors by overpulling their tapes with a force that wil stretch them sufficiently to counterbalance the sag effects. A rule of thumb used by many for 100-f tapes is to apply an estimated pull of approximately 30 Ib. This practice is satisfactory for surveys of low precision, but it is not adequate for those of high precision because the amount of pull required varies for different tapes, different support conditions, and so on. It is also difficult to estimate by ‘hand the force being applied. A better method is to use a spring balance for applying a definite(See nis... — 66 Chapter 4 Distance Consctions tension toa tape. the tension required having been calculated or determined by a standardized testo equal the normal tension of the tape, Miscellaneous Errors Some of the miscellaneous errors that effect the precision of taping are (1) wind blowing plumb ‘bobs; (2) wind blowing tape to one side, causing the same effect as sag; and (3) taping pins not set exactly where plumb bobs touch ground. 4.10 MAGNITUDE OF ERRORS To get some feeling forthe effects of common taping cor, consider Table 41. In this table various sources of eros are listed together withthe variations that would be necessary foreach error to have 8 magnitude of £0001 ft when a 100. distance is measured with « 10Dft tape For the information shown in Table 42itis assume that a 100-t ste tape is used to measure a distance of 100ft. The ground is gently sloping, and the entire length ofthe tape can be held in 2 horizontal position atone time. Iti fre assumed that the measurement is subject tothe set of Table 4-1. Errors of $0.01 ftin 100-t Measurements TE Souree of error Magnitude of enor Incoopée wpe lengit 11111] TUTTI A gaa EE Incorrect tape length orn ‘Temperature variation” ISP “Tension or pull variation” 15Ib Sag’ 7Sin. sag atcenter tne Alignment’ 1Aftatone end Tape not level” 1 Aft difference in elevation Plumbing oor Marking oof Reading tape oon sours Dacpnd F Ket Heron Coal at holed tka sane ‘Needs (Falls Charch, Va: Ametean Congas one “May be ret minima if shew fd as a ae eg 1D mhemutical corrections ae aphid, Table 4-2 Error Calculation Example Source of err Mi termine wh SBE Temperature variation (15°F) toon» C.on0025 Tension or pall variation (SI) doom 6.000081 Plumbing (0.008) bias 6.000009 Marking (0.001) po 00025 Reading tape (0.001 1) Tabet Nase = Doopia Mos probable crue = VOD < do n119p Corresponding precision = ue 03 Source LF Dra wd. Key Horkaual oon Aled tetas Cages on Stig nd Mag. ig a MM lal eppa ha man RO4.12 Taping Precision 67 accidental or random errors shown in the table. At the bottom of the table the magnitude of the most probable total random error is calculated as described in Chapter 2. ‘Should a distance be taped with the most probable error per tape length determined in Table 4-2 and found to be 2240.320ff, the total probable error as described in Chapter 2 will equal Evoa = SEV 0.0119) (V22.40320) = + 0.0s6te GESTIONS FOR GOOD TAPING If the surveyor studies the errors and mistakes that are made in taping, he or she should be able 10 Speed of tig /2 — ay epTinian. Haea tae e aae 56 Setting Up, Leveling. and Centering EDMs 75 ‘The speed of light is only constant in a vacuum. Within the Earth's atmosphere, the speed of light can be affected by temperature, atmoxpheric pressure, and humidity. Many of today’s EDMs have sensors that measure atmospheric conditions and adjust the speed of light used to calculate distances, The pulses generated by a timed-pulse instrument can be many times more powerful than the energy used for a phase-shift instrument, and hence, the TOF method can achieve a much longer distance measurement, This is especially the case if measurements are taken without prisms. If prisms ‘are not used, many timed-pulse instruments can be used to measure distances between 500 and 1,500‘, depending on light conditions and model. With reflecting prisms their range is extended to several miles, Most phase-shift instruments are incapable of reflectorless distance measurements or can only collect distances of less than 100 ft unless reflector is used. Timed-pulse instrumentsare also very safe to use because, despite their higher energy levels, the pulses are short in duration and therefore the laser beam does not accumulate energy. The continuous laser beams that are used in some phase-shift EDMs to extend their range can be hazardous and are classed accordingly. is important to realize that all objects are reflective, and if something moves onto the beam (such as a car or tree limb) the distance to that object will be determined and not the distance to the desired point. To help the user sight on the correct item, timed-pulse instruments make use of a Visible laser