GEOMATICS ENGINEERING

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Kristian Rodgers
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1 GEOMATICS ENGINEERING CHAPTER 2 Direct and Indirect Distance Measurement Methods

2 Distance Measurement Methods Equipment Classification Usage Fieldwork procedure Booking system Adjustment and plotting

3 Introduction Linear measurement is the basis of all surveying. There are two main methods to measure distance: Direct method Measurements are made by tape or chain Indirect method EDM, Transit, stadia or theodolite are used

4 Types of Distances One of the fundamentals of surveying is the need to measure distance. Distances are not necessarily linear, especially if they occur on the spherical earth. We will deal with distances in geometric space, which we can consider a straight line from one point or feature to another.

Methods of Measuring Horizontal Distance Pacing A surveyor must walk a known distance a number of times in his natural way: accuracy = 1:50 Odometer An odometer converts the number of revolutions of

5 Methods of Measuring Horizontal Distance Pacing A surveyor must walk a known distance a number of times in his natural way: accuracy = 1:50 Odometer An odometer converts the number of revolutions of a wheel of known circumference to a distance. Can be used for preliminary surveys. Odometer distance must be converted to horizontal distance when the slope of the ground is steep. Tachometry Distance is measured indirectly with the help of an optical instrument called tachometer. Theodolite can also be used with leveling staff.

6 Methods of Measuring Horizontal Distance Chaining Used where great precision is not required. Chains of 30 m lengths are frequently used. Taping Used for accurate work and may be o iron, or cloth Usually are 30 m in lengths Accuracy: 1:10,000 Electronic distance measurement (EDM) Waves are utilized to measure the distance. Accuracy: 1:10,000 to 1:100,000

7 Pacing

8 Tapping or Distance Measurement by Tape Equipment's Tension handles allow the user to apply a specified tensile force on the tape. Steel tapes are manufactured under fixed conditions of temperature and tensile force (30 meter tape). Tape grips: These allow the user to firmly grasp the steel tape and resist the pull of the tape from the person located on the other end of the tape. Plumb bobs: These are used to locate the tape precisely over a specified point. Chaining pins: These are used to mark tape lengths. Hand level: These are used to establish an approximate horizontal line of sight.

9 Tapping Equipment

10 General Procedure of Tapping Person A: Holds the tension handle located at the zero end of the tape. Person B: Holds the tape reel and uses a tape grip to pull the tape. Person B: Pinches the plumb bob string at a convenient point on the tape. Person A: Holds the plumb bob string along the edge of the tape above his/her intended mark. Person B: Holds the plumb bob over his/her mark. Calls out mark.mark..mark to indicate that the plumb bob is being held over the intended mark. Braces for the tension applied by person A. Person A: Does the actual pulling (10 lbf or N). Reports the tension value and the corresponding tape measurement. Person B: Reports the tape reading at his/her end of the tape.

11 Using a hand level to establish a horizontal line of sight Person B using the tape grip to hold the plumb bob over her mark (a chaining pin)

12 Person A applying 10 lb or N of tension using the tension handle while maintaining the plumb bob over the mark

13 Measured Distance The measured length is determined by subtracting tape reading A from tape reading B. For example: Person B calls out a tape reading of Person A reports a tape reading of The measured length is computed as or meters. The measurement procedure is repeated with one important difference. Person B holds the plumb bob string at a different point on the tape. The two measured lengths are then compared. If the difference between the measurements is less than the allowable tolerance, then the average of the measured lengths between the two points can be considered accurate. If they are not, the length measurements are be repeated until two successive measurements are obtained within the allowable tolerance.

14 General Procedure of Tapping

15 Distance Measurement for Slope Surface

16 Distance Measurement for Slope Surface

17 Distance Measurement for Slope Surface

18 Tapping Corrections In general, the distance measurement obtained in the field will be in error. Errors in a distance measurement can arise from a number of sources: Instrument errors. A tape may be faulty due to a defect in its manufacturing or from kinking. Natural errors. The actual horizontal distance between the ends of the tape can vary due to the effects of: 1. temperature, 2. elongation due to tension, and 3. sagging. Personal errors. Errors will arise from carelessness by the survey crew: 1. poor alignment 2. tape not horizontal 3. improper plumbing 4. faulty reading of the tape

19 Tapping Corrections When tapes are manufactured, a standardized temperature and a standardized tension value are specified by the manufacturer. Although the standard values vary from tape to tape, typical values are T s = 20 C P s = 50 N. Corrections In the field, all your measured lengths are wrong!! A series of corrections are typically required to account for the effects of: Temperature Sagging Tension Scale (Erroneous tape length) Slope correction

20 1. Erroneous Tape Length Tape has a nominal length under certain conditions, a tape stretches with time. Standardization needs to be carried out frequently by using reference tape or baseline.

