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SURE 110 - Fundamentals of Surveying ELECTRONIC DISTANCE MEASUREMENT AGA Geodimeter NASM-2A Robert Burtch Surveying Engineering Department Ferris State University INTRODUCTION Introduced in 1950s evolved into total stations today Types Infrared or laser light utilize transmitter at one end and reflecting prism at other Some are reflectorless Long range 10-20 km Medium range 3-10 km Short range 0.5-3 km Microwave utilize receiver/transmitter at both ends of line Electronic Distance Measurement 1 SURE 110 - Fundamentals of Surveying PRINCIPLES Wave travels along x-axis at velocity of 299,792.5 0.4 km/s Frequency time taken for one complete wavelength Relationship: c = f = wavelength in meters c = velocity, in km/s f = frequency, in hertz (one cycle per second) PRINCIPLES OF EDM MEASUREMENT Electronic Distance Measurement 2 SURE 110 - Fundamentals of Surveying PRINCIPLES Modulated wave leaves EDM then reflected back to instrument measures double distance (2L) Partial wavelength measured from phase delay between transmitted and reflected L= n + meters 2 n whole number of wavelengths partial wavelength PRINCIPLES EDM can send 3-4 modulated waves at different frequencies Find n by substituting these into distance equation Some EDM use pulsed laser emissions Require to determine distance by measuring travel time to and from EDM Electronic Distance Measurement 3 SURE 110 - Fundamentals of Surveying PRINCIPLES Velocity of light affected by Temperature Atmospheric pressure Water vapor content Correction determined using nomograph or automatically in automatic processor by inputting temperature and pressure ATMOSPHERIC CORRECTION Atmospheric correction graph Electronic Distance Measurement 4 SURE 110 - Fundamentals of Surveying ATMOSPHERIC CORRECTION Insignificant for short-wave light-wave EDM Important for long range, especially microwave Error (Parts per Million) Parameter Error Light Wave Microwave Temperature +1 C -1.0 -1.25 Pressure +1mm Hg +0.4 +0.4 Partial water vapor pressure 1 mm Hg -0.05 +7 at 20 C +17 at 45 C EDM INSTRUMENT CHARACTERISTICS Distance range 800 1,000m with average atmospheric conditions and single prism Short-range can be extended to 1,300m with 3 prisms Long-range can be extended to 15 km with 11 prisms Accuracy range Short-range (15 mm + 5 ppm) Long-range (3 mm + 1 ppm) Measuring time - 1.5s short-range, 3.5s longrange Accuracy and time reduced when in tracking mode Electronic Distance Measurement 5 SURE 110 - Fundamentals of Surveying EDM INSTRUMENT CHARACTERISTICS Slope reduction manual or automatic depending on model Average of repeated measurements available on some models Battery capability 1,400 4,200 measurements depending on size of battery and temperature Temperature range - -20 C - +50 C Nonprism measurements available on some models Distances from 100 350 m EDM Prisms Reflect transmitted signal back to EDM Retrodirect capabilities Mounted on tripod or attached to prism pole Forced centering capabilities Electronic Distance Measurement 6 SURE 110 - Fundamentals of Surveying EDM INSTRUMENT ACCURACIES Given in terms of constant error and proportional term based on distance Most fall in range: (3 mm + 1 ppm) to (10mm + 10 ppm) Both EDM instrument & prism corrected for off-center location Usually determined by manufacturer GEOMETRY OF EDM Using EDM when optical target and prism at same height Elev B = Elev A + HI V HR Electronic Distance Measurement 7 SURE 110 - Fundamentals of Surveying GEOMETRY OF EDM EDM instrument mounted on theodolite and target located below prism X = HR hi From which, sin = X cos S EXAMPLE EDM has slope distance AB of 561.276 m. EDM instrument is 1.820 m above station A, and the prism is 1.986 m above station B. The EDM is mounted on a theodolite whose optical center is 1.720 m above the station. The theodolite measured a vertical angle of +6 21 38 to target on prism pole; the target is 1.810 m above station B. Compute both the horizontal distance AB and elevation of station B given an elevation at A of 186.275 m. Electronic Distance Measurement 8 SURE 110 - Fundamentals of Surveying Data given in following figures X = HR hi = (1.986m 1.810m ) (1.820m 1.720m ) = 0.076m X cos 0.076m cos 6 21'38" = S 561.276m = 28" sin = k = + = 6 22' 06" H = S cos k = (561.276 m ) cos 6 22'06" = 557.813 m Elev B = Elev A + hi + V HR = 186.275m + 1.820 m + (561.276 m )(sin 6 22'06") 1.986m = 248.336 m Electronic Distance Measurement 9

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