beam that is used to identify the feature desired, ‘When prisms are not used, these EDMs can be used to obtain distances to topographic features that have vertical components, such as buildings, bridges, or stockpiles of materials. Best results are obtained if the item being observed has a smooth light-colored surface perpendicular to the beam. For such cases distances can be measured with a standard deviation of about + mm + 3 ppm, or parts per million), which is comparable to the accuracies achieved with a prism. For medium-dark to ‘dark surfaces and to corners, edges, and inclined surfaces, the maximum distances are not as large and the accuracies are poorer. Just think of all the measurements that can be taken with one of these instruments without having the rodmen climb all over tanks, buildings, stockpiles of materials, and other items to hold the reflectors, It can also be used to locate shorelines for hydrographic surveys, the inside walls of tunnels, and so on. 5.6 SETTING UP, LEVELING, AND CENTERING EDMS Before setting up the EDM tripod some thought should be given to where you will need to stand in relation tothe instrument to make the necessary observations. In other words, you need to determine how the tripod legs should be placed so that you can comfortably stand between them while sighting (see Figure 5-8). ‘The tripod is ideally placed on solid ground, where the instrument will not settle, as it most certainly will in muddy or swampy areas. For such locations it may be necessary to provide some special support forthe instrument, such as stakes or a platform. The tripod legs should be well spread ‘apart and acljusted so that the instrument is approximately level. The instrumentman walks around the instrument and pushes each leg firmly into the ground. On hillsides itis usually convenient to place one leg uphill and two downhill. Such a setup provides better stability. ‘There ate twotypes of tripods available: extension-leg types and fixed-leg types. Fixed-leg tripods tare mote rigid and provide more stabilily during measurements. On the other hand, extension-leg tripods are more easily transported in vehicles and provide more flexibility in setting up, Dinsction of iets Figure $8. Planning an instrument setup.76 Chapter Electronic Distance Measuring Insruments (EDMs) Figure $9 A tibrach. It contains evel screws, level val, and an optical plummet, [EDMs and oer equipment can easily be interchanged o0 op ofa tribrach, (Courtesy “Topcon Positioning Systems) Positions of the tripod legs. After the instrument is fairly close to being centered the plumb bob (if Used) is removed, Jar ecaren Camp i losened andthe wach sid on he twp top unt the optical ross hair is centered on the station point. rege evel cca. leveling evan th ball saye eel ar se, Ahough the a eae eves ae much ss sensitive than the te eves that willbe dcucen Chapter 6, they A vase ee mate Sih EDMS ol ations nde aber sancoig eee ‘The babble in the bul'seye level is centered by adjising ry. bolt that sticks up from the top of the strument. Once the bubble is roughly centered, sucaty eames akes ver ltl te insane, segue ea et discussed in Section 6.7 of this text, Instruments wi serie Peta ‘tout compensators may have tube levels for Precise leveling of the instrument. 'Pensators may have tube | 5.7 NECESSARY STEPS FOR MEASURING DISTANCES WITH EDMS ater) packs are use! © provide power for operating EDM, The batteries my ust be fully charged befor id work i andecale. The wit saver alee are ne the poss convenient delays SSTY spate battery pack on jobs to avoid EDMs are so completely automated distance with an EDM, itis necessary uo that their use can be leamed Very quickly, To measure a Set up the instrument and the rettene the reflectors, to sight on the5.7 Necessary Steps for Measuring Distances with EDMs 77 pau Figure $-10 Centering the bubble. reflectors, and finally to measure and record the value obtained. These steps are briefly described in this section. 1. The EDM is set up, centered, and leveled at one end of the line to be measured. 2. The prism assembly is placed at the other end of the line and is carefully centered over the cend point, This is accomplished by holding the prism pole vertically over the point with the aid of a level that is attached to the rod, by fastening the prism pole in a tripod or bipod placed over the point, or by using a tripod with a tribrach to which the prism assembly is attached, 3. The height of the instrument tothe axis ofthe telescope and the height of the prism center are ‘measured and recorded. With the adjustable prism poles it is common practice to set the prism assembly to the same height as the EDM telescope, 4, The telescope is sighted toward the prism and the power is turned on, 5, The fine adjustment screws are used (o point the instrument toward the reflector until the ‘maximum-strength returning signal is indicated on a signal scale. 