Ch.3

Chapter 3Distance Measurement

61

3.1 Methods of Linear Measurement

Historically, distances have been directly measured by applying an instrument of knownlength against the distance between two or more ground points. As noted in Appendix G,early (3000 B.C.) Egyptians used ropes for distance measurements, having knots tied atconvenient points on the rope to aid in the measurement process. Much later, in the1500s, Edmund Gunter (see next section) invented a 66-ft chain, comprised of 100 links.The Gunter’s chain has significance for North American surveyors because it was thatinstrument that was originally used to lay out most of the continent’s townships in the1700s and 1800s. In the early 1900s, various types of reel-mounted tapes came into use;these tapes were made of cloth, copper wire-reinforced cloth, fiberglass, and steel; allprecise measurements were made with steel tapes. In the second half of the twentiethcentury, EDM instruments came into wide use, especially as integrated components oftotal stations.

Examples of calculated measurements occur when the desired measurement (perhapsover water) is one side of a triangle whose other side(s) and angles have been measured,also, when the slope distance and slope angle have been measured between two points andthe required horizontal distance is then calculated.

3.1.1 PacingPacing is a useful method of approximate measure. Surveyors can determine the length ofpace that, for them, can be comfortably repeated (for convenience, some surveyors use a3-ft stride). Pacing is particularly useful when looking for survey markers in the field. Theplan distance from a found marker to another marker can be paced off to aid in locatingthat marker. Another important use for pacing is for a rough check of all key points inconstruction layouts.

62 Chap. 3 Distance Measurement

3.1.2 OdometerAutomobile odometer readings can be used to measure from one fence line to another whenthey intersect the road right-of-way. These readings are precise enough to differentiate ruralfence lines and can thus assist in identifying platted property lines. This information is use-ful when collecting information to begin a survey. Odometers are also used on measuringwheels that are simply rolled along the ground on the desired route; this approximate tech-nique is employed where low-order precision is acceptable. For example, surveyors fromthe assessor’s office often check property frontages this way, and police officers sometimesuse this technique when preparing sketches of automobile accident scenes.

3.1.3 Electronic Distance MeasurementMost EDM instruments function by sending a light wave along the path to be measured fromthe instrument station, and then the instrument measures the phase differences between thetransmitted light wave and the light wave as it is reflected back to its source from a reflectingprism at the second point. Pulse laser EDMs operate by measuring the time for a laser pulseto be transmitted to a reflector and then returned to the EDM; with the velocity of lightprogrammed into the EDM, the distance to the reflector and back is quickly determined.

3.1.4 Distances Derived from the Analysis of Position Coordinates

Spatial point positioning can be determined by using satellite-positioning techniques, and byusing various scanning techniques (from satellite, aerial, and ground platforms). Once the spatialcoordinates of ground points are known, it is a simple matter, using trigonometric relationships,to compute the horizontal distances (and directions) between them. Also, when the groundcoordinates of a key survey point marker are known, the surveyor can use a satellite-positioningreceiver to navigate to, and thus locate the marker on the ground (which may be buried).

3.1.5 Subtense BarA subtense bar is a tripod-mounted bar with targets set precisely 2 m apart. The targets arekept precisely 2 m apart by the use of invar wires under slight tension. The subtense bar ispositioned over the point and then positioned perpendicular to the survey line. A theodolite(1-second capability) is used to measure the angle between the targets. The farther thesubtense bar is from the theodolite, the smaller will be the angle subtending the 2-m bar.Because trigonometric functions (tangent) of small angles become less reliable as the angledecreases, the longer the distance, the smaller the angle, and the less precise will be thesolution. This technique is accurate (1/5,000) at short distances, that is, less than 500 ft. Thisinstrument was used to obtain distances over difficult terrain, for example, across freeways,water, or steep slopes. See Figure 3.1. Field use of this instrument has declined with thewidespread use of EDM instruments. Subtense bars have recently been used in calibratingbaselines in electronic coordinate determination: a technique of precise positioning usingtwo or more electronic theodolites interfaced to a computer. This technique has been used,for example, to position robotic welding machines on automobile assembly lines.

Sec. 3.3 Tapes 63

FIGURE 3.1 Subtense bar.

3.2 Gunter’s Chain

The measuring device in popular use during settlement of North America (eighteenth andnineteenth centuries) was the Gunter’s chain; it was 66-ft long and subdivided into 100links. It has more than historical interest to surveyors because many property descriptionsstill on file include dimensions in chains and links. This chain, named after its inventor(Edmund Gunter, 1581–1626), was uniquely suited for work in English units:

Because Gunter’s chains were used in many of the original surveys of North America,most of the continent’s early legal plans and records contain dimensions in chains andlinks. Present-day surveyors occasionally must use these old plans and must make conver-sions to feet or meters.

■ EXAMPLE 3.1An old plan shows a dimension of 5 chains, 32 links. Convert this value to (a) feet and(b) meters.

Solution

(a) 5.32 � 66 � 351.12 ft

(b) 5.32 � 66 � 0.3048 � 107.02 m

10 sq chains = 1 acre (10 * 662 = 43,560 sq. ft)

80 chains = 1 mile

4 rods = 1 chain

1 rod = 25 links

1 chain = 100 links

3.3 Tapes

Woven tapes made of linen, Dacron, and the like can have fine copper strands interwovento provide strength and to limit deformation due to long use and moisture. See Figure 3.2.Measurements taken near electric stations should be made with dry nonmetallic or fiber-glass tapes. Fiberglass tapes have now come into widespread use.


(a)

FIGURE 3.2 Fiberglass tapes. (a) Closed case; (b) open reel; (c) tape graduations. (Courtesy ofCST/Berger, Illinois)

(b)

3.4 Steel Tapes

3.4.1 General BackgroundNot so many years ago, most precise measurements were made using steel tapes.Although EDM is now favored because of its high precision and the quickness ofrepeated measurements, even over rough ground and very long distances, thereare some drawbacks when EDM is used for single distances, particularly in the short-distance situations that regularly crop up in engineering applications. The problems

All tapes come in various lengths, the 100-ft and 30-m tapes being the most popu-lar, and are used for many types of measurements where high precision is not required.All woven tapes should be checked periodically (e.g., against a steel tape) to verify theirprecision.

Many tapes are now manufactured with foot units on one side and metric units on thereverse side. Foot-unit tapes are graduated in feet, 0.10 ft, and 0.05 ft or in feet, inches, and1⁄4 inches. Metric tapes are graduated in meters, centimeters (0.01 m), and 1/2 centimeters(0.005 m).

Sec. 3.4 Steel Tapes 65

with EDM in short-distance situations are twofold: (1) the time involved in setting upthe EDM and the prism, and (2) the unreliable accuracies in some short-distancesituations. For example, if a single-check distance is required in a construction layout,and if the distance is short (especially distances less than one tape-length), it is muchquicker to obtain the distance through taping. Also, because most EDMs now havestated accuracies in the range of �(5 mm � 5 ppm) to �(2 mm � 2 ppm), the 5-mm to2-mm errors occur regardless of the length of distance measured. These errors havelittle impact on long distances but can severely impact the measurement of shortdistances. For example, at a distance of 10.000 m, an error of 0.005 m limits accuracyto 1:2,000. The opportunity for additional errors can occur when centering the EDMinstrument over the point (e.g., an additional 0.001–0.002 m for well-adjusted laserplummets), and when centering the prism over the target point, either by using tribrach-mounted prisms or by using prism-pole assemblies. The errors here can range from2 mm for well-adjusted optical/laser plummets to several millimeters for well-adjustedprism-pole circular bubble levels. When laser or optical plummets are poorlyadjusted and/or when prism-pole levels are poorly adjusted, serious errors can occur indistance measurements—errors that do diminish in relative severity as the distancesmeasured increase. For these reasons, the steel tape remains a valuable tool for theengineering surveyor.