21 2. Slope Correction All plan distances are always quoted as horizontal distances L, therefore any distance not measured on the horizontal will need to be corrected for slope. Slope correction must ALWAYS be considered, and either eliminated in the field or mathematically compensated.

22 3. Tension or Pull Correction OR e pull ( P Ps ) L E x A m

23 4. Temperature Correction Most materials expand and contract with temperature change, and this effects taped distances. If a tape has stretched due to heat it will read shorter than it would at its normal (or standard) temperature. e temp L m xc ( T Ts )

24 5. Sag Correction If the tape cannot be supported for its length then it will hang freely under the influence of gravity. The shape of the tape will take is known as (sag) and can be determined mathematically.

25 Corrected Measured Length Actual length is: OR L a L m C temp( T ) Cst( L) Csag ( S ) Cslope C pull( tension) orp

26 Problem 1 A steel tape of nominal length 30 m was used to measure a line AB by suspending it between supports. The following measurements were recorded. The standardization length of the tape against a reference tape was known to be m at 20 o C and 50 N. If the tape weighs 0.17 N/m and has a cross sectional area of 2 mm 2, calculate the horizontal length of AB. Temp. correction factor = m/ o C

27 Solution to Problem 1

28 Problem 2

29 Solution to Problem 2

30 Solution to Problem 2

31 Theodolite Surveying Distance Measurement by Stadia Method

32 Introduction to Theodolite

33 Theodolite Surveying The system of surveying in which the angles are measured with the help of a theodolite, is called Theodolite surveying. In combination with Leveling Staff theodolite can also be used to measure the distance i.e. called as stadia or tachometric method of distance measurement.

34 THEODOLITE The Theodolite is a most accurate surveying instrument mainly used for : Measuring horizontal and vertical angles Locating points on a line Prolonging survey lines Finding difference of level Setting out grades Ranging curves Tachometric Survey (distance measurement)

35 TRANSIT VERNIER THEODOLITE

36 TRANSIT VERNIER THEODOLITE Details of Upper & Lower Plates

37 TRANSIT VERNIER THEODOLITE

38 CLASSIFICATION OF THEODOLITES Theodolites may be classified as ; A. i) Transit Theodolite. ii) Non Transit Theodolite. B. i) Vernier Theodolites. ii) Micrometer Theodolites.

39 CLASSIFICATION OF THEODOLITES A. Transit Theodolite: A theodolite is called a transit theodolite when its telescope can be transited i.e revolved through a complete revolution about its horizontal axis in the vertical plane, whereas in a- Non-Transit type, the telescope cannot be transited. They are inferior in utility and have now become obsolete.

40 CLASSIFICATION OF THEODOLITES B. Vernier Theodolite: For reading the graduated circle if verniers are used, the theodolite is called as a Vernier Theodolite. Whereas, if a micrometer is provided to read the graduated circle the same is called as a Micrometer Theodolite.

41 Description of a Transit Vernier Theodolite A Transit vernier theodolite essentially consist of the following : 1. Leveling Head. 6. T- Frame. 2. Lower Circular Plate. 7. Plumb bob. 3. Upper Plate. 8. Tripod Stand. 4. Telescope. 5. Vernier Scale.

42 Terms Used in Manipulating a Transit Vernier Theodolite 1. Centering Centering means setting the theodolite exactly over an instrument- station so that its vertical axis lies immediately above the station- mark. It can be done by means of plumb bob suspended from a small hook attached to the vertical axis of the theodolite. The center shifting arrangement if provided with the instrument helps in easy and rapid performance of the centering. 2. Transiting Transiting is also known as plunging or reversing. It is the process of turning the telescope about its horizontal axis through in the vertical plane thus bringing it upside down and making it point, exactly in opposite direction. 3. Swinging the telescope It means turning the telescope about its vertical axis in the horizontal plane. A swing is called right or left according as the telescope is rotated clockwise or counter clockwise.