6. The measurement is accomplished simply by pushing a button. The user may measure in feet ‘or in meters, as desired. The display will be two places beyond the decimal if the mea- surement is in feet, or to three places beyond the decimal if in meters. Ifthe measurements are recorded in a field book, it is not a bad idea to take an extra measurement using different units (feet or meters). Such a habit may enable one to pick up mistakes in recording, such as transposing numbers, 7. The values obtained are recorded in the field book or they may be recorded in an electroni data collector. Total station instruments (discussed in Chapter 10) automatically record the ‘measurements taken.Ho Pe See 78 Chaptes Electronic se Measuring Instruments (EDM) 5.8 ERRORS IN EDM MEASUREMENTS Some people seem to have the impression that measurements made with electronic instruments such ‘as EDMs and total stations are free of errors, The truth, of course, is that errors are present in any ‘ype of measurement, no matter how modem and up-to-date the equipment used may be. The sources of errors in EDM work are the same as for other types of surveying work: personal, natural, and instrumental Personal Errors Personal errors are caused by such items as not setting the instruments or reflectors exactly over the points and not measuring instrument heights and weather conditions perfectly. For precise distance ‘measurement with an EDM, itis necessary to center the instrument and reflector accurately over the ‘end points of the line. Plumb bobs hanging on strings from the centers of instruments have long been used by surveyors for centering over points and are still in use. For very precise work, however, the ‘ptical plummet is preferred over the plumb bob. With the optical plummet, erors in centering can be greatly reduced (usually, to a fraction of a millimeter. Is advantage over the plumb bob is ‘multiplied when there is appreciable wind. The axis of the optical plummet must be checked periodically under lab conditions, ‘Natural Errors ‘The natural errors present in EDM measurement are ca used by variations in temperature, humidity, and pressure. Some EDMs automatically correct for atmospheric variables, fr others its necessary to ‘dial in” corrections into the instruments, and for il eters, itisnecessary to make matherrated corrections. For instruments requiring adjustments, manufacturers provide tables, chars, and explanations in their manuals regarding how the oo instruments itis necessary to correct for temperature, humidity, and pressure, whetees fre chee ‘optical instruments, humidity can be neglected. (The humi 100 mess effect on ight waves, Meteorological daa shouldbe obisined at cock ad ihe rec oad Sometimes at intermediate points and averaged if a higher pretsion i ested Oe te aoc isionis desired. On hot sunny days it isincin rato eet ctey anther sh ayn Instrument Errors EI il "en careful justed and calibrat the equipment, the smaller the error. Beneral, the more expensive 1 um g0es from the electrical cemter of the ponioted agebebe Cea ate eaaetrandtbea ek otheclecretlconeronte seed lowever. the electrical center of an EDM cles not cine ove AMR erehk Stehangac Mevemetetce cece C Hy wt pts5.10 Accuracies of DMs 79 ‘The exact location of the effective center of the reflector is not easy to obtain because of the fact, that light travels through the glass prisms more slowly than it does through air. The effective center is actually Tocated behind the prisms and the distance needs to be subtracted from measured values. This error, which isa constant, may be compensated for at manufacture or it may be done in the field. Its to be realized that on some occasions reflectors made by different manufacturers (and thus having different constants) may be used with the EDM. If an EDM is supposed to be used with a prism with a 30-mm constant but is being used with a reflector with a 40-mm constant, it may be necessary 10 dial the 40mm into the instrument. 