Surveying Ch. 4-6

EDM classification

EDMs are classified as being electro-optical instruments or microwave instruments. The distinction between them is based on the wavelengths of the electromagnetic energy they transmit. Almost all modern EDMs in use today are electro-optical instruments

turning point (TP)

a temporary point whose elevation is determined during the process of leveling

total station

an electronic/optical instrument used in surveying and to record excavations

EDM's different wavelengths

electro-optical, microwave, and infrared

HI

elevation of the line of sight of the telescope from a reference datum

3 major classifications of surveys

first order (class 1 & 2), second order (class 1 & 2), and third order

collimation error

occurs when the collimation axis is not truly horizontal when the instrument is level. The effect is illustrated in the sketch below, where the collimation axis is tilted with respect to the horizontal by an angle α

sensitivity of a level vial

1.The angle, in seconds, subtended by one division on the scale. Thus, if one division on the scale subtends an angle of 20", we say 20" bubble a)The smaller the angle, the more sensitive the level 2.The radius of the tube's curvature a)The larger this radius, the more sensitive the level. 3.For many levels, each scale spacing is 2 mm wide. 4.The more sensitive the level, the more time consuming it is to level it.

geoid

A particular level surface that serves as a datum for all elevations and astronomical measurements

horizontal plane

A plane perpendicular to the local direction of gravity

vertical control

A series of Benchmarks or other points of known elevation established throughout an area.

theodolite

Measures vertical and horizontal angles

phase-shift EDMs

Phase shift devices calculate the number of wavelengths between the instrument and the reflector

line of collimation

the axial line of the telescope of an astronomical or geodetic instrument, or the line which passes through the optical center of the object glass and the intersection of the cross wires at its focus

reciprocal leveling

used in leveling across topographical features such as rivers, lakes, and canyons

estimation

•"Calibrated" eyeball - measuring by experience •Least precise, but used quite a lot especially to catch blunders •Precision: 1/10 ~ 1/20

level surface

•A curved surface that at every point is perpendicular to the local plumb line. -It is best represented by the shape that a large body of still water would take if it were unaffected by tides. Also called an equipotential surface

GPS technology

•A global navigation satellite system •Developed by the U.S. Department of Defense •A constellation of satellites that broadcast radio signals •Receivers intercept several satellite signals in order to determine precise location

horizontal line

•A line in a horizontal plane. It is tangent to a level line at one point

vertical line

•A line parallel to the local direction of gravity as indicated by a plumb-bob. -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.

State Plane Coordinate System (SPCS)

•A set of 124 geographic zones or coordinate systems designed for specific regions of the United States. • Each state contains one or more state plane zones, the boundaries of which usually follow county lines. •There are 110 zones in the contiguous US, with 10 more in Alaska, 5 in Hawaii, and one for Puerto Rico and US Virgin Islands.

distance measurement

•A spectrum of methods ranging from crude to sophisticated; from least precise to highly precise: •Estimation •Pacing •Optical Methods •Stadia •Range Finder •Measuring Wheel •Taping/Chaining •EDM - Electronic Distance Measuring Instruments •GPS - Global Positioning Systems

stadia

•An optical method •Good for mapping •Precision: 1/100 ~ 1/200

vertical datum

•Any level surface to which elevations are referenced. -It is arbitrarily assigned an elevation of zero. -Also known as a reference datum

cross sections

•Are lines of levels or short profiles made perpendicular to the centerline of a project •They provide information for estimating quantities of earthworks •Two types -Route projects -Borrow pits •For route projects, cross sections are taken at regular intervals (50- or 100-ft) and at sudden changes in the centerline profile.

control surveys

•Are reference surveys with precise horizontal and vertical positions. -Vertical - produce benchmarks •NGVD29 and NAVD88: elevation is accurate, but X and Y are approximate -Horizontal - produce horizontal control points (marks); monuments. •NAD27 and NAD83: X and Y are known and accurate, elevation is approximate. •Now, 3-D marks: X,Y, &Z are all accurate.

