General Surveying Theory and Computation PDF

GEn 315 Mine Surveying ENGR. FILLMORE D. MASANCAY, GE, ENP, MSERM 2 General Surveying Theory and Computation  General Surveying Theory and Computation Mine Surveying A type of survey which aims to produce plans that will facilitate mining claims and support underground tunneling. Includes...

GEn 315 Mine Surveying ENGR. FILLMORE D. MASANCAY, GE, ENP, MSERM 2 General Surveying Theory and Computation  General Surveying Theory and Computation Mine Surveying A type of survey which aims to produce plans that will facilitate mining claims and support underground tunneling. Includes underground surveying as practiced in mining and tunneling as well as the surface operations associated with underground work & open-pit mining.  General Surveying Theory and Computation Mine Surveyor Maintains an accurate plan of the mine as a whole. Updates maps of the surface layout to account for new buildings and other structures Surveys underground mine workings in order to keep a record of the mining operation. Calculate ore production and in volume or mass units from the mining operation. Compute volume of accumulated waste on the surface of a mining property.  General Surveying Theory and Computation Person Authorized to Perform a Survey Only duly licensed geodetic engineers (GE) registered under the Geodetic Engineering law (RA 4374 as amended by RA8560 and RA 9200) are authorized to execute such surveys. GE’s in DENR (all types of surveys under the control and supervision of the RTD) GEs in Private Practice may conduct private land surveys, public and government land surveys under supervision of LMB through DENR-LMS. Cadastral surveys subject to existing laws and supervision of LMB through DENR - LMS  General Surveying Theory and Computation Survey Order - instruction issued by the concerned DENR Official to a government GE to conduct public land survey. Survey Authority - permit issued by the concerned DENR official to a private GE to conduct private land survey. DENR Officials who can issue SO/SA MGB Regional Director - Mineral Land Survey  General Surveying Theory and Computation Monument Dimensions and Markings Illustration (DMC 2010-13) Mineral Land Survey Monuments Principal Mineral Land Corners Other Corners of Mineral Land  General Surveying Theory and Computation Principal Mineral Land Corners  General Surveying Theory and Computation Other Corners of Mineral Land  General Surveying Theory and Computation Mine Operation  General Surveying Theory and Computation Conditions underground are very different from those on the surface. Traverses may contain very short legs and run along narrow, dusty corridors. Levels to establish elevations may have to be brought into the workings through deep shaft.  General Surveying Theory and Computation Astronomic observations are not possible, so that underground orientation must be controlled by plumbing wires in a shaft. Rock movement can affect the stability of survey marks and may also cause more serious problems associated with cave-ins, property damage, or loss of life.  General Surveying Theory and Computation Mine surveyors must monitor these rock movements and cooperate closely with geologist and other related specialist.  General Surveying Theory and Computation Monumentations & Marking of points The stations of the horizontal control network called roof markers are usually in the roof (back) or walls of the mining workings.  General Surveying Theory and Computation Monumentations & Marking of points A hole is drilled, a wooden plug is inserted. Markers may also be cemented directly in drilled holes using epoxy glue.  General Surveying Theory and Computation Angle Measurement Accurate centering of instruments is very crucial due to generally short sights in underground traversing. Centering under the roof markers is more difficult than the conventional centering above the marked points. Small area, darkness, difficulties for setting tripod legs on an uneven floor, centering procedures requires a lot of experience.  