5.9 CALIBRATION OF EDM EQUIPMENT tis important to check EDM measurements periodically against the length of a National Geodetic Survey (NGS) base line or other accurate standard. From the differences in the values an instrument ‘constant can be determined. This constant, which isa systematic error, enables the surveyor to make corrections to future measurements. Although a constant is furnished with the equipment, itis subject 10 change. It is as though we have an incorrect-length tape and have to make a numerical correction. With the value so determined, a correction is applied to each subsequent measurement. In addition, a record of the results and dates when the checks were made should be kept in the surveyor's files in case of future legal disputes involving equipment accuracy. Unfortunately, there seems to be a rather large percentage of practicing surveyors who think that EDMs can continually be used accurately, without the necessity of calibration. However, just as ‘other measuring devices, these instruments must be calibrated periodically. Both electro-optical and microwave equipment should be checked against an accurate base line at frequent intervals. The electronically obtained distances should be determined while taking into consideration differences in elevations, meteorological data, and so on. Most mechanical theodolites and automatic levels remain in good calibration for quite afew years when subjectedtonormal usage. Sadly, thisisnotthecase for EDMs (aging of theelectronic components isone reason) and they must be calibrated at least every few months,evenif they are very carefully used. Recognizing the need for frequent calibration ofthese instruments, the NGS in 1974 began setting up calibration base lines around the United States. Today, there are more than 300 such base line. ‘The NGS compiles and publishes a description of base lines for each state showing location, ¢levations, horizontal distances, and other pertinent data. Copies may be obtained by writing to NGS, National Ocean Survey, Rockville, MD, 20852. Copies are also on hand at each state's surveying society offices and on the NGS website at htp://www.ngs.noaa gov. A detailed description of one of these base lines and its location is presented in Figure 5.11 Ifa base line is not available, two points can be set up (as much as 5 miles apart for microwave equipment) and the distances between them measured. A point can be set in between the other two ‘and the two segmental distances measured (sce Figure 5.12). The sum of those two values should be ‘compared with the overall length. Should the three points not be in a line, angles will be needed to ‘compute the components of the two segments to compare with the overall straight-line distance between the end points. The instrument constant can be calculated as follows—noting that the ‘constant will be present in each of the three measurements: \C AB BC instrument constant It is also desirable to check barometers, thermometers, and psychrometers approximately once 4 month or more often if they are subject to heavy use. These checks can usually be made with ‘equipment that is available at most airports. 5.10 ACCURACIES OF EDMS ‘The manufacturers of EDMs usually list their accuracies as a standard deviation. (It is anticipated that 68.3% of measurements of a quantity will have an error equal to or less than the standard deviation.) The manufacturers give values that consist ofa fixed or constant instrumental error thatoq aydwes v 30 wornduosacy Tp, teat 01383200 aunty 805.11 Computation of Horizor I Distances from Slope Distances 81 8 © igure $-12 Calibrating EDM equipment ‘Table 5-1. Typical Standard Error for Precision Values for an EDM. Distance measured [mf] ‘Standard err (mm) Precision 3098.4) 45.15 sss2 40(131.2), 15.20 17692 60 (196.8), 5.30 W321 100 (28.1) 450 i818 500 (1640.4) 37.50 116,667 is independent of distance, plus a measuring error in parts per million (ppm) that varies with the distance being measured. EDMS are listed as having accuracies in the range from as little as + (1 mm instrumental error + ‘a proportional part error of | ppm) up to (10mm +10 ppm), where ppm is parts per million ofthe distance involved ‘The first ofthese errors is of litle significance for long distances but may be very significant for short distances of 100 or 200 ft or less. On the other hand, the proportional part error is of little significance for short ot long distances. It can be seen that for short distances, EDM equipment may ‘on occasion not provide measurements as precise as those obtained by good taping. Itis assumed that a particular EDM manufacturer provides a standard deviation for one of their instruments as being equal to +(5mm + 5 ppm). With these data the estimated standard error and precision for the measurement of a 100-m distance with this instrument can be computed as follows, where the 100m is converted to millimeters by muliplying it by 1000, 5x 100 x 1000 +++") 3s 1 (100}(1000) ~ 18,182 Error £5.5mn Precision In the same fashion the estimated values for standard error and precisions that would be obtained when measuring several other distances with this instrument are shown in Table 5-1 From the values shown you can see that depending on the precision desired, distances of 