Steel tapes (Figure 3.3) are manufactured in both foot and metric units and come ina variety of lengths, graduations, and unit weights. Commonly used foot-unit tapes are of100-, 200-, and 300-ft lengths, with the 100-ft length being the most widely used.Commonly used metric-unit tapes are of 20-, 30-, 50-, and 100-m lengths. The 30-mlength is the most widely used because it closely resembles the 100-ft length tape in fieldcharacteristics.

Generally, lightweight tapes are graduated throughout and are used on the reel; heav-ier tapes are designed for use off the reel (drag tapes) and do not have continuous small-interval markings. Drag tapes are popular in route surveys (highways, railways, etc.),whereas lightweight tapes are more popular in building and municipal works.

FIGURE 3.3 Steel tape and plumb bob.


FIGURE 3.4 Various steel tape markings (hundredth marks not shown). (a) Fully graduated tape;(b) cut tape; (c) add tape.

Invar tapes are composed of 35 percent nickel and 65 percent steel. This alloy has avery low coefficient of thermal expansion, which made this tape useful for pre-EDM pre-cise distance measurement. Steel tapes are occasionally referred to as chains, a throwbackto early surveying practice.

3.4.2 Types of ReadoutsSteel tapes are normally graduated in one of three ways; consider a distance of 38.82 ft (m):

1. The tape is graduated throughout in feet and hundredths (0.01) of a foot, or in metersand millimeters (see Figures 3.3 and 3.4). The distance (38.82 ft) is read directlyfrom the steel tape.

2. The cut tape is marked throughout in feet, with the first and last foot graduated intenths and hundredths of a foot [Figure 3.4(a)]. The metric cut tape is markedthroughout in meters and decimeters, with the first and last decimeters graduatedin millimeters. A measurement is made with the cut tape by one surveyor holdingthe even-foot mark (39 ft in this example). This arrangement allows the othersurveyor to read a distance on the first foot (decimeter), which is graduated inhundredths of a foot (millimeters). For example, the distance from A to B inFigure 3.4(a) is determined by holding 39 ft at B and reading 0.18 ft at A.Distance AB � 38.82 ft (i.e., 39 ft cut 0.18). Because each measurement involvesthis type of mental subtraction, care and attention are required from the surveyorto avoid unwelcome blunders.

3. The add tape is also marked throughout in feet, with the last foot graduated inhundredths of a foot. An additional foot, graduated in hundredths, is included priorto the zero mark. For metric tapes, the last decimeter and the extra before-the-zero

Sec. 3.5 Taping Accessories and Their Use 67

decimeter are graduated in millimeters. The distance AB in Figure 3.4(b) isdetermined by holding 38 ft at B and reading 0.82 ft at A. Distance AB is 38.82 ft(i.e., 38 ft add 0.82).

As noted, cut tapes have the disadvantage of creating opportunities for subtractionmistakes; the add tapes have the disadvantage of forcing the surveyor to adopt awkwardmeasuring stances when measuring from the zero mark. The full meter add tape isthe most difficult to use correctly because the surveyor must fully extend his or herleft (right) arm (which is holding the end of the tape) to position the zero mark onthe tape over the ground point. The problems associated with both add and cut tapes canbe eliminated if, instead, the surveyor uses tapes graduated throughout. These tapes areavailable in both drag- and reel-type tapes.

3.5 Taping Accessories and Their Use

3.5.1 Plumb BobPlumb bobs are normally made of brass and weigh from 8 to 18 oz, with 10 and 12 ozbeing the most common. Plumb bobs are used in taping to transfer from tape to ground (orvice versa) when the tape is being held off the ground to maintain its horizontal alignment.Plumb bobs (and their strings) are also used routinely to provide theodolite or total stationsightings. See Figures 3.5 and 3.9.

3.5.2 Hand LevelThe hand level (Figure 3.6) can be used to keep the steel tape horizontal when measuring.The surveyor at the lower elevation holds the hand level, and a sight is taken back at thehigher-elevation surveyor. For example, if the surveyor with the hand level is sighting withthe instrument cross hair horizontally on his or her partner’s waist, and if both are roughlythe same height, then the surveyor with the hand level is lower by the distance from eye towaist. The low end of the tape is held that distance off the ground (using a plumb bob),the high end of the tape being held on the mark.

FIGURE 3.5 Use of a plumb bob.


(a)

FIGURE 3.6 (a) Hand level.(Courtesy of CST/Berger, Illinois) (b) Hand-level application.

Figure 3.7(a) shows an Abney hand level (clinometer). In addition to the level bubbleand cross hair found on the standard hand level, the clinometer can take vertical angles(to the closest 10 minutes). The clinometer is used mainly to record vertical angles forslope distance reduction to horizontal or to determine the heights of objects. These twoapplications are illustrated in Examples 3.2 and 3.3.

■ EXAMPLE 3.2For height determination, a value of 45º is placed on the scale. The surveyor movesback and forth until the point to be measured is sighted [e.g., the top of the buildingshown in Figure 3.7(b)]. The distance from the observer to the surveyor at the baseof the building is measured with a fiberglass tape. The hand level can be set to zeroto determine where the surveyor’s eye height intersects the building wall. The par-tial height of the building (h1) is equal to this measured distance (i.e., h1/measureddistance � tan 45º � 1). If the distance h2 [eye height mark above the ground;Figure 3.7(b)] is now added to the measured distance, the height of the building (inthis example) is found. In addition to determining the heights of buildings, thistechnique is particularly useful in determining the heights of electric power linesfor highway construction clearances. In Figure 3.7(b), if the measured distance to the second surveyor at the building is 63.75 ft, and if the horizontal line of sight hits the building (the clinometer scale is set to zero for horizontal sights) at5.55 ft (h2), the height of the building is 63.75 � 5.55 � 69.30 ft.

■ EXAMPLE 3.3The clinometer is useful when working on route surveys for which extended-lengthtapes (300 ft or 100 m) are being used. The long tape can be used in slope positionunder proper tension. (Because the tape will be touching the ground in many places,it will be mostly supported, and the tension required will not be too high.) The cli-nometer can be used to measure the slope angle for each tape measurement. These

Sec. 3.5 Taping Accessories and Their Use 69

(a)

FIGURE 3.7 (a) Abney hand level; scale graduated in degrees with a vernier reading to 10 minutes.(Courtesy of CST/Berger, Illinois) (b) Abney hand-level application in height determination. (c) Abneyhand-level typical application in taping.

CourseSlope Angle Line 22–23

Horizontal Distance (ft)

300 �1°14� 299.93

300 �1°32� 299.89

300 �0°52� 299.97

161.72 �1°10� 161.69

Line 22 � 23 � 1,061.48

(c)

slope angles and related slope distances can be used later to compute the appropriatehorizontal distances. The angles, measured distances, and computed distances for afield survey are summarized in Figure 3.7(c).