General Surveying Theory and Computation Mine Orientation Surveys Direct Traversing through inclided Adit If the mine is accessible by means of adits or inclined transportation roads, the orientation process is comparatively simple and limited to running a traverse between the surface geodetic network and points of the underground control network.  General Surveying Theory and Computation Indirect Traversing through Vertical Shaft Process of orientation is supposed to give coordinates of at least one point and azimuth of one line of the underground network in the surface coordinate system.  General Surveying Theory and Computation Indirect Traversing through Vertical Shaft Thin Steel/Piano wires with very high tensile strength (200kg/mm2 or larger) are suspended in the vertical shaft used for plumbing. Wire should be as thin as possible and load should be as heavy as possible. Plumb Bob – weight (in kilograms) is usually 1/3 of H (depth of plumbing in meters).  General Surveying Theory and Computation Supporting Beams Wire Drums Indirect Traversing through Vertical Shaft Steel/Piano Wire In shallow shaft when weight is small, plumb bob should be submerged in a container with oil to reduce the oscillations of the plumb line. Survey Marker Plumb Bob submerged in Oil  General Surveying Theory and Computation For Surface Operation Aerial Photogrammetric instruments – aerial cameras. GNSS Receivers/Real-time kinematic (RTK) - measures the relative positions using 2 Global Navigation Satellite System (GNSS) antennas in real-time.  General Surveying Theory and Computation For Underground Operation Theodolite - optical instrument for measuring angles. Engineer’s Transit - measuring horizontal angles  General Surveying Theory and Computation For Underground Operation Total Station - an electronic theodolite integrated with electronic distance measurement to measure both vertical and horizontal angles.  General Surveying Theory and Computation Special conditions in the underground surveys: Space Limitations Small space instruments of special designs with extension tripod legs or suspension rods are used. Very short & steep (or vertical) sights Special methods of observations are necessary with particular care to avoid the accumulation of excessive errors in measurements  General Surveying Theory and Computation Special conditions in the underground surveys: Instrument station markers are on the roof Modification of the traverse procedures. Darkness Special arrangements for illumination of both the instrument and target. Slope distances Vertical angles are measured and 3-Dimensional coordinates of instrument stations are determined.  General Surveying Theory and Computation Types of Angles Vertical Angle – formed by 2 intersecting lines in a vertical plane, one of these lines horizontal. Zenith Angle – complementary angle to the vertical angle and is directly above the observer. Nadir Angle – angle below the observer.  General Surveying Theory and Computation Meridians - line of reference on the mean surface of the earth joining North and South poles. 4 Types  Astronomical / True Meridians  Magnetic Meridian  Grid Meridian  Assumed Meridian  General Surveying Theory and Computation Astronomical / True Meridian A plane passing through a point on the surface of the earth and containing the earth’s axis of rotation defines the astronomical or true meridian at that point. Astronomical meridians are determined by observing the position of the sun or a star. Astronomical or true meridians on the surface of the earth are lines of geographic longitude and they converge toward each other at the poles.  General Surveying Theory and Computation Magnetic Meridian Parallel with the magnetic lines of force of the earth. The earth acts very much like a bar magnet with a north magnetic pole located considerably south of the north pole defined by the earth’s rotational axis. The magnetic pole is not fixed in position, but rather changes its position continually. The direction of a magnetized needle defines the magnetic meridian at that point at that time. Because the magnetic meridian changes as magnetic north changes, magnetic meridians do not make good lines of reference.  