100 ft ‘or less can theoretically be measured as precisely or more precisely with a steel tape than with this typical EDM. Despite the fact that these short distances can an occasion be mi tapes than with EDMs, tapes are not often used in practice. The average surveying crew is so accustomed to using EDMSs that, if at all possible, they avoid the more difficult process of taping. In fact, they tape so rarely that they probably would find it quite difficult 0 achieve the high precisions desired and they would be quite prone to making mistakes sured more precisely with 5.11 COMPUTATION OF HORIZONTAL DISTANCES FROM SLOPE DISTANCES. All EDM equipment is used to measure slope distances. For most models the values obtained are corrected for the appropriate meteorological and instrumental corrections and then reduced to horizontal components. It is possible at the same time to determine the vertical components (or differences in elevations) for the slope distance. Ifthe distance involved is rather short and/or the82. Chapter Flectonic Distance Measuring Instruments (EDMs) precision is not extremely high, the horizontal distance (h) equals the slope distance times the cosine Of the vertical angle a: A= scosa For greater distances and higher precision requirements, earth's curvature and atmospheric refraction will need to be considered. With many of the newer instruments, however, the ‘computations are made automatically. As with taping along slopes. the horizontal values may be computed by making corrections with the slope correction formula (described in Section 4.5) by using the Pythagorean theorem, or by applying trigonometry. Ifthe slope is quite steep, say greater than 10% to 15%, the slope correction formula (which is only approximate) should not be used. ‘To compute horizontal distances itis necessary either to determine the elevations at the ends of the line or to measure vertical angles at one or both ends. Example 5.1 illustrates the simple calculations involved when the elevations are known, EXAMPLE 5.1 A slope distance of 1654.32 Was neared beten vo pinu Wiha EDM Ics assured tt | the atmospheric and instrumental eomeetions have been made. Ifthe difference im clevasion between the two points is 183.36ft and ifthe eights of the EDM and its reflector above the ‘round are equal, determine the horizontal distance between the two pins sing | (4) The slope correction formula, (b) The Pythagorean theorem, SOLUTION () Using the slope correction formula: (183.86)? 257 yaesaaa)~ |? ‘n= 1654.32 10.22 ~ 644.1001 (b) Using the Pythagorean theorem for right tangles f= y/(1654,32)° — (183.86) = 1644 o7n stance measured was parallel to the ground: that is, the heights of the EDM and the reflector above the end poin i esbdd ‘equal, that fact must be accounted for in the TT in nen eit ‘Some EDMs have the capability of vertical calculations,5.13 Summary Comments on EDMs 83 Despite the simplicity of EDM operation, however, itis advisable to have personnel trained as thoroughly as possible to get optimum results, No matter how fine and expensive the instruments used for a survey, they are of litle value if they are not used knowledgeably. If a company spends. ‘thousands of dollars for EDM equipment but will not spend an extra few hundred dollars for detailed equipment training, the result will probably be poor economy. A rather common practice among instrument companies is for one of their representatives to provide a few hours or even a day of training when an instrument is delivered. Such a short period is, probably not sufficient to obtain the best results and to protect the large investment in equipment. ‘Some manufacturers offer a week-long training course. Participation in such a course is normally a wise investment and will yield long-range dividends. In addition, surveyors should consider attending workshops or short courses on EDM theory and practice given by the NGS and by ‘manufacturers and universities, 5.13 SUMMARY COMMENTS ON EDMS. EDMS enable us to measure short or long distances quickly and accurately over all types of terrain. Survey or traverse points can quickly be selected without having to choose those to which we can conveniently tape. Ifthe instruments do not convert slope distances to horizontal components, we hhave to make the conversions. Furthermore, it becomes necessary to consider earth's curvature and atmospheric refraction in determining horizontal components if elevation differences at the ends of ‘Tine are more than a few hundred feet and/or if the required accuracy is >1/50,000, We particularly need to remember that all instruments get out of adjustment and thus need to be checked against a standard at frequent intervals. ‘An important and common use