Surveying - Traverse - Web
CIVL 1112Surveying - Traverse CalculationsSurveying - Traverse1/13Surveying - TraverseIntroduction Almost all surveying requires some calculations toreduce measurements into a more useful form fordetermining distance, earthwork volumes, land areas,etc. A traverse is developed by measuring the distance andangles between points that found the boundary of a site We will learn several different techniques to compute thearea inside a traverseSurveying - TraverseDistance - TraverseMethods of Computing Area A simple method that is useful for rough area estimatesis a graphical method In this method, thetraverse is plotted to scaleon graph paper, and thenumber of squares insidethe traverse are countedBACDDistance - TraverseMethods of Computing AreaBaADistance - TraverseMethods of Computing AreaB1Area ABC ac sin 2b aAcCb Area ABD 1ad sin 2Area BCD 1bc sin 2 CdcDArea ABCD Area ABD Area BCD
CIVL 1112Surveying - Traverse CalculationsDistance - TraverseSurveying - TraverseMethods of Computing AreaBbAArea ABE c Balancing AnglesCa De2/13Area CDE d1ae sin 2 Before the areas of a piece of land can be computed, it isnecessary to have a closed traverse The interior angles of a closed traverse should total:1cd sin 2(n - 2)(180 )where n is the number of sides of the traverseE To compute Area BCD more data is requiredSurveying - TraverseSurveying - TraverseBalancing AnglesBalancing AnglesAError of closureBD A surveying heuristic is that the total angle should notvary from the correct value by more than the square rootof the number of angles measured times the precision ofthe instrument For example an eight-sided traverse using a 1’ transit,the maximum error is: 1' 8 2.83 ' 3'CAngle containing mistakeSurveying - TraverseSurveying - TraverseBalancing AnglesLatitudes and Departures If the angles do not close by a reasonable amount,mistakes in measuring have been made The closure of a traverse is checked by computing thelatitudes and departures of each of it sides If an error of 1’ is made, the surveyor may correct oneangle by 1’ If an error of 2’ is made, the surveyor may correct twoangles by 1’ each If an error of 3’ is made in a 12 sided traverse, thesurveyor may correct each angle by 3’/12 or 15”NNBLatitude ABBearing EWBearing AWCDeparture ABLatitude CDSDeparture CDDSE
CIVL 1112Surveying - Traverse CalculationsSurveying - Traverse3/13Surveying - TraverseLatitudes and DeparturesError of Closure The latitude of a line is its projection on the north–southmeridian Consider the following statement:N The departure of a line isits projection on the east–west lineBLatitude ABEWBearing A“If start at one corner of a closed traverse and walk its linesuntil you return to your starting point, you will have walked asfar north as you walked south and as far east as you havewalked west”Departure AB A northeasterly bearing has: latitude and departure latitudes 0 Thereforeand departures 0SSurveying - TraverseSurveying - TraverseError of ClosureError of Closure When latitudes are added together, the resulting error iscalled the error in latitudes (EL) If the measured bearings and distances are plotted on asheet of paper, the figure will not close because of ELand ED The error resulting from adding departures together iscalled the error in departures (ED)Error of closureB EDELACLatitudes and Departures - Example EL Precision 2 ED 2EclosureperimeterTypical precision: 1/5,000 for rural land, 1/7,500 forsuburban land, and 1/10,000 for urban landDSurveying - TraverseEclosure Surveying - TraverseLatitudes and Departures - ExampleANDeparture ABS 6 15’ WN 42 59’ E189.53’234.58’B W (189.53 ft.)sin(6 15') 20.63 ft.AWEE142.39’175.18’S 29 38’ ES 6 15’ WLatitude AB189.53 ft.N 12 24’ W S (189.53 ft.)cos(6 15 ') 188.40 ft.197.78’DN 81 18’ WCBS
CIVL 1112Surveying - Traverse CalculationsSurveying - TraverseSurveying - TraverseLatitudes and Departures - ExampleLatitudes and Departures - ExampleBearingSideNDeparture BC E (175.18 ft.)sin(29 38 ') 86.62 ft.BW4/13ABBCCDDEEAdegreem inutes6298112421538182459SSNNNLength .18 ft.Latitude BCS 29 38’ E S (175.18 ft.)cos(29 38 ') 152.27 ft.CSSurveying - TraverseSurveying - TraverseLatitudes and Departures - ExampleBearingSideABBCCDDEEAEclosure SSNNN EL Precision 2degreem inutes6298112421538182459 ED 2Group Example Problem 1Length -20.63486.617-195.504-30.576159.933-0.163AS 77 10’ EWEWWE 0.079 2 0.163 0.182 ft.0.182 ft.Eclosure 939.46 ft.perimeter651.2 ft.660.5 ft.826.7 ft.215,176BN 29 16’ EDS 38 43’ W491.0 ft.N 64 09’ WCSurveying - TraverseSurveying - TraverseBalancing Latitudes and DeparturesGroup Example Problem 1 Balancing the latitudes and departures of a traverseattempts to obtain more probable values for the locationsof the corners of the traverseSideABBCCDDELength 1.2826.7491.0660.5LatitudeDeparture A popular method for balancing errors is called thecompass or the Bowditch rule The “Bowditch rule” as devised by NathanielBowditch, surveyor, navigator and mathematician, asa proposed solution to the problem of compasstraverse adjustment, which was posed in theAmerican journal The Analyst in 1807.