inconsistent pull

•C_P=(P_1-P) L/AE -Where: •Cp = total elongation in tape length in feet •L = total length of line •P1 = actual pull applied to tape in pounds •P = standard pull in pounds •E = modulus of elasticity of steel (29,000,000 lb/in.2) •A = cross sectional area of tape in square inches

natural errors

•Caused by variations in -Temperature -Humidity -Pressure •These factors affect the index of refraction and thereby modifies the wavelength of electromagnetic energy.

automatic level

•Commonly used on building sites •Internal compensator can automatically level the instrument •Measures difference in elevation between the line of sight and a point

second order surveys

•Densify the national network •Subsidiary metropolitan control •Less accurate •Used for -Control along tidal boundaries -Large construction projects -Interstate Highways -Urban renewal Small reservoirs

accuracy in EDM

•EDM instrument accuracies are stated in terms of an instrumental error and a measuring error, which are proportional to the distance measured. •Typically, accuracy is given as ±{5 mm + 5 ppm(parts per million)}. Here, the first numerical ±5 mm is the instrument error, which is independent of the measurement, and the second numerical 5-ppm (i.e. 5 ppm = 5 mm/km) denotes the distance related error. •High end receivers are getting accuracies up to ±(3 mm + 1 ppm), whereas the low end receivers are getting accuracies up to ±(10 mm + 10 ppm). •The second part of the error, known as a proportional part error (10ppm), is insignificant for most works, and the constant part of the error ±(5 mm) is less significant as the distance being measured lengthens. •At 100 m, an error of ±5 mm represents 1/20,000 accuracy, whereas for 1000 m, the same instrument error represents 1/200,000 accuracy. •For most accurate works, both the EDM instrument and the prism reflectors must be corrected for off-center characteristics.

determining M

•EDM instruments cannot determine the number of whole wavelengths in an unknown distance by transmitting only one frequency and wavelength. •The instrument transmits a series of three or four modulated waves at different frequencies. •By substituting the resulting values of λ and p in the above equation for three or four different frequencies, the value of m can be found. The instruments are designed to carry out this procedure within seconds, and display the value of L. •The velocity of light (electromagnetic waves) through the atmosphere can be affected by: •Temperature •Atmospheric pressure •Water vapor content in the atmosphere •The corrections are calculated automatically in the instrument itself by inputting the values for temperature and pressure.

time-pulse EDMs

•Employ a signal that is transmitted by a laser diode •To obtain a measurement, the time of flight (TOF) required for a signal to travel to and from and object is calculated by: distance = speed of light / 2

differential leveling

The establishment of differences in elevation between two or more points with respect to a datum

adjustment in proportion to distance

The logical correction to the measured elevation of a particular point in a level circuit should be to the total correction as the distance to that point from the beginning point is to the total circuit distance.

profile leveling procedure

-Set instrument at a convenient point -Take BS of a BM -Calculate HI -Take a series of intermediate foresights (IFS) at regular intervals (50-,100-ft) and at points where sudden changes in elevation occur (such as tops and bottoms of river banks, edges and center lines of roads and ditches, etc) -If necessary, take FS on a TP, move the instrument to another position and take another series of readings.

profile leveling data collection

-Set stakes along the center line of the project at regular intervals, say 50 ft or 100 ft. -Distancing from the starting point are indicated by stationing. •Points along the route with even multiples of 100ft are referred to as full stations: 0+00, 1+00, 2+00 etc •Intermediate stations ---> plus stations: 2 +34.65 ≡ 234.65 ft

barometric leveling

A type of indirect leveling in which differences of elevation are determined from differences of atmospheric pressure observed with altimeters or barometers

errors in EDM

Recall: accuracies of EDMI are quoted in two parts: the instrumental (constant) error, which is significant for short distances, and the measuring error, which is significant for long distances. Major error components in a measured distance are instrument and target miscentering, and the specified constant and scalar errors of the EDMI

benchmark

permanent mark that establishes a point of known elevation

methods of determining differences in elevation

taping or electronic, differential, barometric, and trigonometric

adjustment of simple level circuits

•Error is called misclosure -Loop misclosure - return to starting BM -Section misclosure - closure is made to another BM. •Actions -Adjust: If misclosure is within tolerance -Repeat run: If misclosure is outside tolerance limits •Adjustment Methods: -In proportion to distance -In proportion to the number of instrument setups

