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MRS SITI KAMARIAH MD SA’AT 019-5706232 sitikamariah@unimap.edu.my ERT252 GEOMATIC ENGINEERING

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LINEAR MEASUREMENT

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Introduction 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. In this course we will deal with distances in geometric space, which we can consider a straight line from one point or feature to another.

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Distance Measurements Distance between two points can be horizontally, slope or vertically recorded in feet/meters. Horizontal and slope distance can be measured using fibreglass tape/steel tape/using electronic distance measuring device. Vertical distance can be measured using a tape, as in construction work, with a autolevel and staff. It also can be determine by trigonometry.

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Slope, Vertical and Horizontal Distances

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Distance Measurements

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Distance Measurement Equipment

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ELECTRONIC DISTANCE MEASUREMENT (EDM) EDM is very useful in measuring distances that are difficult to access or long distances. It measures the time required for a wave to sent to a target and reflect back.

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Taping (or chaining) Taping is applied to measurement with a steel tape or synthetic tape (plastic or fiberglass). All standard in lengths – 100 m, 50m, 30 m, 20 m. It is fairly quick, easy and cheap, and hence is the most common form of distance measurement.

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Taping (or chaining) Unfortunately, taping is prone to errors and mistakes. For high accuracy, steel tape should be used which is graduated in mm and calibrated under standard temp (20 degree) and tension (5kg). Be careful, easily break. Synthetic tape is more flexible graduated in 10mm

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Taping

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Tape must always be straight Tape must not be twisted Use chaining arrows for intermediate points Tape horizontally if possible Tape on the ground if possible Slope taping needs to be reduced Catenary taping requires correction Step taping suits some applications Taping on smooth level/sloping ground

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Tape must be straight… required distance measured obstruction measured distance required distance

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For very long distance

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Length AB = 4 x Full tape distance + 1 Short section REMEMBER ! It works only on smooth ground or uniform slope surfaces For very long distance

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Use chaining arrows… required distance measured distance measured distance required distance

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Sloping Ground Measurement

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Slope Measurement

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Instrumental errors – actual length can be different from nominal length because of a defect in manufacture or repair on as a result of kinks. Natural errors – the horizontal distance of a tape varies because of effects of temperature, wind and weight of tape itself. Personal errors – Tape persons may be careless in setting pins, reading tape or manupulating equipment. Sources of Error in Taping

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Taping Errors Systematic Taping Errors Random Taping Error 1. Slope 2. Standardization length2. Temperature 3. Temperature3. Tension and Sag 4. Tension & Sag4. Alignment 5. Marking & Plumbing Typical taping errors: Incorrect length of tape Temperature other than standard

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Taping Corrections For synthetic tapes, only Standardized Tape Length correction and Slope corrections will be applied The best accuracy that can be achieved is the order of 1:1000 When using steel tapes, if only Standardized Tape Length and slope corrections are considered, the best possible accuracy that can be obtained in the range 1:5000. If tension and temperature are added into consideration, accuracy can be increased to better than 1:10000 ~ 1: 20000 Sag only applies if tape is supported only at ends

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Example: A distance of 220.450 m was measured with a steel band of nominal length 30 m. On standardization the tape was found to be 30.003 m. Calculate the correct measured distance, assuming the error is evenly distributed throughout the tape. Error per 30 m, C = 3 mm Correction for total length = = 220.45(0.003)/30 =0.022 m Correct length is 220.450 + 0.022 = 220.472 m Standard Length Correction Where Ca = correction of absolute length C = correction to be applied to the tape L= measured length l = nominal length of the tape

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Consider a 50-m tape measuring on a slope with a difference in height of 5 m. The correction for slope is = –25/100 = –0.250 m Slope Correction

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E is modulus of elasticity of tape in N/mm 2 = 2.1 x 10 5 N/mm2 for steel A is cross-sectional area of the tape in mm 2 L is measured length in m; and Po is the standard pull P is pull applied during measurement As the tape is stretched under the extra tension, the correction is positive. If less than standard, the correction is negative. Tension correction

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Consider a 50-m tape with a cross-sectional area of 4 mm 2, a standard tension of 50 N and a value for the modulus of elasticity of E = 210 kN/mm 2. Under a pull of 90 N the tape would stretch by Tension correction

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Where Tm = mean temperature during measurement To = temperature of standardization Coefficient of expansion of steel α = 3.5 × 10 –6 per o C If L = 50 m and the different of temperature and standard temperature (20 o C) in temperature is ± 2°C then = ? Temperature Correction

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Consider a 50-m heavy tape of w = 1.7 kg with a standard tension of 80 N: Sag Correction

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Summary : Correction Slope correction Standardization correction Tension correction Temperature correction Sag correction

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Example 1: Length recorded on tape HeightTemperature Tension applied A1A2 23.512 m21.50 m23.50 m28 o C100 N A steel tape of nominal length 30 m was used to check the distance between two offset pegs A1 and A2. The following results were obtained. Compared to 25.000 m baseline, the tape read 24.994 m with 50 N tensions applied to at 15 o C. The cross sectional area of the tape is 2.0 mm2 and it weigh 4.5 N. Calculate the horizontal length A1 to A2.