General Surveying Theory and Computation Magnetic Declination The magnetic poles are not points but oval areas located about 2,000 km away from the actual location of the geographic poles of the earth. These areas are not fixed and may move to a different location everyday, perhaps as far as 50 km. The horizontal angle and direction by which the needle of a compass deflects from the true meridian at any particular locality is called magnetic declination.  General Surveying Theory and Computation Grid Meridian In plane surveys it is convenient to perform the work in a rectangular XY coordinate system in which one central meridian coincides with a true meridian. All remaining meridians are parallel to this central true meridian. The methods of plane surveying, assume that all measurements are projected to a horizontal plane and that all meridians are parallel straight lines.  General Surveying Theory and Computation Assumed Meridian An assumed meridian is an arbitrary direction assigned to some line in the survey from which all other lines are referenced. This could be a line between two property monuments, the centerline of a tangent piece of roadway, or even the line between two points set for that purpose. The important point to remember about assumed meridians is that they have no relationship to any other meridian and thus the survey cannot be readily (if at all) related to other surveys  General Surveying Theory and Computation Instruments for Angle and Direction measurement Compass – hand-held instrument for determining the horizontal direction of a line with reference to the magnetic meridian. Theodolite - precision instrument used for measuring angles both horizontally and vertically. Total Station - optical surveying instrument that uses electronics to calculate angles and distances  General Surveying Theory and Computation Compass Surveying - directions of points and lines are determined by means of a magnetic compass. Most compasses are magnetic, meaning they use the Earth's magnetic field to indicate direction. They typically have a needle that aligns itself with the Earth's magnetic north.  General Surveying Theory and Computation Magnetic compass - consists of a magnetic needle mounted on a pivot at the center of a graduated circle in a metal box covered with a glass plate. It is constructed so that the angle between a line of sight and the magnetic meridian can be measured. The line of sight, with the horizontal circle, can be rotated in the horizontal plane while the needle continues to point to magnetic north. The point of the needle marks the angle made by the magnetic meridian and the line of sight.  General Surveying Theory and Computation Magnetic needle - slender, magnetized steel rod that, when freely suspended at its center of gravity, points to magnetic north. Magnetic Declination - horizontal angle between the magnetic meridian and the true (geodetic) meridian. Magnetic poles do not coincide with the axis of the earth.  General Surveying Theory and Computation Sample Problems: The observed compass bearing of a line in 1981 was S 37O30’ E and the magnetic declination of the place then was known to be 3O10’ W. It has also discovered that during the observation, the local attraction of the place at that moment of 5O E existed. Find the true azimuth of the line.  General Surveying Theory and Computation Sample Problems: Magnetic NorthTrue North The observed compass bearing of a line in 1981 was S 37O30’ E and the magnetic declination of 5O the place then was known to be 3O10’ W. It has 3O10’ 1O50’ also discovered that during the observation, the local attraction of the place at that moment of 5O A True Bearing E existed. Find the true azimuth of the line. =37O30’- 1O50’ = 35O40’ True Azimuth=360O-35O40’= 324O20’ 37O30’ B PRACTICE SOLVING! Please grab a pen, paper, and calculator  PRACTICE SOLVING! Problem: The observed compass bearing of a line in 1981 was S 66O27’ W and the magnetic declination of the place then was known to be 2O18’ E. It has also discovered that during the observation, the local attraction of the place at that moment of 3O 15’ W existed. Find the true azimuth of the line.  