3.5.3 Additional Taping AccessoriesRange poles are 6-ft wooden or aluminum poles with steel points. The poles are usuallypainted red and white in alternate 1-ft sections. Range poles [Figure 3.8(a)] are used in tap-ing and theodolite work to provide alignment sights. The clamp handle [Figure 3.8(b)]


helps grip the tape at any intermediate point without bending or distorting the tape. Tensionhandles [Figure 3.8(c)] are used in precise work to ensure that the appropriate tension isbeing applied. They are graduated to 30 lb, in 1/2-lb graduations (50 N � 1.24 lb).

Chaining pins (marking arrows) come in sets of eleven. They are painted alternatelyred and white and are 14–18 in. long. Chaining pins are used to mark intermediate pointson the ground; the pin is pushed into the ground at an angle of 45° to the ground and at 90°to the direction of the measurement (to keep the tape clear of the measuring process).In route surveying, the whole set of pins is used to mark out the centerline. The rearsurveyor is responsible for checking the number of whole tape lengths by keeping anaccurate count of the pins collected. Eleven pins are used to measure out 1,000 ft.

Tape repair kits are available so that broken tapes can be put back into servicequickly. The repair kits come in three main varieties: (1) punch pliers and repaireyelets, (2) steel punch block and rivets, and (3) tape repair sleeves. The secondtechnique (punch block) is the only method that gives lasting repair; although the tech-nique is simple, great care must be exercised to ensure that the integrity of the tape ismaintained.

Plumb bob targets are also used to provide alignment sights (Figure 3.9). The plumbbob string is threaded through the upper and lower notches so that the target centerline issuperimposed on the plumb bob string. The target, which can be adjusted up and down thestring for optimal sightings, is preferred to the range pole because of its portability—it fitsin the surveyor’s pocket.

(a)

FIGURE 3.8 Taping accessories. (a) Two-section range pole; (b) tape clamp handle; (c) tension handle.

Sec. 3.6 Taping Techniques 71

FIGURE 3.9 Plumb bob cordtarget used to provide an instru-ment sighting.

3.6 Taping Techniques

Taping is normally performed with the tape held horizontally. If the distance to be meas-ured is across smooth, level land, the tape can simply be laid on the ground and the endmark lined up against the initial survey marker; the tape is properly aligned and tensioned,and then the zero mark on the tape can be marked on the ground. If the distance betweentwo marked points is to be measured, the tape is read as already described in Section 3.4.2.

If the distance to be measured is across sloping or uneven land, at least one end of thetape must be raised up from the ground to keep the tape horizontal. The raised end of thetape is referenced back to the ground mark with the aid of a plumb bob (Figure 3.10).Normally the only time that both ends of the tape are plumbed is when the ground—orother obstruction—rises between the marks being measured (Figure 3.11).

3.6.1 Measuring ProceduresThe measurement begins with the head surveyor carrying the zero end of the tape forwardtoward the final point. He or she continues walking until the tape has been unwound andthe rear surveyor calls, “Tape,” thus alerting the head surveyor to stop walking and to


FIGURE 3.10 Horizontal taping; plumb bob used at one end.

FIGURE 3.11 Horizontal taping; plumb bob used at both ends.

prepare for measuring. If a drag tape is being used, the tape is removed from the reel and aleather thong is attached to the reel end of the tape (the zero end is already equipped witha leather thong). If the tape is not designed to come off the reel, the winding handle isfolded to the lock position so that the reel can be used to help hold the tape. The rearsurveyor can keep the head surveyor on line by sighting a range pole or other target thathas been erected at the final mark. In precise work, these intermediate marks can bealigned by theodolite.

The rear surveyor holds the appropriate graduation against the mark from which themeasurement is being taken. The head surveyor, after ensuring that the tape is straight,slowly increases tension to the proper amount and then marks the ground with a chainingpin or other marker. Once the mark has been made, both surveyors repeat the measuringprocedure to check the measurement. If necessary, corrections are made and the check pro-cedure is repeated.

If the ground is not horizontal (determined by estimation or by use of a hand level),one or both surveyors must use a plumb bob. While plumbing, the tape is often held atwaist height, although any height between the shoulders and the ground is common.Holding the tape above the shoulders creates more chance for error because the surveyormust move his or her eyes up and down to include both the ground mark and the tape

Sec. 3.6 Taping Techniques 73

graduation in his or her field of view. When the surveyor’s eyes are on the tape, the plumbbob may move off the mark, and when his or her eyes are on the ground mark, theplumb bob string may move off the correct tape graduation.

The plumb bob string is usually held on the tape with the left thumb (for right-handed people); take care not to cover the graduation mark completely because, as thetension is increased, it is not unusual for the surveyor to take up some of the tensionwith the left thumb, causing the thumb to slide along the tape. If the graduations havebeen covered completely with the left thumb, the surveyor is not aware that the thumb(and thus the string) has moved, resulting in an erroneous measurement. When plumb-ing, hold the tape close to the body to provide good leverage for applying or holding ten-sion, and to transfer accurately from tape to ground, and vice versa. If the rear surveyoris using a plumb bob, he or she shouts out “Mark,” or some other word indicating that atthat instant in time, the plumb bob is right over the mark. If the head surveyor is alsousing a plumb bob, he or she must wait until both plumb bobs are simultaneously overtheir respective marks.

You will discover that plumbing and marking are difficult aspects of taping. You mayfind it difficult to hold the plumb bob steady over the point and at the same time apply theappropriate tension. To help steady the plumb bob, hold it only a short distance above themark and continually touch down to the point. This momentary touching down dampensthe plumb bob oscillations and generally steadies the plumb bob. Do not allow the plumbbob point to rest on the ground or other surface because you could obtain an erroneousmeasurement.

3.6.2 Breaking TapeA slope is sometimes too steep to permit an entire tape length to be held horizontal. Whenthis occurs, shorter measurements are taken, each with the tape held horizontal; theseshorter measurements are then totaled to provide the overall dimension. This technique,called breaking tape, must be done with greater care because the extra marking and meas-uring operations provide that many more opportunities for the occurrence of randomerrors—errors associated with marking and plumbing. There are two common methods ofbreaking tape. First, the head surveyor takes the zero end forward one tape length and thenwalks back to a point where he or she can hold the tape horizontal with the rear surveyor;if working downhill, the tape can be held at shoulder height. With a plumb bob, the groundcan be marked at an even foot or meter graduation (say, 80 ft or 25 m). The rear surveyorthen comes forward and holds that same graduation on the ground mark while the headsurveyor moves forward to the next pre-selected tape graduation, which is also to be heldat shoulder height (say, 30 ft or 10 m). This procedure is repeated until the head surveyorcan hold the zero graduation and thus complete one full tape length. In the second methodof breaking tape, the head surveyor can proceed forward only until his or her shoulders arehorizontal with the rear surveyor’s knees or feet and can then mark the zero end on theground. The rear surveyor, who is probably holding an even foot or meter right on themark, calls out that value, which is then recorded. This process is repeated until the wholedistance has been measured and all the intermediate measurements are totaled for the finalanswer. See Figure 3.12, which shows the distance AB, comprising the increments AL,LM, and MB.


FIGURE 3.12 Breaking tape.