43 4. Face Left If the vertical circle of the instrument is on the left side of the observer while taking a reading, the position is called the face left and the observation taken on the horizontal or vertical circle in this position, is known as the face left observation. 5. Face Right If the vertical circle of the instrument is on the right side of the observer while taking a reading,the position is called the face right and the observation taken on the horizontal or vertical circle in this position, is known as the face right observation. 6. Changing Face It is the operation of bringing the vertical circle to the right of the observer, if originally it is to the left, and vice versa. It is done in two steps; Firstly revolve the telescope through in a vertical plane and then rotate it through in the horizontal plane i.e. first transit the telescope and then swing it through

44 7. Line of Collimation It is also known as the line of sight. It is an imaginary line joining the intersection of the cross- hairs of the diaphragm to the optical centre of the object- glass and its continuation. DIAPHRAGM LINE OF COLLIMATION 8. Axis of the telescope TELESCOPE It is also known an imaginary line joining the optical centre of the objectglass to the center of eye piece. OBJECT GLASS. AXIS OF THE TELESCOPE TELESCOPE

45 9. Axis of the Level Tube It is also called the bubble line. It is a straight line tangential to the longitudinal curve of the level tube at the center of the tube. It is horizontal when the bubble is in the center. 10. Vertical Axis It is the axis about which the telescope can be rotated in the horizontal plane. 11. Horizontal Axis It is the axis about which the telescope can be rotated in the vertical plane. It is also called the trunion axis.

46 Adjustment of a Theodolite The adjustments of a theodolite are of two kinds :- 1. Permanent Adjustments. 2. Temporary Adjustments. 1) Permanent adjustments: The permanent adjustments are made to establish the relationship between the fundamental lines of the theodolite and, once made, they last for a long time. They are essential for the accuracy of observations.

47 Adjustment of a Theodolite 2. Temporary Adjustment The temporary adjustments are made at each set up of the instrument before we start taking observations with the instrument. There are three temporary adjustments of a theodolite:- i) Centering ii) iii) Leveling Focusing

48 Centering of a Theodolite

49 Leveling of a Theodolite

50 Focusing of a Theodolite

51 Leveling Staff

52 Stadia Stadia is a rapid method of measuring distances. Along with the center cross hairs, transits are equipped with two additional cross hairs known as stadia hairs.

53 Definition sketch we can define D as the horizontal distance from the transit to the rod the stadia interval (S) as the distance between the rod reading at the top stadia hair and the rod reading at the bottom stadia hair

54 Horizontal distance When the line of sight is horizontal, the distance (D) from the instrument to the rod is given by: where K is the stadia interval factor (commonly 100) C is a constant (a property of the instrument) S is the difference in the stadia hair rod readings. Many modern transits have the following properties: K = 100 C = 0 (internal-focusing) C = 0.3 (external-focusing) It is your responsibility to check the constant values for your instrument. They are provided on the instrument case and they are not all the same.

55 Example Find the distance from the transit given the following information: K = 100 C = 0 upper stadia reading = m middle reading = m lower stadia reading = m

56 Inclined Sightings (Distance) Due to topography, many stadia shots are inclined. In other words, the line of sight associated with the transit is not horizontal.

57 Inclined Sightings (Distance) We need to modify the equation to account for the inclined line of sight The horizontal distance (H) between the transit and the rod is found using the following expression where α is the vertical angle corresponding to the line of sight note: the angle of inclination can be either positive or negative (i.e. you are shooting down a steep hill)

58 Example Let s use the same numbers as the previous example with the exception that the line of sight is inclined at an angle of 4 degrees. Find the horizontal distance from the transit given the following information: K = 100 C = 0 S = α = 4

59 Vertical Distance we can define the vertical distance (V) as the distance between the rod reading and the instrument (HI). The vertical distance (V) between the rod reading and the instrument is given by:

60 Elevation of the Point finally, we are interested in computing the elevation of the location situated under the survey rod or

61 Elevation of the Point Let s finish off our example by assuming that our HI has been established to be The elevation at the corresponding point of interest would then be found using:

62 Electromagnetic Distance Measurement (EDM) 62

ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM) 63 First introduced by Swedish physicist Erik Bergstrand (Geodimeter) in 1948. Used visible light at night to accurately measure distances of up to 40km.