PRACTICE SOLVING! Solution: True North Magnetic North The observed compass bearing of a line in 1981 was S 66O27’ W and the magnetic declination of 3O15’ the place then was known to be 2O18’ E. It has 0O57’ 2O18’ also discovered that during the observation, the local attraction of the place at that moment of 3O A 15’ W existed. True Bearing =66O27’- 0O57’ = 65O30’ True Azimuth=65O30’ B 66O27’  General Surveying Theory and Computation Traverse - series of lines connecting successive instrument stations of a survey. The relative position of the stations is determined by the direction and length of the lines. In land surveys the lines are the boundaries of the land; in topographic surveys the lines are the control net to which physical features are tied. The traverse is also used as control for construction surveys. General Surveying Theory and Computation  General Surveying Theory and Computation Traversing - act of marking the lines that is establishing traverse stations and making the necessary observations as one of the most basic and widely practiced means of determining the relative locations of points. Purpose of Traverse Locate the unknown points relative to each other and to locate all points within the traverse relative to a common grid.  General Surveying Theory and Computation Sideshots Sideshots - A reading or measurement from a survey station to locate a point that is off the traverse or that is not intended to be used as a base for the extension of the survey.  General Surveying Theory and Computation 2 Types: Open - series of lines that do not return to the starting point. It is used in route surveying for the location of highways, pipelines, canals, and so on. To check the accuracy of an open traverse, the traverse must start and end at points of known position. Closed/Loop – starts & ends at the same point. Because it is a closed polygon, the interior angles and the lengths of the sides may be checked for accuracy and mathematically adjusted.  General Surveying Theory and Computation Angle Closure The sum of the interior angles of a polygon depends on the number of sides of the polygon. For a triangle, the sum is 180°; for a four-sided polygon, the sum is 360°. For any polygon with n sides, the sum is Sum of angles = (n-2) (180°)  General Surveying Theory and Computation Error of Closure - is the measure of the precision of a survey. Error of Closure= (𝜟𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆)𝟐 +(𝜟𝑫𝒆𝒑𝒂𝒓𝒕𝒖𝒓𝒆)𝟐  General Surveying Theory and Computation Relative Precision - measure of the accuracy of the traverse relative to its length. It is often used to assess the quality of the measurements and to ensure that the errors are within acceptable limits. 𝑬𝒓𝒓𝒐𝒓 𝒐𝒇 𝑪𝒍𝒐𝒔𝒖𝒓𝒆 RP= 𝑻𝒐𝒕𝒂𝒍 𝑻𝒓𝒂𝒗𝒆𝒓𝒔𝒆 𝑳𝒆𝒏𝒈𝒕𝒉  General Surveying Theory and Computation Latitude - projection of a side of a traverse on the north-south (y) axis of a rectangular coordinate system. Latitude = (Cosine bearing)(Length) Departure - projection of a side of a traverse on the east-west (x) axis of a rectangular coordinate system. Departure = (Sine bearing)(Length)  General Surveying Theory and Computation Traverse Adjustment Steps  Compute the angular error and adjust to make the sum of the angles agree with equation formula for interior angles.  Compute the bearings for each course.  Compute the latitudes and departures.  Compute the error of closure.  Compute the relative precision of error.  Compute the latitude and departure corrections for each course.  Adjust the latitudes and departures by different methods.  