3.6.3 Taping SummaryThe rear surveyor follows these steps when taping:

1. Aligns the head surveyor by sighting to a range pole or other target, which is placedat the forward station.

2. Holds the tape on the mark, either directly or with the aid of a plumb bob. He or shecalls out “Mark,” or some other word to signal that the tape graduation—or theplumb bob point marking the tape graduation—is momentarily on the mark.

3. Calls out the station and tape reading for each measurement and listens for verificationfrom the head surveyor.

4. Keeps a count of all full tape lengths included in each overall measurement.

5. Maintains the equipment (e.g., wipes the tape clean at the conclusion of the day’swork or as conditions warrant).

The head surveyor follows these steps during taping:

1. Carries the tape forward, ensuring that the tape is free of loops, which can lead tokinks and tape breakage.

2. Prepares the ground surface for the mark (e.g., clears away grass, leaves, etc.).

3. Applies proper tension after first ensuring that the tape is straight.

4. Places marks (e.g., chaining pins, wood stakes, iron bars, nails, rivets, cut crosses).

5. Takes and records measurements of distances and other factors (e.g., temperature).

6. Supervises the taping work.

3.7 Taping Corrections

3.7.1 General BackgroundAs noted in Section 1.12, no measurements can be perfectly performed; thus, all measure-ments (except for counting) must contain some errors. Surveyors must use measuring tech-niques that minimize random errors to acceptable levels and they must make corrections

Sec. 3.8 Systematic Taping Errors and Corrections 75

Systematic Taping Errors* Random Taping Errors†

1. Slope 1. Slope2. Erroneous length 2. Temperature

3. Temperature 3. Tension and sag4. Tension and sag 4. Alignment

5. Marking and plumbing

*See Section 3.8. †See Section 3.9.

3.7.2 Standard Conditions for the Use of Steel TapesTape manufacturers, noting that steel tapes behave differently in various temperature,tension, and support situations, specify the accuracy of their tapes under the followingstandard conditions:

Field conditions usually dictate that some or all of the above standard conditions cannot bemet. The temperature is seldom exactly 68ºF (20ºC), and because many measurements aretaken on a slope, the condition of full support is also not regularly fulfilled when one endof the tape is held off the ground, to keep it horizontal, and plumbed.

3.8 Systematic Taping Errors and Corrections

The previous section outlined the standard conditions for a steel tape to give preciseresults. The standard conditions referred to a specific temperature and tension and to acondition of full support. In addition, the surveyor must be concerned with horizontal ver-sus slope distances and with ensuring that the actual taping techniques are sufficientlyprecise to provide the desired accuracy. Systematic errors in taping are slope, erroneouslength, temperature, tension, and sag. The effects of slope and tension/sag on field meas-urements are discussed in the next section; the techniques for computing corrections forerrors in erroneous length, temperature, tension, and sag are discussed in Appendix F.

3.8.1 Slope CorrectionsSurvey distances can be measured either horizontally or on a slope. Survey measurementsare usually shown on a plan; if they are taken on a slope, they must then be converted tohorizontal distances (plan distances) before they can be plotted. To convert slope distances

to systematic errors that can affect the accuracy of the survey. Typical taping errors aresummarized below:

Foot System Metric System

1. Temperature � 68ºF 1. Temperature � 20ºC2. Tape fully supported throughout 2. Tape fully supported throughout3. Tape under a tension of 10 lb 3. Tape under a tension of 50 N (Newtons)

(a 1 lb force � 4.448 N, so 50 N � 11.24 lbs)


FIGURE 3.13 Computation of the elevation of station 1 � 50.

to their horizontal equivalents, the surveyor must know the slope angle (u), the zenith angle(90 – u), or the vertical distance (V ):

(3.1)

Equation 3.1 can also be written as follows:

where u is the angle of inclination and is the zenith angle.

(3.2)

where V is the difference in elevation. See Example 3.4, part (c).Slope can also be defined as gradient, or rate of grade. The gradient is expressed

as a ratio of the vertical distance over the horizontal distance; this ratio, whenmultiplied by 100, gives a percentage gradient. For example, if the ground rises 2 ft (m)in 100 ft (m), it is said to have a 2-percent gradient (i.e., 2/100 � 100 � 2). Ifthe ground rises 2 ft (m) in 115 ft (m), it is said to have a 1.74-percent gradient (i.e.,2/115 � 100 � 1.739).

If the elevation of a point on a gradient is known (Figure 3.13), the elevation of anyother point on that gradient can be calculated as follows:

If the elevations of two points, as well as the distance between them (Figure 3.14), areknown, the gradient between can be calculated as follows:

Gradient =5.40

337.25* 100 = +1.60%

Distance = 337.25

Elevation difference = 5.40

Elevation at 1 + 50 = 564.22 - 3.75 = 560.47 ft

Difference in elevation = 150 * a 2.5

100b = -3.75

H = 2S2 - V2

(90 - u)

H

S= sin (90 - u) or H = S sin (90 - u)

H (horizontal)

S (slope)= cos u

Sec. 3.8 Systematic Taping Errors and Corrections 77

■ EXAMPLE 3.4 Slope Corrections

(a) Given the slope distance (S) and slope angle u, use Equation 3.1 and Figure 3.15to find the horizontal distance (H):

(b) Given the slope distance (S) and the gradient (slope), find the horizontal distance.See Figures 3.16 and 3.17. First, find the vertical angle (u).

Second, use Equation 3.1 to determine the horizontal distance (H).

H = 113.268 m

H

113.281 = cos 0.85937°

u = 0.85937°

1.50

100 = tan u

= 41.178 m

= 141.216 cos 1° 20œH = S cos u

H

S = cos u

FIGURE 3.14 Gradient computation.

FIGURE 3.15 Horizontaldistance computation.

FIGURE 3.16 Slope angledetermination.

FIGURE 3.17 Horizontaldistance computation.


FIGURE 3.18 Horizontal distancecomputation (metric).

(c) Metric units: Given the slope distance (S ) and difference in elevation (V ), useEquation 3.2 and Figure 3.18 to find the horizontal distance (H).

Foot units: Given the slope distance (S ) and the difference in elevation (V), useEquation 3.2 and Figure 3.19 to find the horizontal distance (H).

3.8.2 Tension/SagThe error in measurement due to sag can sometimes be eliminated by increasing theapplied tension. Tension that eliminates sag errors is known as normal tension. Normaltension ranges from about 19 lb (light 100-ft tapes) to 31 lb (heavy 100-ft tapes).

(3.3)

This formula gives a value for Pn that eliminates the error caused by sag. The formula issolved by making successive approximations for Pn until the equation is satisfied. Thisformula is not used often because of the difficulties in determining the individual tapecharacteristics. See Table F.1 for the units employed in the tension and sag correctionformulas found in Appendix F.

■ EXAMPLE 3.5 Experiment to Determine Normal TensionNormal tension can be determined experimentally for individual tapes, as shown inthe following procedure:

1. Lay the tape flat on a horizontal surface; an indoor corridor is ideal.

2. Select (or mark) a well-defined point on the surface at which the 100-ft mark is held.

3. Attach a tension handle at the zero end of the tape. Apply standard tension—say,10 lb—and mark the surface at 0.00 ft.

4. Repeat the process, switching personnel duties and ensuring that the two marksare, in fact, exactly 100.00 ft apart.

Pn =0.204 W1AE

1Pn - Ps

= 99.8 ft

= 99.807 ft

H = 2(99.822 - 1.62)

= 253.074 m

= 2(253.1012 - 3.7212)

H = 2S2 - V2

FIGURE 3.19 Horizontal distancecomputation (foot units).