stadia readings

•Estimate distance between rod and instrument •Rod intercept is the difference between stadia readings •rod intercept = upper stadia - lower stadia •Estimated distance •distance ~ rod intercept x stadia multiplier •Stadia multiplier typically = 100 -Indicated on inside of instrument case or in Instructional Manual

precision guides

•Excellent leveling - readings to the nearest 0.001 ft -Sights no greater than 300 ft. -Allowable misclosure: ±0.05√M; M is length of circuit in miles •Corresponds to ±12mm√K for 3rd order control surveys •For average leveling C = 0.01√n (ft) •For simple construction survey C = 0.02√n (ft) •n = number of instrument set ups.

instrumental errors

•Include -Drift from calibration due to wear, tear and time. -Presence of Reflector Constant, K •Can be as large as 70 mm and varies with reflectors •The correct value has to be determined and be added to correct the observed distances

personal errors

•Include: -Inaccurate setups of EDM instruments and reflectors over stations. (see Table 6.2) -Faulty measurements of instrument and reflector heights -Errors in determining atmospheric pressure and temperatures •Mistakes need to be avoided -A common mistake is failing to set the temperature and pressure of the instrument before taking measurements. (see Table 6.3)

third order surveys

•Less accurate than 2nd order •Used for -Local control surveys -Small engineering projects -Small scale topo maps -Boundary surveys

leveling

•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 the other points can be determined through leveling. •Leveling results are useful in many situations: -Design of highways, railroads, canals, sewers, water supply systems -Laying out construction projects -Calculation of earthwork volumes -Investigate drainage characteristics of an area Study subsistence and crustal motion of the Earth

range finder

•Many types •Used: - By the military •Artillery •Submarines - periscope •In Golf •For Hunting Precision: 1/100 ~ 1/200

tape corrections

•Measurements are done in two ways: -The distance between two points is desired -A required distance is required to be laid-off. •For Distance Between two points: -Long tapes measure short; add a correction -Short tapes measure long, subtract a correction •For a laid-off distance: -Long tapes measure long; subtract -Short tapes measure short; add

EDM instruments without reflectors

•Most modern EDM instruments can measure distances using reflecting prisms. The measuring surface itself is used as a reflector. •Some models use time pulsed infrared signals, transmitted by a laser diode. •These EDM instruments can be used conventionally using reflecting prisms for distances up to 4 km. Their capability of measuring distances without prisms limits to 80-250 m, depending upon the light conditions (cloudy days and night darkness provide better measurement of distances) and the smoothness of the reflecting surface. •Usually, when measuring with prisms, the accuracy comes to around ± (3 mm + 1 ppm) for top end models. But the accuracy drops to 610 mm when measurements are taken without prisms. •Targets with light colored flat surfaces perpendicular to the measuring beam provide the best range accuracies.

incorrect length of tape

•NIST (National Institute of Standards and Technology) standardizes a tape: -680F, 12-lb pull, fully supported throughout -680F, 20-lb pull, supported at the ends only •C_L=((l-l^′)/l^′ )L •Where: CL = correction to be applied to L •L = measured length of line •l = actual length of tape l' = nominal length of tape

pacing

•Normal walking •Different from person to person •Usually expressed as # of paces/100ft •e.g 36paces/100 or 18paces/50 or 9 paces/25 ft •Not the same thing as "stride" •1 stride is approximately equal to 2 paces •Precision: 1/50~ 1/200

electronic distance measurement (EDM)

•Original EDMs were individual units used only for distance measurements. •EDM instruments used as a modular component in modern total stations also work under the same principle of separate EDM instruments. •Definitions -Visible light: that part of the EM spectrum to which the eye is sensitive (λ = 0.4 - 0.7 microns) -Infrared light: has frequencies below the visible portion of the spectrum with λ = 0.7 - 1.2 microns -An Electro-optical instrument is one that transmits modulated light, either visible or infrared. -A reflector consists of several retroreflective glass cube corner prisms mounted on a tripod. -A laser is one of several devices that produces a very powerful single-color beam of light A microwave is an EM radiation that has a long wavelength and a low frequency. The microwaves used in distance measurements have wavelengths from 10 -100 microns