General Surveying Theory and Computation Solution: Compute the Latitudes, Departures, Error of Closure, and Relative Precision of the traverse ABCDE. STATION LENGTH BEARING A 647.25 S 53 4 43.2 E B 203.03 S 1 41 2.4 E C 720.35 N 15 31 54.4 E D 610.24 N 75 24 39.8 W E 285.13 S 26 9 42 W  TRAVERSE General Surveying Theory and Computation Solution: Compute the Latitudes, Departures, Error of Closure, and Relative Precision of the Latitude traverse ABCDE. 1. Shift Rec (Length, Bearing) N= + (Positive) S= - (Negative) STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 B 203.03 S 1 41 2.4 E -202.942 C 720.35 N 15 31 54.4 E 694.045 D 610.24 N 75 24 39.8 W 153.708 E 285.13 S 26 9 42 W -255.919  General Surveying Theory and Computation Solution: Compute the Latitudes, Departures, Error of Closure, and Relative Precision of the traverse ABCDE. 1. Shift Rec (Length, Bearing) Departure E= + (Positive) W= - (Negative) STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 B 203.03 S 1 41 2.4 E -202.942 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 D 610.24 N 75 24 39.8 W 153.708 -590.565 E 285.13 S 26 9 42 W -255.919 -125.715  General Surveying Theory and Computation Solution: Compute the Latitudes, Departures, Error of Closure, and Relative Precision of the traverse ABCDE. STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 B 203.03 S 1 41 2.4 E -202.942 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 D 610.24 N 75 24 39.8 W 153.708 -590.565 E 285.13 S 26 9 42 W -255.919 -125.715 SUM 2,466 0.077 0.026 Error of Closure= (𝛥𝐿𝑎𝑡𝑖𝑡𝑢𝑑𝑒)2 +(𝛥𝐷𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒)2 = (0.077)2 +(0.026)2 =0.08 m 𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝐶𝑙𝑜𝑠𝑢𝑟𝑒 0.08 1 𝟏 RP= = = = 𝑇𝑜𝑡𝑎𝑙 𝑇𝑟𝑎𝑣𝑒𝑟𝑠𝑒 𝐿𝑒𝑛𝑔𝑡ℎ 2,466 30,825 𝟑𝟎,𝟎𝟎𝟎  General Surveying Theory and Computation For any closed traverse the linear misclosure must be adjusted (or distributed) throughout the traverse to “close” or “balance” the figure. This is true even though the misclosure is negligible in plotting the traverse at map scale. Methods  Compass Rule (Bowditch method)  Transit Rule  General Surveying Theory and Computation Compass Rule / Bowditch method - rule that adjusts the departures and latitudes of traverse courses in proportion to their lengths. (𝒍𝒂𝒕𝒊𝒕𝒖𝒅𝒆 𝒎𝒊𝒔𝒄𝒍𝒐𝒔𝒖𝒓𝒆)(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒊𝒏𝒆) Correction in latitude= - 𝑻𝒓𝒂𝒗𝒆𝒓𝒔𝒆 𝒑𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 ( 𝒅𝒆𝒑𝒂𝒓𝒕𝒖𝒓𝒆 𝒎𝒊𝒔𝒄𝒍𝒐𝒔𝒖𝒓𝒆)(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒊𝒏𝒆) Correction in departure= - 𝑻𝒓𝒂𝒗𝒆𝒓𝒔𝒆 𝒑𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓  General Surveying Theory and Computation Transit Rule – latitude and departure corrections depend on the length of latitude and departure of the course. (𝑨𝒃𝒔𝒐𝒍𝒖𝒕𝒆 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆 𝒐𝒇 𝒕𝒉𝒂𝒕 𝒔𝒊𝒅𝒆)(𝑻𝒐𝒕𝒂𝒍 𝑬𝒓𝒓𝒐𝒓 𝒊𝒏 𝑳𝒂𝒕𝒊𝒕𝒖𝒓𝒆) Correction in latitude of any side = - 𝑨𝒓𝒊𝒕𝒉𝒎𝒆𝒕𝒊𝒄 𝑺𝒖𝒎 𝒐𝒇 𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆𝒔 (𝑨𝒃𝒔𝒐𝒍𝒖𝒕𝒆 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑫𝒆𝒑𝒂𝒓𝒕𝒖𝒓𝒆 𝒐𝒇 𝒕𝒉𝒂𝒕 𝒔𝒊𝒅𝒆)(𝑻𝒐𝒕𝒂𝒍 𝑬𝒓𝒓𝒐𝒓 𝒊𝒏 𝑫𝒆𝒑𝒂𝒓𝒕𝒖𝒓𝒆) Correction in departure of any side= - 𝑨𝒓𝒊𝒕𝒉𝒎𝒆𝒕𝒊𝒄 𝑺𝒖𝒎 𝒐𝒇 𝑫𝒆𝒑𝒂𝒓𝒕𝒖𝒓𝒆𝒔  General Surveying Theory and Computation Sample Problem: Adjust the given traverse ABCDE using Compass Rule. STATION LENGTH BEARING A 647.25 S 53 4 43.2 E B 203.03 S 1 41 2.4 E C 720.35 N 15 31 54.4 E D 610.24 N 75 24 39.8 W E 285.13 S 26 9 42 W  General Surveying Theory and Computation Solution: Latitude Adjust the given traverse ABCDE using Compass Rule. N= + (Positive) 1. Shift Rec (Length, Bearing) S= - (Negative) STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 B 203.03 S 1 41 2.4 E -202.942 C 720.35 N 15 31 54.4 E 694.045 D 610.24 N 75 24 39.8 W 153.708 E 285.13 S 26 9 42 W -255.919  General Surveying Theory and Computation Solution: Departure Adjust the given traverse ABCDE using Compass Rule. E= + (Positive) W= - (Negative) 1. Shift Rec (Length, Bearing) STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 B 203.03 S 1 41 2.4 E -202.942 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 