CIVL 1112Surveying - Traverse Calculations5/13Surveying - TraverseSurveying - TraverseBalancing Latitudes and DeparturesBalancing Latitudes and DeparturesA The compass method assumes:1) angles and distances have same error2) errors are accidentalS 6 15’ WN 42 59’ E189.53’234.58’ The rule states:BE“The error in latitude (departure) of a line is to thetotal error in latitude (departure) as the length of theline is the perimeter of the traverse”142.39’175.18’S 29 38’ EN 12 24’ W197.78’DSurveying - TraverseN 81 18’ WCSurveying - TraverseLatitudes and Departures - ExampleLatitudes and Departures - ExampleRecall the results of our example problemRecall the results of our example problemBearingSideABBCCDDEEASSNNNLength (ft)degreem NNNdegreem inutes6298112421538182459WEWWELength 20.63486.617-195.504-30.576159.933-0.163Surveying - TraverseSurveying - TraverseBalancing Latitudes and DeparturesBalancing Latitudes and DeparturesNNLatitude ABDeparture AB S (189.53 ft.)cos(6 15 ') 188.40 ft. AWECorrection in Lat ABLAB ELperimeterS 6 15’ W189.53 ft.B W (189.53 ft.)sin(6 15 ') 20.63 ft.AWCorrection in Lat AB EL LAB 189.53 ft.BCorrection in Lat AB 939.46 ft.Correction in Dep ABLAB EDperimeterS 6 15’ WCorrection in Dep AB perimeterS 0.079 ft. 189.53 ft. E 0.016 ft.ED LAB perimeterSCorrection in Dep AB 0.163 ft. 189.53 ft. 939.46 ft. 0.033 ft.
CIVL 1112Surveying - Traverse Calculations6/13Surveying - TraverseSurveying - TraverseBalancing Latitudes and DeparturesBalancing Latitudes and DeparturesNNLatitude BCDeparture BC S (175.18 ft.)cos(29 38 ') 152.27 ft. BWECorrection in LatBCLBC ELperimeter175.18 ft.S 29 38’ ECorrection in LatBC CSCorrection in LatBC EL LBC E (175.18 ft.)sin(29 38 ') 86.62 ft.BWES 29 38’ E939.46 ft.ED LBC Correction in DepBC perimeter 0.079 ft. 175.18 ft. Correction in DepBCLBC perimeterED175.18 ft.perimeterCS 0.015 ft.Correction in DepBC 0.163 ft. 175.18 ft. 0.030 ft.939.46 ft.Surveying - TraverseSurveying - TraverseBalancing Latitudes and DeparturesBalancing Latitudes and DeparturesLength (ft.) itude Departure0.0160.015BalancedLatitude Departure0.0330.030Length (ft.) itude Departure0.0160.0150.0330.030BalancedLatitude Departure-188.388-152.253Corrected latitudes and departuresCorrections computed on previous slidesSurveying - TraverseSurveying - TraverseBalancing Latitudes and DeparturesBalancing Latitudes and DeparturesLength (ft.) itude 330.0300.0340.0250.041BalancedLatitude No error in corrected latitudes and Combining the latitude and departure calculations withcorrections gives:SideCorrectionsLength (ft.) Latitude Departure Latitude DepartureBearingBalancedLatitudeDeparturedegree m 0.000-20.60186.648-195.470-30.551159.9740.000
CIVL 1112Surveying - Traverse CalculationsSurveying - TraverseSurveying - TraverseGroup Example Problem 2Group Example Problem 3Balance the latitudes and departures for the followingtraverse.In the survey of your assign site in Project #3, you willhave to balance data collected in the following form:CorrectionsBalancedLength (ft) Latitude Departure Latitude Departure Latitude 22-0.72BN 69 53’ EAN600.0450.0750.01800.07/1351 23’713.93 ft. 105 39’606.06 ft.781.18 ft.78 11’C124 47’391.27 ft.DSurveying - TraverseSurveying - TraverseCalculating Traverse AreaGroup Example Problem 3In the survey of your assign site in Project #3, you willhave to balance data collected in the following form:SideCorrectionsLength (ft.) Latitude Departure Latitude DepartureBearingBalancedLatitudeDeparturedegree m inutesAB NBCCDDA6953E713.93606.06391.27781.18Eclosure Precision The meridian distance of a line is the