EDM

•Pole 16.5 ft •Chains - chaining -66'/100 links •Mostly used in the 1800s •1 acre = 10 chain^2 i.e. 10 x (66x66) = 43560 square ft. -Precision: 1/300 •Steel Tape - taping -100 ft (30 m) is the standard -Used extensively until the 1970s -Precision: •Ordinary taping: 1/500 •Precise taping: 1/500,000

taping or chaining

•Pole 16.5 ft •Chains - chaining -66'/100 links •Mostly used in the 1800s •1 acre = 10 chain^2 i.e. 10 x (66x66) = 43560 square ft. -Precision: 1/300 •Steel Tape - taping -100 ft (30 m) is the standard -Used extensively until the 1970s -Precision: •Ordinary taping: 1/500 •Precise taping: 1/500,000

precise leveling

•Practices that improve the precision of leveling: -Setting up tripod legs firmly in solid ground -Allowing the least time possible between BS and FS readings for each setup -Using clearly marked solid TPs -Limiting sight distances to 300ft or less, -Careful plumbing of level rods, -Avoiding leveling during strong winds and severe heat waves -Keeping lines of sight at least 2 ft above the ground because of atmospheric refraction effects.

first order surveys

•Primary national control network •Metropolitan area surveys •Scientific studies -Very accurate surveys used for •Military & defense •Sophisticated engineering projects •Dams •Tunnels

profile leveling

•Process of determining a series of elevations along a fixed line -Used for location, design, and construction of highways, canals, railroads, water lines, etc •Consists of a line of differential levels with a series of intermediate shots taken during the process.

Earth's curvature and atmospheric refraction

•So far, we have been assuming that when the the instrument is level, the line of sight will represent a level line. •This is not true. There is distortion due to: •Earth's curvature •Refraction of light due to atmospheric conditions.

distance measurements by taping

•Sources of Error in Taping -Instrumental errors -Natural errors -Personal errors •Tape Corrections -Incorrect length of tape -Effect of temperature -Effect of tension -Sag Off-line and Slope

principles of EDM

•The principle of the measurement device in EDM is that it calculates the distance by measuring the phase shift during the radiated electromagnetic wave (such as an infrared light or laser light or microwave) from the EDM's main unit, which returns by being reflected through the reflector, which is positioned at a measurement point. •Measurement Method: -Phase shift: more accurate Timed pulses: better range

GPS

•USDoD's NAVigation Satellite Timing and Ranging (NAVSTAR) Global Positioning System -Utilizes the GNSS - Global Navigation Satellite Systems -Development of the first generation of satellite positioning systems started in 1958 and became fully operational in 1993. •Other Satellite Navigation Systems -GLONASS - Russian -Galileo System - European Union -BeiDou System - China

measuring wheel (odometer)

•Used in construction •Used by the police (crime scene and accident investigation) •Precision: 1/200 ~ 1/300

trigonometric leveling

•Used to determine elevations of inaccessible points such as: -Mountain peaks -Church steeples -Offshore platforms •Increasingly common with the advent of total stations which allow for the quick and easy measurements of several quantities such as slope distance and vertical angles from a single setup

foresight (FS)

•a sight taken to any point to determine its elevation. -Often called minus sights (-S)

backsight (BS)

•a sight taken to the level rod held on a point of known elevation (BM or TP) to determine the height of the instrument (HI). -Also called a plus sight (+S)

rough leveling

•preliminary surveys in which readings are taken to the nearest 0.1 ft; -Sights of up to 1000 ft may be used -Allowable misclosure is ±0.4√M; M is length of circuit in miles

average leveling

•rod readings are taken to the nearest 0.01 ft -Sights of up to 500 ft may be used -About 90% of all leveling -Allowable Misclosure: ±0.1√M; M is length of circuit in miles

elevation

•the vertical distance above or below a reference level -Also called the height above a datum and orthometric height.