D 610.24 N 75 24 39.8 W 153.708 -590.565 E 285.13 S 26 9 42 W -255.919 -125.715  General Surveying Theory and Computation Solution: Adjust the given traverse ABCDE using Compass Rule. STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 B 203.03 S 1 41 2.4 E -202.942 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 D 610.24 N 75 24 39.8 W 153.708 -590.565 E 285.13 S 26 9 42 W -255.919 -125.715 SUM 2,466 0.077 0.026  General Surveying Theory and Computation 4. Adjusted Lat= (-388.815) – ((0.077) (647.25)) Solution: 2,466 Adjust the given traverse ABCDE using Compass Rule. ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.835 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.948 C 720.35 N 15 31 54.4 E 694.045 192.889 694.024 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.688 E 285.13 S 26 9 42 W -255.919 -125.715 -255.929 SUM 2,466 0.077 0.026 0.000  General Surveying Theory and Computation 4. Adjusted Dep= (517.451) – ((0.026) (647.25) Solution: 2,466 Adjust the given traverse ABCDE using Compass Rule. ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.833 517.444 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.951 5.964 C 720.35 N 15 31 54.4 E 694.045 192.889 694.013 192.881 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.701 -590.571 E 285.13 S 26 9 42 W -255.919 -125.715 -255.930 -125.718 SUM 2,466 0.077 0.026 0.000 0.000  General Surveying Theory and Computation Solution: Adjust the given traverse ABCDE using Compass Rule. ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.833 517.444 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.951 5.964 C 720.35 N 15 31 54.4 E 694.045 192.889 694.013 192.881 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.701 -590.571 E 285.13 S 26 9 42 W -255.919 -125.715 -255.930 -125.718 SUM 2,466 0.077 0.026 0.000 0.000  General Surveying Theory and Computation Solution: Adjust the given traverse ABCDE using Compass Rule. FINAL ANSWER ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.833 517.444 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.951 5.964 C 720.35 N 15 31 54.4 E 694.045 192.889 694.013 192.881 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.701 -590.571 E 285.13 S 26 9 42 W -255.919 -125.715 -255.930 -125.718 SUM 2,466 0.077 0.026 0.000 0.000  General Surveying Theory and Computation Sample Problem: Adjust the given traverse ABCDE using Transit Rule. STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 B 203.03 S 1 41 2.4 E -202.942 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 D 610.24 N 75 24 39.8 W 153.708 -590.565 E 285.13 S 26 9 42 W -255.919 -125.715  General Surveying Theory and Computation Solution: Adjust the given traverse ABCDE using Transit Rule. STATION LENGTH BEARING LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 B 203.03 S 1 41 2.4 E -202.942 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 D 610.24 N 75 24 39.8 W 153.708 -590.565 E 285.13 S 26 9 42 W -255.919 -125.715 SUM OF ERRORS 0.077 0.026 SUM [ABSOLUTE VALUE] 1,695.429 1,432.586  General Surveying Theory and Computation 4. Adjusted Lat= (-388.815) – ((ABS(388.815)) (0.07 Solution: 1,695.429 Adjust the given traverse ABCDE using Transit Rule. ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.833 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.951 C 720.35 N 15 31 54.4 E 694.045 192.889 694.013 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.701 E 285.13 S 26 9 42 W -255.919 -125.715 -255.930 SUM OF ERRORS 0.077 0.026 SUM [ABSOLUTE VALUE] 1,695.429 1,432.586  General Surveying Theory and Computation 4. Adjusted Dep= (517.451) – ((ABS(517.451)) (0.02 Solution: 1,432.586 Adjust the given traverse ABCDE using Transit Rule. ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.833 517.442 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.951 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 694.013 192.885 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.701 -590.576 E 285.13 S 26 9 42 W -255.919 -125.715 -255.930 -125.717 SUM OF ERRORS 0.077 0.026 SUM [ABSOLUTE VALUE] 1,695.429 1,432.586  General Surveying Theory and Computation Solution: Adjust the given traverse ABCDE using Transit Rule. ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.833 517.442 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.951 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 694.013 192.885 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.701 -590.576 E 285.13 S 26 9 42 W -255.919 -125.715 -255.930 -125.717 SUM OF ERRORS 0.077 0.026 0.000 0.000 SUM [ABSOLUTE VALUE] 1,695.429 1,432.586  General Surveying Theory and Computation Solution: Adjust the given traverse ABCDE using Transit Rule. FINAL ANSWER ADJUSTED ADJUSTED STATION LENGTH BEARING LATITUDE DEPARTURE LATITUDE DEPARTURE A 647.25 S 53 4 43.2 E -388.815 517.451 -388.833 517.442 B 203.03 S 1 41 2.4 E -202.942 5.966 -202.951 5.966 C 720.35 N 15 31 54.4 E 694.045 192.889 694.013 192.885 D 610.24 N 75 24 39.8 W 153.708 -590.565 153.701 -590.576 E 285.13 S 26 9 42 W -255.919 -125.715 -255.930 -125.717 SUM OF ERRORS 0.077 0.026 0.000 0.000 SUM [ABSOLUTE VALUE] 1,695.429 1,432.586  General Surveying Theory and Computation Leveling - process of finding the difference in elevation of points on the earth.  General Surveying Theory and Computation Level surface A (curved) surface orthogonal to the plumb line everywhere. A still body of water unaffected by tides is a good analogy.  General Surveying Theory and Computation Vertical line Direction of gravity. Direction indicated by a plumb line. In general, it deviates from a line emanating from the geometric center of the Earth.  General Surveying Theory and Computation Horizontal plane A plane tangent to a level surface (orthogonal to the plumb line). The collimation axis (line of sight) of a levelling instrument that is in correct adjustment. Once levelled, it defines a horizontal plane as the instrument is rotated.  General Surveying Theory and Computation Vertical datum - Any level surface to which heights are referenced. Mean Sea Level (MSL) - Mean height of sea level  General Surveying Theory and Computation Elevation - vertical distance from a datum to a point on the earth. Turning Point - a temporary point on which an elevation has been established and which is held while the instrument is moved to a new location  General Surveying Theory and Computation Height of instrument - vertical distance from the datum to the line of sight. Plumb line - vertical line, usually established by a pointed metal bob hanging on a string or cord.  General Surveying Theory and Computation Turning point - a temporary point on which an elevation has been established and which is held while the instrument is moved to a new location. Bench mark - a marked point of known elevation from which other elevations may be established.  General Surveying Theory and Computation Automatic Level Stadia Rod Tripod  General Surveying Theory and Computation Types of Leveling  Fly  Check  Profile / L-Section  Cross  Reciprocal  Trigonometric  Barometric  Hypsometric  Simple  Differential  General Surveying Theory and Computation Simple - simplest method used when it is required to find the difference in elevation between 2 points.  General Surveying Theory and Computation Sample Problem: From the given data of a simple leveling as shown in the tabulation: STATION B.S F.S Elev.(m) 1 5.87 392.25 2 7.03 6.29 3 3.48 6.25 4 7.25 7.08 5 10.19 5.57 6 9.29 4.45 7 4.94 Determine the Following: 1. Difference in Elevation of Station 7 and 5. 2. Difference in Elevation of Station 7 and 4. 3. Elevation of Station 4  General Surveying Theory and Computation Solution: From the given data of a simple leveling as shown in 1. Difference in Elevation of Station 7 and 5. the tabulation: Add Subtract HI= Elev+BS STATION B.S HI F.S Elev.(m) Elev=HI-FS 1 5.87 398.12 392.25 2 7.03 6.29 391.83 3 3.48 6.25 Add Column for Height of Instrument 4 7.25 7.08 5 10.19 5.57 6 9.29 4.45 7 4.94  General Surveying Theory and Computation Solution: From the given data of a simple leveling as shown in 1. Difference in Elevation of Station 7 and 5. the tabulation: HI= Elev+BS STATION B.S HI F.S Elev.