Sec. 3.9 Random Taping Errors 79

5. Raise the tape off the surface to a comfortable height (waist). While the surveyor atthe 100-ft end holds a plumb bob over the point, the surveyor at the zero end slowlyincreases tension until his or her plumb bob is also over the mark. The tension readfrom the tension handle will be normal tension for that tape. The readings arerepeated several times, and the average results are used for subsequent field work.

The most popular steel tapes (100 ft) now in use require a normal tension of about 24 lb.For most 30-m steel tapes now in use (lightweight), a normal tension of 90 N (20 lb) is appro-priate. For structural and bridge surveys, very lightweight 200-ft tapes are available and can beused with a comfortable normal tension—in some cases, about 28 lb.

3.9 Random Taping Errors

Random errors occur because surveyors cannot measure perfectly. A factor of estimation isalways present in all measuring activities (except counting). In the previous section, vari-ous systematic errors were discussed; in each of the areas discussed, there was also theopportunity for random errors to occur. For example, the temperature problems all requirethe determination of temperature. If the temperature used is the estimated air temperature,a random error could be associated with the estimation. The temperature of the tape canalso be significantly different from that of the air. In the case of sag and tension, randomerrors can exist when one is estimating applied tension or even estimating between gradu-ations on a spring balance. The higher the precision requirements, the greater must be thecare taken in all aspects of the survey.

In addition to the above-mentioned random errors are perhaps more significantrandom errors associated with alignment, plumbing, marking, and estimating horizontalpositions. Alignment errors occur when the tape is inadvertently aligned off the true path(Figure 3.20). Usually a rear surveyor can keep the head surveyor on line by sighting arange pole marking the terminal point. It would take an alignment error of about 11/2 ft toproduce an error of 0.01 ft in 100 ft. Because it is not difficult to keep the tape aligned byeye to within a few tenths of a foot (0.2–0.3 ft), alignment is not normally a major concern.Note that, although most random errors are compensating, alignment errors are cumulative(misalignment can randomly occur on the left or on the right, but in both cases, the result ofthe misalignment is to make the measurement too long). Alignment errors can be nearlyeliminated on precise surveys by using a theodolite to align all intermediate points.

Marking and plumbing errors are often the most significant of all random tapingerrors. Even experienced surveyors must exercise great care to place a plumbed mark

FIGURE 3.20 Alignment errors.


accurately within 0.02 ft of true value—in a distance of 100 ft. Horizontal measurements,taken with the tape fully supported on the ground, can be determined more accurately thanmeasurements that are taken on a slope and require the use of plumb bobs. Also ruggedterrain conditions that require many breaks in the taping process will cause marking andplumbing errors to multiply significantly.

Errors are also introduced when surveyors estimate a horizontal tape position for aplumbed measurement. The effect of this error is identical to that of the alignment errorpreviously discussed, although the magnitude of these errors is often larger than alignmenterrors. Skilled surveyors can usually estimate a horizontal position to within 1 ft (0.3 m)over a distance of 100 ft (30 m). Even experienced surveyors can be seriously in error,however, when measuring across side-hills, where one’s perspective with respect to thehorizon can be distorted. Using a hand level can largely eliminate these errors.

3.10 Techniques for “Ordinary” Taping Precision

“Ordinary” taping has been referred to as taping at the level of 1/5,000 accuracy. Thetechniques used for “ordinary” taping, once mastered, can easily be maintained. It ispossible to achieve an accuracy level of 1/5,000 with little more effort than is requiredto attain the 1/3,000 level. Because the bulk of all taping measurements is at either the1/3,000 or the 1/5,000 level, experienced surveyors often use 1/5,000 techniques evenfor 1/3,000 level work. This practice permits good measuring work habits to be rein-forced continually without appreciably increasing surveying costs. Because of the widevariety of field conditions that can be encountered, absolute specifications cannot beprescribed. The specifications in Table 3.1 can be considered typical for “ordinary”1/5,000 taping.

To determine the total random error in one tape length, take the square root of thesum of the squares of the individual maximum anticipated errors, as shown in the follow-ing example:

Accuracy = 0.018/100 = 1/5,400 or Accuracy = 0.0056/30 = 1/5,400Error = 1(0.000337) = 0.018 ft or Error = 1(0.000031) = 0.0056 m

Feet Meters

0.0052 0.00142

0.0062 0.00182

0.0052 0.00152

0.0012 0.00042

0.0152 0.00462

0.0052 0.00152

0.000337 0.000031

Sec. 3.11 Mistakes in Taping 81

Table 3.1 SPECIFICATIONS FOR 1/5,000 ACCURACY

Maximum Effect on One Tape Length

Source of Error 100 ft 30 m

Temperature estimated to closest 7ºF (4ºC) �0.005 ft �0.0014 mCare is taken to apply at least normal tension (lightweight tapes),

and tension is known to within 5 lb (20 N) �0.006 ft �0.0018 m

Slope errors are no larger than 1 ft/100 ft (0.30 m/30 m) �0.005 ft �0.0015 mAlignment errors are no larger than 0.5 ft/100 ft (0.15 m/30 m) �0.001 ft �0.0004 m

Plumbing and marking errors are at a maximum of 0.015 ft/100 ft (0.0046 m/30 m) �0.015 ft �0.0046 m

Length of tape is known to within �0.005 ft (0.0015 m) �0.005 ft �0.0015 m

3.11 Mistakes in Taping

If errors can be associated with inexactness, mistakes must be thought of as being blunders.Whereas errors can be analyzed and to some degree predicted, mistakes are unpredictable.Just one undetected mistake can nullify the results of an entire survey; thus, it is essential toperform the work so that you minimize the opportunity for mistakes to occur and also allowfor verification of the results.

Setting up and then rigorously following a standard method of performing the meas-urement minimizes the opportunities for the occurrence of mistakes. The more standardizedand routine the measurement manipulations, the more likely it is that the surveyor will spota mistake. The immediate double-checking of all measurements reduces the opportunitiesfor mistakes to go undetected and at the same time increases the precision of the measure-ment. In addition to checking all measurements immediately, the surveyor is constantlylooking for independent methods of verifying the survey results.

Gross mistakes can often be detected by comparing the survey results with distancesscaled (or read) from existing plans. The simple check technique of pacing can be a valuabletool for rough verification of measured distances—especially construction layout distances.The possibilities for verification are limited only by the surveyor’s diligence and imagination.

Common mistakes encountered in taping are the following:

1. Measuring to or from the wrong marker.

2. Reading the tape incorrectly or transposing figures (e.g., reading or recording 56instead of 65).

3. Losing proper count of the number of full tape lengths involved in a measurement.

4. Recording the values incorrectly in the notes. Sometimes the note keeper hears therear surveyor’s callout correctly, but then transposes the figures when he or sheenters it into the notes. This mistake can be eliminated if the note keeper calls outeach value as it is recorded. The rear surveyor listens for these callouts to ensure thatthe numbers called out are the same as the data originally given.


FIGURE 3.21 Taping field notes for a closed traverse.

5. Calling out figures ambiguously. The rear surveyor can call out 20.27 as “twenty(pause) two seven.” This might be interpreted as 22.7. To avoid mistakes, thisnumber should be called out as “twenty, decimal (or point), two, seven.”