east–westdistance from the midpoint of the line to the referencemeridian The meridian distance is positive ( ) to the east andnegative (-) to the westft.1Surveying - TraverseCalculating Traverse AreaNSurveying - TraverseCalculating Traverse AreaAN 42 59’ ES 6 15’ W234.58 ft.189.53 ft.BES 29 38’ E142.39 ft.ReferenceMeridian The best-known procedure for calculating land areas isthe double meridian distance (DMD) method175.18 ft.N 12 24’ W175.18 ft.D N 81 18’ WC The most westerly and easterly points of a traverse maybe found using the departures of the traverse Begin by establishing a arbitrary reference line and usingthe departure values of each point in the traverse todetermine the far westerly point
CIVL 1112Surveying - Traverse CalculationsSurveying - TraverseSurveying - TraverseCalculating Traverse AreaLength (ft.) 0D-30.551EDCalculating Traverse AreaCorrectionsLatitude 0.0250.041NBalancedLatitude eridian86.648E142.39 ft.175.18 ft.D N 81 18’ WANMeridian distanceof line ABNB The meridian distance of line AB isequal to:Athe meridian distance of EA ½ the departure of line EA ½ departure of ABB The DMD of line AB is twice themeridian distance of line AB:AEEdouble meridian distance of EA the departure of line EA departure of ABEDMD of line EA is thedeparture of lineSurveying - TraverseDMD CalculationsNABECDMD CalculationsThe meridian distance ofline EA is:Meridian distanceof line ABS 29 38’ ESurveying - TraverseDMD CalculationsC189.53 ft.N 12 24’ WSurveying - TraverseDS 6 15’ W234.58 ft.ECCPoint E is the farthestto the westAReferenceMeridianN 42 59’ E175.18 ft.159.974NABAB8/13Surveying - TraverseDMD CalculationsThe DMD of any side is equal to:the DMD of the last side the departure of the last side the departure of the presentsideDMDAB DMDEA depEA depABSideABBCCDDEEABalancedLatitude 0186.648-195.470-30.551159.974The DMD of line AB is departure of line ABDMD-20.601
CIVL 1112Surveying - Traverse CalculationsSurveying - TraverseSurveying - TraverseDMD CalculationsSideABBCCDDEEADMD CalculationsBalancedLatitude 01 86.648 -195.470-30.551159.974SideDMD-20.60145.447The DMD of line BC is DMD of line AB departure of line AB the departure of line BCSurveying - 5.470 -63.375-30.551 -289.397159.974Surveying - TraverseABBCCDDEEABalancedLatitude 0.601-20.60145.44786.648-63.375-195.470-30.551 -289.397159.974 -159.974The DMD of line EA is DMD of line DE departure of line DE the departure of line EATraverse Area - Double Area The sum of the products of each points DMD and latitudeequal twice the area, or the double areaBalancedLatitude 0.60145.447-63.375Surveying - TraverseDMD CalculationsABBCCDDEEA-20.60186.648 -195.470 -30.551159.974The DMD of line CD is DMD of line BC departure of lineBC the departure of line CDSideThe DMD of line DE is DMD of line CD departure of lineCD the departure of line DESide-188.388-152.25329.933139.080171.627DMD CalculationsBalancedLatitude DDEEABalancedLatitude DepartureSurveying - TraverseDMD 9.974DMD-20.60145.447-63.375-289.397-159.974Notice that the DMD values can be positive or negativeSideABBCCDDEEABalancedLatitude 0186.648-195.470-30.551159.974DMDDouble Areas-20.6013,88145.447-63.375-289.397-159.974 The double area for line AB equals DMD of line AB timesthe latitude of line AB