(m) Elev=HI-FS 1 5.87 398.12 392.25 ∑BS - ∑FS = 43.11-34.58 = 8.53 m 2 7.03 398.86 6.29 391.83 ∆Elev = 400.78-392.25 = 8.53 m 3 3.48 396.09 6.25 392.61 ∆Elev7-5 = 400.78-390.69 = 10.09 m 4 7.25 396.26 7.08 389.01 5 10.19 400.88 5.57 390.69 6 9.29 405.72 4.45 396.43 7 4.94 400.78 SUM 43.11 34.58  General Surveying Theory and Computation Solution: From the given data of a simple leveling as shown in 2. Difference in Elevation of Station 7 and the tabulation: 4. STATION B.S HI F.S Elev.(m) HI= Elev+BS Elev=HI-FS 1 5.87 398.12 392.25 2 7.03 398.86 6.29 391.83 ∆Elev7-4 = 400.78-389.01 = 11.77 m 3 3.48 396.09 6.25 392.61 4 7.25 396.26 7.08 389.01 5 10.19 400.88 5.57 390.69 3. Elevation of Station 4 = 389.01 m 6 9.29 405.72 4.45 396.43 7 4.94 400.78 SUM 43.11 34.58  General Surveying Theory and Computation Differential - used to find the difference in the elevation between points if they are too far apart or the difference in elevation between them is too much.  General Surveying Theory and Computation 1 Sample Set-up and Computation: 2 3 4 STATION BS HI FS IFS ELEV. BM1 (328.70 m) BM1 2.32 331.02 328.70 1 1.7 329.32 2 2.2 328.82 HI TP1 3 1.2 329.82 5 4 0.9 330.12 6 TP1 2.77 330.36 3.43 327.59 HI 7 5 2.2 328.16 6 3.7 326.66 TP2 7 1.6 328.76 TP2 2.22 329.52 3.06 327.30 8 8 2.8 326.72 HI 9 3.6 325.92 10 2.0 327.52 11 1.1 328.42 9 BS BM2 BM2 2.45 327.07 FS 10 11 ? IFS 7.31 8.94  General Surveying Theory and Computation Sample Problem: From the given data of a differential leveling as shown in the tabulation: STATION B.S F.S IFS Elev.(m) BM1 0.95 125.50 0+00 3.0 0+10 2.3 TP1 3.13 0.64 Determine the Following: 0+20 2.7 1. Difference in Elevation of Station TP1 and 0+30 2.8 TP2. 0+40 3.1 2. Difference in Elevation of Station BM1 0+50 0.5 and 0+40. 0+60 0.8 3. Elevation of Station 0+70 TP2 2.16 1.28 TP3 1.35 3.50 0+70 3.0 BM2 1.99  General Surveying Theory and Computation Solution: From the given data of a differential leveling as shown in the tabulation: STATION B.S HI F.S IFS Elev.(m) BM1 0.95 126.45 125.50 HI= Elev+BS 0+00 3.0 123.45 Elev=HI-FS 0+10 2.3 124.15 TP1 3.13 128.94 0.64 125.81 Checking: 0+20 2.7 126.24 0+30 2.8 126.14 ∑BS - ∑FS = 7.59-7.41= 0.18 m 0+40 3.1 125.84 ∆Elev = 125.68-125.50=0.18 m 0+50 0.5 128.44 0+60 0.8 128.14 TP2 2.16 129.82 1.28 127.66 TP3 1.35 127.67 3.50 126.32 0+70 3.0 124.67 BM2 1.99 125.68 SUM 7.59 7.41  General Surveying Theory and Computation Solution: From the given data of a differential leveling as shown in the tabulation: STATION B.S HI F.S IFS Elev.(m) 1. Difference in Elevation of BM1 0.95 126.45 125.50 Station TP1 and TP2. 0+00 3.0 123.45 =127.66-125.81= 1.85 m 0+10 2.3 124.15 TP1 3.13 128.94 0.64 125.81 0+20 2.7 126.24 0+30 2.8 126.14 2. Difference in Elevation of 0+40 3.1 125.84 Station BM1 and 0+40. 0+50 0.5 128.44 =125.84-125.50= 0.34 m 0+60 0.8 128.14 TP2 2.16 129.82 1.28 127.66 TP3 1.35 127.67 3.50 126.32 3. Elevation of Station 0+70 0+70 3.0 124.67 =124.67 m BM2 1.99 125.68 SUM 7.59 7.41 PRACTICE SOLVING! Please grab a pen, paper, and calculator  PRACTICE SOLVING! Problem: From the given data of a differential leveling as shown in the tabulation: STATION BS FS IFS ELEV (m) TP1 0.02 500.50 2 2.50 3 2.30 Determine the Following: TP2 2.10 0.70 1. Difference in Elevation of Station TP1 and 5 3.30 6. 6 3.50 TP3 3.30 0.80 2. Difference in Elevation of Station 3 and TP4 1.10 0.40 9. 9 5.00 3. Elevation of Station TP5. TP5 0.30  PRACTICE SOLVING! Problem: From the given data of a differential leveling as shown in the tabulation: STATION BS HI FS IFS ELEV (m) TP1 0.02 500.52 500.50 HI= Elev+BS Elev=HI-FS 2 2.50 498.02 3 2.30 498.22 TP2 2.10 501.92 0.70 499.82 Checking: 5 3.30 498.62 6 3.50 498.42 ∑BS - ∑FS = 6.52-2.20= 4.32 m ∆Elev = 504.82-500.50=4.32 m TP3 3.30 504.42 0.80 501.12 TP4 1.10 505.12 0.40 504.02 9 5.00 500.12 TP5 0.30 504.82 SUM 6.52 2.20 Thank You!