6. Not identifying correctly the zero point of the tape when a cloth or fiberglass tape isused. This mistake can be avoided if the surveyor checks unfamiliar tapes before use.The tape itself can be used to verify the zero mark.

7. Making arithmetic mistakes in sums of dimensions and in error corrections (e.g., temperature). These mistakes can be identified and corrected if each memberof the crew is responsible for checking (and initialing) all computations.

3.12 Field Notes for Taping

Section 1.15 introduced field notes and stressed the importance of neatness, legibility,completeness, and clarity of presentation. Sample field notes will be included in thistext for all typical surveying operations. Figures 3.21 and 3.22 represent typical fieldnotes from taping surveys.

Sec. 3.12 Field Notes for Taping 83

FIGURE 3.22 Taping field notes for building dimensions.

Figure 3.21 shows the taping notes for a traverse survey. The sides of the tra-verse have been measured forward and back, with the results being averaged (mean)if the discrepancy is within acceptable limits (0.015 in this example). Observe thatthe notes are clear and complete and generally satisfy the requirements listed inSection 1.15.

Figure 3.22 shows taping notes for a building dimension survey. In this example,the measurements are entered right on the sketch of the building. If the sketch has linesthat are too short to show the appropriate measured distance, those distances can beentered neatly in an uncrowded portion of the sketch, with arrows joining the measure-ments to the correct lines on the sketch. In this example, the required building wallshave been measured, with the results entered on the sketch. Each wall is remeasured,and if the result is identical to the first measurement, a check mark is placed beside thatmeasurement; if the result varies, the new measurement is also entered beside theoriginal. If the two measurements do not agree within the specified tolerance (0.02 m),the wall is measured again until the tolerance has been met. Compare the page of fieldnotes in Figure 3.22 to the requirements listed in Section 1.15.


3.13 Electronic Distance Measurement

EDM, first introduced in the 1950s by the founders of Geodimeter Inc., has undergonecontinual refinement since those early days. The early instruments, which were capableof very precise measurements over long distances, were large, heavy, complicated, andexpensive. Rapid advances in related technologies have provided lighter, simpler, andless expensive instruments. These EDM instruments are manufactured for use withtheodolites and as modular components of total station instruments. Technologicaladvances in electronics continue at a rapid rate—as evidenced by recent market surveysindicating that most new models of electronic instruments have been on the market forless than 2 years.

Current EDM instruments use infrared light, laser light, or microwaves. Theonce-popular microwave systems use a receiver/transmitter at both ends of the meas-ured line, whereas infrared and laser systems utilize a transmitter at one end of themeasured line and a reflecting prism at the other end. EDM instruments come in longrange (10–20 km), medium range (3–10 km), and short range (0.5–3 km). Some laserEDM instruments measure relatively shorter distances (100–2,000 m) without a reflect-ing prism, reflecting the light directly off the feature (e.g., building wall) beingmeasured. Microwave instruments were often used in hydrographic surveys and have ausual upper measuring range of 50 km. Although microwave systems can be used inpoorer weather conditions (fog, rain, etc.) than can infrared and laser systems, theuncertainties caused by varying humidity conditions over the length of the measuredline may result in lower accuracy expectations. Hydrographic EDM measuring andpositioning techniques have largely been supplanted, in a few short years, by globalpositioning system (GPS) techniques (see Chapter 7).

EDM devices can be mounted on the standards or the telescope of most theodo-lites; they can also be mounted directly in a tribrach. When used with an electronictheodolite, the combined instruments can provide both the horizontal and the verticalposition of one point relative to another. The slope distance provided by an add-on EDMdevice can be reduced to its horizontal and vertical equivalents by utilizing the slopeangle provided by the theodolite. In total station instruments, this reduction is accom-plished automatically.

3.14 Electronic Angle Measurement

The electronic digital theodolite, first introduced in the late 1960s by Carl Zeiss Inc., setthe stage for modern field data collection and processing. (See Figure 4.7, which showselectronic angle measurement using a rotary encoder and photoelectric converters.) Whenthe electronic theodolite is used with a built-in EDM device (e.g., Trimble 3300 series;Figure 3.23) or an add-on and interfaced EDM device (e.g., Wild T-1000; Figure 3.24), thesurveyor has a very powerful instrument. Add to that instrument an onboard microproces-sor that automatically monitors the instrument’s operating status and manages built-insurveying programs, and a data collector (built-in or interfaced) that stores and processes

Sec. 3.14 Electronic Angle Measurement 85

FIGURE 3.23 Trimble total station. The Trimble 3303total stations incorporate DR technology (no prismrequired) and include the choice of the integrated ZeissElta control unit, detachable Geodimeter control unit orhandheld TSCe data collector, and a wide range of softwareoptions. (Courtesy of Trimble Geomatics & EngineeringDivision, Dayton, Ohio)

FIGURE 3.24 Wild T-1000 electronictheodolite, shown with DI 1000 DistomatEDM and the GRE 3 data collector. (Courtesyof Leica Geosystems)


3.15 Principles of EDM

Figure 3.25 shows a wave of wavelength l. The wave is traveling along the x-axis with avelocity of 299,792.458 km/s (in vacuum). The frequency of the wave is the time taken forone complete wavelength:

(3.4)

where l� wavelength in metersc � velocity in km/sf � frequency in hertz (one cycle per second)

Figure 3.26 shows the modulated electromagnetic wave leaving the EDM device andbeing reflected (light waves) or retransmitted (microwaves) back to the EDM device. Youcan see that the double distance (2L) is equal to a whole number of wavelengths (nl), plusthe partial wavelength (f) occurring at the EDM instrument:

(3.5)

The partial wavelength (f) is determined in the instrument by noting the phase delayrequired to match the transmitted and reflected or retransmitted waves precisely. Someinstruments can count the number of full wavelengths (nl) or, instead, the instrument cansend out a series (three or four) of modulated waves at different frequencies. (The frequencyis typically reduced each time by a factor of 10 and, of course, the wavelength is increased

L =(nl + f)

2 meters

l =c

f

measurements and attribute data, and you have what is known as a total station. (Totalstations are described in more detail in Chapters 4 and 5.)

FIGURE 3.25 Light wave.

Sec. 3.15 Principles of EDM 87

each time also by a factor of 10.) By substituting the resulting values of l and f intoEquation 3.5, the value of n can be found. The instruments are designed to carry out this pro-cedure in a matter of seconds and then to display the value of L in digital form.

The velocity of light (including infrared) through the atmosphere can be affected by(1) temperature, (2) atmospheric pressure, and (3) water-vapor content. In practice, thecorrections for temperature and pressure can be performed manually by consultingnomographs similar to that shown in Figure 3.27, or the corrections can be performed

FIGURE 3.26 Principles ofEDM measurement. (Courtesyof Leica Geosystems)

FIGURE 3.27 Atmospheric correctiongraph. (Courtesy of SOKKIA Corp.)


Table 3.2 ATMOSPHERIC ERRORS

Error (Parts per Million)

Parameter Error Light Wave Microwave

Temperature (t) �1ºC �1.0 �1.25Pressure (p) �1 mm Hg �0.4 �0.4Partial water-vapor pressure (e) 1 mm Hg �0.05 � 7 at 20ºC

�17 at 45ºC

3.16 EDM Characteristics

Following are the typical characteristics of recent models of add-on EDM devices.Generally, the more expensive instruments have longer distance ranges and higher precision.