of EDMs and total stations is the measurement of lines without the necessity of setting up anywhere along the lines. For illustrative purposes it is desired to determine the distances AB and BC (see Figure 5.13) with the instrument set up at point X. The distances XA, XB, and XC are accurately determined and then the angles a and B shown in the figure are measured as described in subsequent chapters. Finally, the distances and directions of the li AB and BC are computed as is also described in later chapters. Figure 5-13 Determine te distances and directions of AB and BC without setting up along:84° Chapters Electronic Dist PROBLEMS 1 If the manufacturer of a particular EDM states that the Purported accuracy with their instrument is (4mm +. ppm), what error can be expected if a distance of 2,000 is measured? (Ans. = 16mm) 5.2. Repeat Problem 5.1 assuming the distance measured is, 2.400 ft and the purported accuracy is £(004ft + Tppm) 3 What are the advantages of EDMSs over steel tapes for distance measurement? SA What atmospheric conditions need to be measured and factored in when using EDMSs of the infrared type? 5.5 The slope distances shown were measured with an EDM, ‘The vertical angles (measured from the horizontal) were also determined. Caleulate the horizontal distance for each case Slope distance (ft) Vertical angle 3. 386.76 +5180" (Ans: 385.11 A) b.2144.96 #2120" (Ans: 2138.78) 5.6 The slope distances shown were measured with an EDM, In addition, the slope. percentages shown were determined, Compute the horizontal distances and differences in elevation, Slope distance (N) Slope percentage 2.79233, b.112808, nce Measuring Instruments (EDM) US ee $7 The slope distances shown were measured with an EDM. While the differences in elevation between the ends of each line were determined by leveling. What are the horizontal distances? Slope distance (ft) Elevation difference (ft) 27M 78 26.54 (Ans.: 734308) b.Bes1 68 (Ans: 1382.64) e971 +1832 (Ans.: 971,998) Hoy H ee ‘58 The horizon length of a line is 2043.84ft. If the ‘erica angle from the horizontal is 12°24’, what is the slope distance? $9) The slope distance between two points was measured with an EDM and found to be 1223.88 ft. If the zenith angle (Ghe angle ftom the vertical to the ine) is 95°25'14”, compute the horizontal distance, (Ans. 1218418) S10 Repeat Problem 5.9 assuming the slope distance meas ted is 1808.77 and the zenith angle is 87°15'35" Bil AREDM asset upat point A (elevation 605.45) and tied fo measure the slope distance o a reflector at point B {Gl vation 573.861) If he heights of the EDM und reflect (Ans: 117291f0)Chapter 6 Introduction to Leveling 6.1 IMPORTANCE OF LEVELING ‘The determination of elevations using surveying techniques is a comparatively simple but extremely important process. Leveling is a method of determining the difference in elevations between a series Of points. If one point is at a known elevation, then the relative elevations of all ofthe other points. ccan be determined through leveling, The significance of relative elevations cannot be exaggerated, ‘They are so important that one cannot imagine a construction project in which they are not critical, From terracing on a farm or the building of a simple wall to the construction of drainage projects ot the largest buildings and bridges, the control of elevations is of the greatest importance. 6.2 BASIC DEFINITIONS Presented below are a few introductory definitions that are necessary for the understanding of the ‘material to follow. In this chapter and the next, additional definitions are presented as needed for the discussion of leveling. Several of these terms are illustrated in Figure 6-1 ‘A vertical line isa line parallel to the direction of gravity. At a particular point its the direction assumed by a plumb-bob string when the plumb bob is allowed to swing freely and eventually comes to rest Due to the earth’s curvature, plumb-bob lines at points some distance apart are not parallel, but in plane surveying they are assumed to be. A level surface isa surface of constant elevation that is perpendicular to a plumb line at every point. It is best represented by the shape that a large body of still water would take if it were unaffected by tides. ‘The elevation of a particular point is the vertical distance above or below a reference level surface (normally, sea level) AA level line is a curved line in a level surface all points of which are of equal elevation, ‘A horizontal line is a straight-line tangent to a level line at one point 6.3 REFERENCE ELEVATIONS OR DATUMS For a large percentage of surveys, itis reasonable to use some convenient point as a reference or

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