63 ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM) 63 First introduced by Swedish physicist Erik Bergstrand (Geodimeter) in Used visible light at night to accurately measure distances of up to 40km. In 1957, the first Tellurometer, designed by South African, Dr. T.L. Wadley, was launched. The Tellurometer used microwaves to measure distances up to 80km day or night. First models bulky and power hungry, they revolutionized survey industry which, until their arrival, relied on tape measurements for accurate distance determinations. The picture above shows the remote unit of the CA1000 Tellurometer, which was used extensively in the 70 s and 80 s.

64 64 Introduction to EDM EDM instruments, as the name implies utilizes electromagnetic energy for measuring distances between two points. Electromagnetic waves can be represented in the form of periodic sinusoidal waves. The time taken for an alternating current to go through one complete cycle of values is called period of the wave. One cycle of the wave motion is completed when one period has been completed and number of cycles per unit time is called as frequency (Hertz-one cycle per sec). Wavelength (λ) = velocity of radiation (V) / f

65 Propagation of Electromagnetic Energy 65 Velocity of EM energy V = ƒ λ ƒ is the frequency in hertz (cycles/second) λ is the wavelength In vacuum the velocity of electromagnetic waves equals the speed of light. V = c/n n >1, n is the refractive index of the medium through which the wave propagates c is the speed of light = m/sec f λ = c/n or λ = c/fn Note that n in any homogeneous medium varies with the wavelength λ. White light consists of a combination of wavelengths and hence n for visible light is referred to as a group index of refraction. For EDM purposes the medium through which electromagnetic energy is propagated is the earths atmosphere along the line being measured. It is therefore necessary to determine n of the atmosphere at the time and location at which the measurement is conducted.

66 Propagation of Electromagnetic Energy The refractive index of air varies with air density and is derived from measurements of air temperature and atmospheric pressure at the time and site of a distance measurement. For an average wavelength λ: n a = 1 + ( n g -1 ) x p - 5.5e x T T Where n g is the group index of refraction in a standard atmosphere (T=0 C, p=760mm of mercury, 0.03% carbon dioxide) n g = 1+ ( /λ / λ 4 ) x 10-7 p is the atmospheric pressure in mm of mercury (torr) T is the dry bulb temperature in C and e is the vapor pressure Where e= e +de and e =4.58 x 10a, a=(7.5t )/(237.3+T ), de=-( p ( T ) (T-T ) and T is the wet-bulb temperature So measuring p, T and T will allow for the computation of n for a specific λ 66

67 Amplitude THE FRACTION OF A WAVELENGTH AND THE PHASE ANGLE r λ 180 θ 0 ½λ ½λ - r 270 ¼λ ¼λ ¼λ ¼λ θ λ 360 A fraction of a wavelength can be determined from a corresponding phase angle θ Note: For θ = 0 the fraction is 0 For θ = 90 the fraction is ¼ For θ = 180 the fraction is ½ For θ = 270 the fraction is ¾ For θ = 360 the fraction is 1 EDM INSTRUMENTS CAN MEASURE PHASE ANGLES

68 Principles of Electronic Distance Measurement If an object moves at a constant speed of V over a straight distance L in a time interval t, then L= V t = (c/n) t Knowing the speed of light c and being able to determine the refractive index, we could measure the time interval it takes for an electromagnetic wave to move from A to B to determine the distance L between A and B. But since the speed of light (c) is very high, the time interval t would need to be measured extremely accurately. Instead, the principle of EDM is based on the following relationship: A L = (m + p) λ λ λ λ λ λ λ λ λ λ λ λ λ m is an integer number of whole wavelengths, p is a fraction of a wavelength So L can be determined from λ, m and p L 68 p B

69 69 Distance Measuring by EDM How the process works can be shown using the velocity equation. Velocity = Distance Time The instrument broadcasts a focused signal that is returned by a prism or reflection from the object. Therefore, if the speed of the signal is known (speed of light), and the time for the signal to travel to the target and back is known, the distance can be calculated. Rearranging the equation for distance results in: Distance = Velocity x Time