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Slope correction slope correction = – 0.0851 m Standardization correction standardisation correction = + 0.0056 m Tension correction tension correction = + 0.0029 m Temperature correction Sag correction Horizontal length A1 to A2 = Solution

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ELECTRONIC DISTANCE MEASUREMENT (EDM) EDM is very useful in measuring distances that are difficult to access or long distances. It measures the time required for a wave to sent to a target and reflect back.

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Principles of EDM Operation: A wave is transmitted and the returning wave is measured to find the distance traveled. V= f λ

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General Principle of EDM Electromagnetic energy – Travels based on following relation: Intensity modulate EM energy to specific frequency Distances determined by calculating the number of wavelengths traveled.

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35 Errors are generally small and insignificant for short distances. For longer distances they can be more important. Errors can be accounted for manually, or by the EDM if it has the capability. Principles of EDM

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EDM Classifications Described by form of electromagnetic energy. – First instruments were primarily microwave (1947) – Present instruments are some form of light, i.e. laser or near-infrared lights. Described by range of operation. – Generally microwave are 30 - 50 km range. (med) Developed in the early 70’s, and were used for control surveys. – Light EDM’s generally 3 - 5 km range. (short) Used in engineering and construction

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EDM Properties They come in long (10-20 km), medium (3-10 km), and short range (.5-3 km). Range limits up to 50 km They are typically mounted on top of a theodolite, but can be mounted directly to a tribrach. Total station = Theodolite with built in EDM + Microprocessor

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EDM Characteristics 750-1000 meters range Accurate to ±5mm + 5 ppm Operating temperature between -20 to +50 degrees centigrade 1.5 seconds typical for computing a distanc, 1 second when tracking. Slope reduction either manual or automatic. Some average repeated measurements. Signal attenuation. battery operated and can perform between 350 and 1400 measurements.

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EDM Accessories

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40 Uses Total stations are ideal for collecting large numbers of points. They are commonly used for all aspects of modern surveying. Only when harsh conditions, exist or distances are short will a transit and tape be used.

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Measures and Records: Horizontal Angles Vertical Angles and Slope Distances Calculates: Horizontal Distance Vertical Distance Azimuths of Lines X,Y,Z Coordinates Layout Etc.

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Made from cube corners Have the property of reflecting rays back precisely in the same direction. They can be tribrach-mounted and centered with an optical plummet, or they can be attached to a range pole and held vertical on a point with the aid of a bulls-eye level.

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Observation using EDM

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Personal: Careless centering of instrument and/or reflector Faulty temperature and pressure measurements Incorrect input of T and p Instrumental Instrument not calibrated Electrical center Prism Constant (see next slide) Natural Varying ‘met’ along line Turbulence in air Sources of Errors in EDM

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Systematic Errors Microwave – Atmospheric conditions Temperature Pressure Humidity - must have wet bulb and dry bulb temperature. – Multi-path Reflected signals can give longer distances

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Systematic Errors Light – Atmospheric conditions Temperature Pressure – Prism offset Point of measurement is generally behind the plumb line. Today usually standardized as 30mm.

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Instrumental Errors Both the prism and EDM should be corrected for off- center characteristics. The prism/instrument constant (about 30 to 40 mm) can be measured by measure AC, AB, and BC and then constant = AC-AB-BC o-------------------------------o-------------o A B C 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.

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Problems using EDM Total stations are dependant on batteries and electronics. The LCD screen does not work well when it is cold. Battery life is also short, batteries and electronics both do not work well when wet. Total stations are typically heavier that a transit and tape Loss of data is an important consideration

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COMPUTATION OF HORIZONTAL LENGTH FROM SLOPE DISTANCE USING EDM

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By Elevation Differences H = √(L 2 -d 2 ) d=(elevation A + h e ) – (elevation B + h r )

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Example: A slope distance of 165.360 m (corrected for meteorological conditions) was measured from A to B, whose elevations were 447.401 and 445.389 m above datum, respectively. Find the horizontal length of line AB if the height of EDM instrument and reflector were 1.417 and 1.615 m above their respective stations. Ans: d = 1.814 m. H = 165.350 m

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By Vertical Angles If using zenith angle, z: H = L sin z If using angle, α : H = L cos α

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A C B γ α β A O H β Plane Geometry

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List five types of common errors in taping. List the procedures for taping a horizontal distance of 4% slopes. List the possible errors when measuring a distance with EDM. Calculate the horizontal length between A and B where he, hr, elevation A, elevation B and measured slope length were 1.415, 1.681,143.129, 166.195 and 2042.664 m, respectively. Quiz

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Thank You

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CHAPTER 3 LINEAR MEASUREMENTS

CHAPTER 3 LINEAR MEASUREMENTS

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