Distance range: 800 m–1 km (single prism with average atmospheric conditions).

Short-range EDM can be extended to 1,300 m using 3 prisms.

Long-range EDM can be extended to 15 km using 11 prisms (Leica Geosystems).

Accuracy range:

�(5 mm � 5 ppm) for short-range EDM.

�(2 mm � 1 ppm) for long-range EDM.

Measuring time: 1.5 s for short-range EDM to 3.5 s for long-range EDM.(Both accuracy and time are considerably reduced for tracking modemeasurements.)

Slope reduction: manual or automatic on some models.

Average of repeated measurements: available on some models.

Battery capability: 1,400–4,200 measurements, depending on the size and condi-tion of the battery and the temperature.

automatically on some EDM devices by the onboard processor/calculator after the valuesfor temperature and pressure have been entered.

For short distances using light-wave EDM, atmospheric corrections have arelatively small significance. For long distances using light-wave instruments and espe-cially microwave instruments, atmospheric corrections can become quite important.Table 3.2 shows the comparative effects of the atmosphere on both light waves andmicrowaves.

At this point, it is also worth noting that several studies of general EDM useshow that more than 90 percent of all distance determinations involve distances of1,000 m or less and that more than 95 percent of all layout measurements involvedistances of 400 m or less. The values in Table 3.2 seem to indicate that, for the typeof measurements normally encountered in the construction and civil engineeringfields, instrumental errors and centering errors hold much more significance than doatmosphere-related errors.

Sec. 3.17 Prisms 89

3.17 Prisms

FIGURE 3.28 Various target andreflector systems in tribrach mounts.(Courtesy of Topcon PositioningSystems, Inc.)

Prisms are used with electro-optical EDM (light, laser, and infrared) to reflect the trans-mitted signals (Figure 3.28). A single reflector is a cube corner prism that has the charac-teristic of reflecting light rays back precisely in the same direction as they are received.This retro-direct capability means that the prism can be somewhat misaligned with respectto the EDM instrument and still be effective. Cutting the corners off a solid glass cubeforms a cube corner prism; the quality of the prism is determined by the flatness of thesurfaces and the perpendicularity of the 90º surfaces. Prisms can be tribrach-mounted on atripod, centered by optical or laser plummet, or attached to a prism pole held vertical ona point with the aid of a bull’s-eye level. Prisms must be tribrach-mounted, however, if ahigher level of accuracy is required.

In control surveys, tribrach-mounted prisms can be detached from their tribrachsand then interchanged with a theodolite/total station similarly mounted at the other end ofthe line being measured. This interchangeability of prism and theodolite/total station(also targets) speeds up the work because the tribrach mounted on the tripod is centeredand leveled only once. Equipment that can be interchanged and mounted on tribrachsalready set up is known as forced-centering equipment.

Prisms mounted on adjustable-length prism poles are portable and thus are particularlysuited for stakeout and topographic surveys. Figure 3.29 shows the prism being steadied bythe use of a bipod—instead of a single prism pole. It is particularly important that prismsmounted on poles or tribrachs be permitted to tilt up and down so that they can be perpendi-cular to short-distance signals that are being sent from much higher or lower positions.

Temperature range: –20ºC to �50ºC. (Note: In the northern United States andCanada, temperatures can easily drop below –20ºC during the winter months.)

Nonprism measurements: available on some models; distances from 100 to 1,200 m(see Section 2.21).


FIGURE 3.29 Steadying the EDMreflector by using a bipod. (Courtesy ofSECO Manufacturing, Redding, CA.Photo by Eli Williem)

3.18 EDM Instrument Accuracies

EDM accuracies are stated in terms of a constant instrumental error and a measuringerror proportional to the distance being measured. Typically, accuracy is claimed as�(5 mm � 5 ppm) or �(0.02 ft � 5 ppm). The 5 mm (0.02 ft) is the instrument errorthat is independent of the length of the measurement, whereas the 5 ppm (5 mm/km)denotes the distance-related error.

Most instruments now on the market have claimed accuracies in the range of �(2 mm �1 ppm) to �(10 mm � 10 ppm). The proportional part error (ppm) is insignificant for mostwork, and the constant part of the error assumes less significance as the distances being meas-ured lengthen. At 10 m, an error of 5 mm represents an accuracy of 1:2,000; at 100 m, an errorof 5 mm represents an accuracy of 1/20,000. At 1,000 m, the same instrumental error repre-sents an accuracy of 1/200,000.

When dealing with accuracy, note that both the EDM and the prism reflectors mustbe corrected for their off-center characteristics. The measurement being recorded goesfrom the electrical center of the EDM device to the back of the prism (allowing for

Sec. 3.19 EDM Without Reflecting Prisms 91

refraction through glass) and then back to the electrical center of the EDM device. TheEDM device manufacturer at the factory compensates for the difference betweenthe electrical center of the EDM device and the plumb line through the tribrach center.The prism constant (–30 to –40 mm) is eliminated either by the EDM device manufac-turer at the factory or in the field.

The EDM/prism constant value can be field-checked in the following manner. A long line (>1 km) is laid out with end stations and an intermediate station (Figure 3.30).The overall distance AC is measured, along with partial lengths AB and BC. The constantvalue will be present in all measurements; therefore,

(3.6)

the constant can also be determined by measuring a known baseline, if one can be conve-niently accessed.

AC - AB - BC = instrument/prism constant

3.19 EDM Without Reflecting Prisms

Some EDM instruments (Figure 3.31) can measure distances without using reflectingprisms—the measuring surface itself is used as a reflector. Both phase-shift technology(Section 3.15) and time-of-flight technology (TOF), also known as pulsed lasers, can be usedfor reflectorless measurement. When the reflecting surface is uneven or not at right angles tothe measuring beam, varying amounts of the light pulses are not returned to the instrument.When using longer-range pulsed-laser techniques, as many as 20,000 pulses per second areemployed to ensure that sufficient data are received. The pulsing of this somewhat stronglaser emission still results in a safety designation of Class I—the safest designation. The useof Class II, III, and IV lasers requires eye protection (see also Section 5.10). Another consid-eration is that various surfaces have different reflective properties; for example, a brightwhite surface at a right angle to the measuring beam may reflect almost 100 percent of thelight, but most natural surfaces reflect light at a rate of only 18 percent (Table 3.3).

EDM instruments can be used conventionally with the reflecting prisms for dis-tances up to 4 km; when used without prisms, the range drops to 100 up to 2,000 m,depending on the equipment, light conditions (cloudy days and night darkness providebetter measuring distances), angle of reflection from the surface, and reflective proper-ties of the measuring surface. With prisms, the available accuracy is about �(1–3 mm �1 ppm); without prisms, the available accuracy ranges from �(3 mm � 3 ppm) up toabout �10 mm. Targets with light-colored and flat surfaces perpendicular to the measur-ing beam (e.g., building walls) provide the best ranges and accuracies. Because of thedifferent reflective capabilities of various surfaces, comparison of different surveyequipment must be made based on standard surfaces; the Kodak Gray Card has beenchosen as such a standard. This card is gray on one side and white on the other. Thewhite side reflects 90 percent of white light and gray side reflects 18 percent of white

FIGURE 3.30 Method of determining the instrument-reflector constant.