CIVL 1112Surveying - Traverse CalculationsSurveying - TraverseSurveying - TraverseTraverse Area - Double AreaTraverse Area - Double Area The sum of the products of each points DMD and latitudeequal twice the area, or the double areaSideABBCCDDEEABalancedLatitude 0186.648-195.470-30.551159.974DMDDouble 74Surveying - TraverseBalancedLatitude ing - TraverseBalancedLatitude Departure1 acre 43,560 ft.2-20.60186.648-195.470-30.551159.974 The sum of the products of each points DMD and latitudeequal twice the area, or the double -20.60186.648-195.470-30.551159.974DMDDouble 289.397-27,456-159.974 The double area for line EA equals DMD of line EA timesthe latitude of line EA The sum of the products of each points DMD and latitudeequal twice the area, or the double areaSideDMDDouble -40,249-159.974-27,4562 Area -72,641Area BalancedLatitude DepartureTraverse Area - Double Area The sum of the products of each points DMD and latitudeequal twice the area, or the double area-188.388-152.25329.933139.080171.627DMDDouble -159.974Surveying - TraverseTraverse Area - Double AreaABBCCDDEEA-20.60186.648-195.470-30.551159.974 The double area for line CD equals DMD of line CD timesthe latitude of line CDSideDMDDouble 289.397-159.974 The double area for line DE equals DMD of line DE timesthe latitude of line DESide-188.388-152.25329.933139.080171.627Traverse Area - Double Area The sum of the products of each points DMD and latitudeequal twice the area, or the double BalancedLatitude DepartureSurveying - TraverseTraverse Area - Double AreaABBCCDDEEA The sum of the products of each points DMD and latitudeequal twice the area, or the double areaSide The double area for line BC equals DMD of line BC timesthe latitude of line BCSide10/1336,320 ft.20.834 acreABBCCDDEEABalancedLatitude Departure-188.388-152.25329.933139.080171.6271 acre 43,560 ft.2-20.60186.648-195.470-30.551159.974DMDDouble -40,249-159.974-27,4562 Area -72,641Area 36,320 ft.20.834 acre
CIVL 1112Surveying - Traverse CalculationsSurveying - TraverseTraverse Area - Double Area11/13Surveying - TraverseTraverse Area - Double Area The word "acre" is derived from Old English æcer(originally meaning "open field", cognate to Swedish"åker", German acker, Latin ager and Greek αγρος(agros). The word "acre" is derived from Old English æcer(originally meaning "open field", cognate to Swedish"åker", German acker, Latin ager and Greek αγρος(agros). The acre was selected as approximately the amount ofland tillable by one man behind an ox in one day. A long narrow strip of land is more efficient to plough thana square plot, since the plough does not have to be turnedso often. This explains one definition as the area of a rectangle withsides of length one chain (66 ft.) and one furlong (tenchains or 660 ft.). The word "furlong" itself derives from the fact that it is onefurrow long.Surveying - TraverseTraverse Area - Double Area The word "acre" is derived from Old English æcer(originally meaning "open field", cognate to Swedish"åker", German acker, Latin ager and Greek αγρος(agros).Surveying - TraverseTraverse Area – Example 4 Find the area enclosed by the following traverseSideBalancedLatitude ble Areas200.0400.0100.0-300.0-400.02 Area 1 acre 43,560 ft.2Surveying - TraverseDPD CalculationsArea ft. 2acreSurveying - TraverseRectangular Coordinates The same procedure used for DMD can be used thedouble parallel distances (DPD) are multiplied by thebalanced departures Rectangular coordinates are the convenient methodavailable for describing the horizontal position of surveypoints The parallel distance of a line is the distance from themidpoint of the line to the reference parallel or east–westline With the application of computers, rectangularcoordinates are used frequently in engineering projects In the US, the x–axis corresponds to the east–westdirection and the y–axis to the north–south direction