70 70 EDM Advantages and Disadvantages Advantages of EDM s 1. Precise measurement of distance. 2. Line of sight instrument 3. Capable of measuring long distances 4. Reflector less are single person operation Disadvantages of EDM s 1. Electronic = batterers 2. Accuracy affected by atmospheric conditions. 3. Can be expensive Error ± (2 mm + 2 ppm x D)

71 Distance Measurement by Total Station 71

72 72 Distance Measurement by Total Station Point the instrument at a prism or reflector (which is vertical at the point). Push the measure button and record the distance. We can measure horizontal or slope distance, It is important to note which readings is being collected. If your are measuring the slope distance, the zenith angle must be recorded to allow the computation of horizontal distance. If you are collecting topographic data with elevations, it is important that the height of the instrument and the height of the prism be recorded.

Sources of Error in EDM: Personal: Careless centering of instrument and/or reflector Faulty temperature and pressure measurements Incorrect input of T and p 73

73 Sources of Error in EDM: Personal: Careless centering of instrument and/or reflector Faulty temperature and pressure measurements Incorrect input of T and p 73 Instrumental Instrument not calibrated Electrical center Prism Constant (see next slide) Natural Varying met along line Turbulence in air Remember: L = (m + p) λ

74 A B C Sources of Error in EDM: Determination of System Measuring Constant 1. Measure AB, BC and AC 2. AC + K = (AB + K) + (BC + K) 3. K = AC- (AB + BC) 4. If electrical center is calibrated, K represents the prism constant. 74 Blunders: Incorrect met settings Incorrect scale settings Prism constants ignored Incorrect recording settings (e.g. horizontal vs. slope) Good Practice: Never mix prism types and brands on same project!!! Calibrate regularly!!!

Distance Measuring Methods--GPS 75 GPS (global Positioning System) is a system of 21-24 satellites in orbit around the earth.

75 Distance Measuring Methods--GPS 75 GPS (global Positioning System) is a system of satellites in orbit around the earth. Each satellite knows its position and uses a unique signal to continuously broadcasts this information. Along with the position information is a time signal. When a GPS receiver receives a signal from at least four (4) satellites it can compute its position by trilateration. The receiver position can be expressed in degrees of latitude and longitude, or distance (meters) using Universal Transverse Mercator (UTM) coordinates.

76 76 Distance Measuring Methods-- GPS~ cont. Because UTM distances are based on a x-y coordinate system, distances between points can be determined by simple math. Example: Determine the distance between Stillwater and Oklahoma City when the UTM coordinates for Stillwater are E & N and the UTM coordinates for Oklahoma City are E & N

77 77 Distance Measuring Methods GPS ~ Example Subtracting the coordinates gives the two sides of a right triangle. The hypotenuse of the triangle is the distance between the two towns (44.6 mi). HD = = m = 44.6 mi

78 Numerical Problems-Distance Measurement 78

79 79 Problem-1 The readings given below were made with a tachometric theodolite having a multiplying constant (K) of 100 and no additive constant (C). The reduced level at station A was m and the height of the instrument axis is 1.35 m above the ground. Calculate the gradient expressed as the horizontal distance one meter rise or fall vertically between the stations B and C. Station To Vertical angle Stadia readings A B C /1.524/ /1.356/0.600

80 80

81 81 Problem-2 A tachometric readings were taken from an instrument station A the reduced level of which was m to a staff station B. Instrument multiplying constant (K) is 100, additive constant 360 mm, staff held vertical. The height of instrument is 1.38 m and vertical angle is 30 deg. The stadia readings are 0.714, 1.007, and respectively. Calculate the horizontal and vertical distances.

82 82 Problem-3 In a line ABC, AB measures m, BC measures m and AC measures m using a particular EDM reflector combination,. A line measures m with this instrument-reflector combination. What is the correct length of the line? Solution: K = AC (AB+BC) = ( ) = Corrected length of line = (-0.158) = m

Measurement of Horizontal Distances. the distance between two points means the horizontal distance

Measurement of Horizontal Distances the distance between two points means the horizontal distance Pacing Mechanical Devices Taping * Tachymetric Photogrammetric * Electronic Distance Measurement (EDM)