(b)

Table 3.3 TRIMBLE DR RANGE TO VARIOUS TARGET SURFACES

Surface Dr300� Dr Standard

Kodak White Card, 90% 800m (2,625 ft) 240m (787 ft)Kodak Gray Card, 18% 300m (984 ft) 120m (393 ft)Concrete 400m (1,312 ft) 100m (328 ft)Wood 400m (1,312 ft) 200m (656 ft)Light rock 300m (984 ft) 150m (492 ft)Dark rock 200m (656 ft) 80m (262 ft)

Source: From Direct Reflex EDM Technology for the Surveyor and Civil Engineer, R. Hoglund and P. Large,2005, Trimble Survey, Westminister, Colorado, USA.

(a)

FIGURE 3.31 Distance measurement without reflectors. (a) Wild T1010 electronic theodolite, togetherwith an interfaced DIOR 3002S prismless EDM (angle accuracy is 3� ). (b) Illustrations of two possible usesfor this technique. Upper: tunnel cross sections. Lower: profiling a difficult-access feature. (Courtesy of LeicaGeosystems)

Problems 93

light. An EDM range to a Kodak Gray Card (18 percent reflective) is considered a goodindicator of typical surveying capabilities.

EDM instruments also provide quick results (0.8 s in rapid mode and 0.3 s in trackingmode), which means that applications for moving targets are possible. Applications areexpected for near-shore hydrographic surveying and in many areas of heavy construction.This technique is already being used, with an interfaced data collector, to measure crosssections automatically in mining applications—with plotted cross sections and excavatedvolumes automatically generated by digital plotter and computer. Other applicationsinclude cross-sectioning above-ground excavated works and material stockpiles; measuringto dangerous or difficult access points, for example, bridge components, cooling towers, anddam faces; and automatically measuring liquid surfaces, for example, municipal waterreservoirs and catchment ponds. These new techniques may have some potential in indus-trial surveying, where production line rates require this type of monitoring.

EDM instruments can be used with an attached visible laser, which helps to identifypositively the feature being measured; that is, the visible laser beam is set on the desiredfeature so that the surveyor can be sure that the correct surface, not some feature just beside orbehind it, is being measured. Some instruments require the surveyor to measure to possiblyconflicting objects (e.g., utility wires that may cross the line of sight closer to the instrument).In this situation, the surveyor first measures to the possibly conflicting wires and then directsthe total station software only to show measurements beyond that range. Because the meas-urement is so fast, care must be taken not to measure mistakenly to an object that may tem-porarily intersect the measuring signal, for example, a truck or other traffic. See Section 5.10for additional information on reflectorless distance measurement. Table 3.3 (the result ofTrimble’s research) shows ranges for reflectorless measurements using both TOF or pulsed-laser (DR300�) technology and phase-shift techniques (DR standard).

Problems3.1 Answer the following statements T (true) or F (false):

(a) EDM tracking mode is a more precise technique, than is EDM regular mode(b) A sag error is introduced when not enough tension is applied to a steel tape laid

directly on a road surface(c) A steel tape measurement was entered in the field book as being 100.00 ft.

Because the temperature at the time of measurement was 53°F, resulting in thetape shrinking to only 99.99 ft, 0.01 ft must be added to the recorded distance tohave the corrected value

(d) A 3.63-percent slope is one that rises 10.08 ft (m) in 277.77 ft (m)(e) An EDM, with a specified accuracy of �(0.02 ft � 5 ppm) was used to layout a

20.00-ft bridge component; this procedure would be more precise than would bethe proper use of a fully supported steel tape used at 68°F

(f) Random taping errors can occur when the plumbed tape is not held exactly horizon-tal each time the tape is used. Because the surveyor may hold the tape too high onsome occasions and too low other times, these random errors will cancel out and notaffect the accuracy of the survey

(g) Invar steel is used to make steel tapes that are less susceptible to temperaturevariations


(h) The average time to complete an EDM distance measurement is 15 s(i) A Kodak Gray Card reflects only 50 percent of white light

3.2 Describe the relative advantages and disadvantages of measuring with steel tapes andwith EDMs.

3.3 Give two examples of possible uses for each of the following field measurementtechniques: (a) pacing, (b) odometer, (c) EDM, (d) subtense bar, (e) fiberglass tape,(f) steel tape.

3.4 The following measurements were taken from an early topographic survey where themeasurements were made with a Gunter’s chain. Convert each of these measurementsto both feet and meters: (a) 18 chains, 61 links; (b) 80.01 chains; (c) 9 chains, 37 links;(d) 5 chains, 11 links.

3.5 You must determine the ground clearance of an overhead electrical cable. Surveyor Bis positioned directly under the cable (surveyor B’s position can be checked by hissighting past the string of a plumb bob, held in his outstretched hand, to the cable);surveyor A sets her clinometer to 45º and then backs away from surveyor B until theoverhead electrical cable is on the cross hair of the leveled clinometer. At this point,surveyors A and B determine the distance between them to be 43.6 ft. Surveyor A thensets the clinometer to 0º and sights surveyor B; this horizontal line of sight cutssurveyor B at a distance of 3.8 ft above the ground. Determine the ground clearance ofthe electrical cable.

3.6 A 100-ft cut steel tape was used to check the layout of a building wall. The rear surveyorheld 71 ft while the head surveyor cut 0.68 ft. What is the distance measured?

3.7 A 100-ft add steel tape was used to measure a partial baseline distance. The rear surveyorheld 50 ft, while the head surveyor held 0.27 ft. What is the distance measured?

3.8 The slope distance between two points is 17.277 m, and the slope angle is 1º42�. Computethe horizontal distance.

3.9 The slope distance between two points is 98.17 ft, and the difference in elevationbetween them is 8.45 ft. Compute the horizontal distance.

3.10 A distance of 133.860 m was measured along a 2-percent slope. Compute the horizontaldistance.

3.11 To verify the constant of a particular prism, a straight line ABC is laid out. The EDMinstrument is first set up at A, with the following measurements recorded:

The EDM instrument is then set up at B, where distance BC is recorded as 289.595 m.Determine the prism constant.

3.12 The EDM slope distance between two points is 2,183.71 ft, and the vertical angle is�2º45�30 � (the vertical angles were read at both ends of the line and then averaged). Ifthe elevation of the instrument station is 285.69 ft and the heights of the instrument,EDM, target, and reflector are all equal to 5.08 ft, compute the elevation of the targetstation and the horizontal distance to that station.

3.13 A line AB is measured at both ends as follows:

Instrument at A, slope distance � 1458.777 m, zenith angle � 92º40�40 �

Instrument at B, slope distance � 1458.757 m, zenith angle � 87º20�00 �

The heights of the instrument, reflector, and target are equal for each observation.(a) Compute the horizontal distance AB.(b) If the elevation at A is 211.841 m, what is the elevation at B?

AC = 488.255 m, AB = 198.690 m

Problems 95

3.14 A coaxial EDM instrument at station K (elevation � 232.47 ft) is used to sight stationsL, M, and N, with the heights of the instrument, target, and reflector equal for eachsighting. The results are as follows:

Instrument at STA. L, zenith angle � 86º30�, EDM distance � 3,000.00 ft

Instrument at STA. M, zenith angle � 91º30�, EDM distance � 3,000.00 ft

Instrument at STA. N, zenith angle � 90º00�, EDM distance � 2,000.00 ft

Compute the elevations of L, M, and N