CIVL 1112Surveying - Traverse CalculationsSurveying - TraverseSurveying - TraverseRectangular Coordinates ExampleRectangular Coordinates ExampleIn this example, the length of AB is 300 ft. and bearing isshown in the figure below. Determine the coordinates ofpoint ByLatitude AB 300 ft. cos(42 30’) 221.183 ft.BIn this example, it is assumed that the coordinates of pointsA and B are know and we want to calculate the latitude anddeparture for line AByALatitude AB -400 ft.xDeparture AB x B – x ADeparture AB 220 ft.x B 200 202.667 402.667 ft.BSurveying - TraverseRectangular Coordinates ExampleRectangular Coordinates ExampleyConsider our previous example, determine the x and ycoordinates of all the 51159.974xCSurveying - TraverseRectangular Coordinates ExampleyAE x coordinatesE 0 ft.BDA E 159.974 159.974 ft.xCB A – 20.601 139.373 ft.SideABBCCDDEEABalance dLatitude De 86.648-195.470-30.551159.974ABBCCDDEEAD C – 195.470 30.551 ft.E D – 30.551 0 ft.Rectangular Coordinates ExampleyA (159.974, 340.640)C 0 ft.D C 29.933 ft.CxB (139.373, 152.253)E D 139.080 169.
1 sin 2 Area ABC ac . a proposed solution to the problem of compass traverse adjustment, which was posed in the American journal The Analyst in 1807. CIVL 1112 Surveying - Traverse Calculations 4/13. Surveying - Traverse The compass method assumes:
Sep 05, 2016 · Engineering Surveying -1 CE212 Compass Surveying Lecture 2016, September 03-04 Muhammad Noman. Compass Surveying Chain surveying can be used when the area to be surveyed is comparatively is
shore of Little Traverse Bay to protect the harbor at Harbor Springs. Little Traverse Light (45 25'10"N., 84 58'39"W.), 72 feet above the water, is shown from a white skeleton tower on the end of the point. Harbor Springs, MI, on the north shore of Little Traverse Bay, is a fine small -craft harbor of refuge affording security in any weather.
THE 2016 TRAVERSE IS HERE. With a boldly styled exterior designed around a rich and refined interior, Chevrolet Traverse invites you in. Traverse offers seating for up to eight,1 best-in-class maximum cargo space, 2 ingenious safety technology and upscale features like an available built-in 4G LTE3 Wi-Fi hotspot. 4 No wonder Traverse was named
Route Surveying 20 Road Construction Plans and Specifications. 21. Land Surveying Lab 22 Legal Principles of Surveying 23 GPS/GIS Surveying 24 Advanced Surveying Practices 25 Soil Mechanics 26 Concrete and Hot-Mix Asphalt Testing 27. Water and Water Distribution. 28 Spec
1. State the Objectives of Surveying? 2. What is basic principle on which Surveying has been classified? And explain them? 3. Differentiate between Plane Surveying & Geodetic Surveying? 4. State the various types of functional classification of Surveying? 5. State t
Traverse L T Z A WD in Crystal Red T intcoat (extra-cost color). GRACE POWER Chevrolet 2-Year Scheduled Maintenance Coverage 1 is included with the purchase or lease of a new 2014 Chevrolet Traverse. This fully transferable program is in addition to the Traverse st
Kaseya Traverse Unified Cloud, Network, Server & Application Monitoring Kaseya Traverse is a next-generation software solution for monitoring the performance of hybrid cloud and IT infrastructure in enterprise and Managed Service Provider (MSP) environments. Traverse provides a correlated and service-oriented view of the IT
Any dishonesty in our academic transactions violates this trust. The University of Manitoba General Calendar addresses the issue of academic dishonesty under the heading “Plagiarism and Cheating.” Specifically, acts of academic dishonesty include, but are not limited to:
