Surveying - Traverse. Surveying - Traverse. Distance - Traverse. Distance - Traverse. CIVL 1112 Surveying - Traverse Calculations 1/13.

Transcription

1 IVL alculations /3 Introduction lmost all surveing requires some calculations to reduce measurements into a more useful form for determining distance, earthwork volumes, land areas, etc. traverse is developed b measuring the distance and angles between points that found the boundar of a site e will learn several different techniques to compute the area inside a traverse istance - Traverse Methods of omputing rea simple method that is useful for rough area estimates is a graphical method In this method, the traverse is plotted to scale on graph paper, and the number of squares inside the traverse are counted istance - Traverse Methods of omputing rea istance - Traverse Methods of omputing rea a c b rea ac sin d a b c rea ad sin rea bc sin rea rea rea

2 IVL alculations /3 istance - Traverse Methods of omputing rea alancing ngles e a d b c rea ae sin rea cd sin efore the areas of a piece of land can be computed, it is necessar to have a closed traverse The interior angles of a closed traverse should total: (n - )(80 ) where n is the number of sides of the traverse To compute rea more data is required alancing ngles alancing ngles rror of closure surveing heuristic is that the total angle should not var from the correct value b more than the square root of the number of angles measured times the precision of the instrument For eample an eight-sided traverse using a transit, the maimum error is: ngle containing mistake ' 8.83' 3' alancing ngles If the angles do not close b a reasonable amount, mistakes in measuring have been made Latitudes and epartures The closure of a traverse is checked b computing the latitudes and departures of each of it sides If an error of is made, the surveor ma correct one angle b If an error of is made, the surveor ma correct two angles b each Latitude earing eparture If an error of 3 is made in a sided traverse, the surveor ma correct each angle b 3 / or 5 earing eparture Latitude

3 IVL alculations 3/3 Latitudes and epartures The latitude of a line is its projection on the north south meridian Latitude earing eparture The departure of a line is its projection on the east west line northeasterl bearing has: latitude and departure rror of losure onsider the following statement: If start at one corner of a closed traverse and walk its lines until ou return to our starting point, ou will have walked as far north as ou walked south and as far east as ou have walked west Therefore latitudes = 0 and departures = 0 rror of losure hen latitudes are added together, the resulting error is called the error in latitudes ( L ) The error resulting from adding departures together is called the error in departures ( ) rror of losure If the measured bearings and distances are plotted on a sheet of paper, the figure will not close because of L and rror of closure L closure L Precision closure Tpical precision: /5,000 for rural land, /7,500 for suburban land, and /0,000 for urban land Latitudes and epartures - ample Latitudes and epartures - ample eparture ft. (89.53 ft.)sin(6 5') 0.63 ft. Latitude (89.53 ft.)cos(6 5') ft.

4 IVL alculations 4/3 Latitudes and epartures - ample Latitudes and epartures - ample eparture (75.8 ft.)sin(9 38') 86.6 ft. ide earing Length (ft.) Latitude eparture ft. Latitude (75.8ft.)cos(938') 5.7ft. Latitudes and epartures - ample Group ample Problem ide earing Length (ft.) Latitude eparture ft ft closure L Precision closure 0.8 ft. 0.8 ft ft. 5, ft ft. Group ample Problem ide earing Length (ft.) Latitude eparture alancing Latitudes and epartures alancing the latitudes and departures of a traverse attempts to obtain more probable values for the locations of the corners of the traverse popular method for balancing errors is called the compass or the owditch rule The owditch rule as devised b athaniel owditch, surveor, navigator and mathematician, as a proposed solution to the problem of compass traverse adjustment, which was posed in the merican journal The nalst in 807.

5 IVL alculations 5/3 alancing Latitudes and epartures The compass method assumes: ) angles and distances have same error ) errors are accidental The rule states: The error in latitude (departure) of a line is to the total error in latitude (departure) as the length of the line is the of the traverse alancing Latitudes and epartures ft ft ft ft ft. 8 8 Latitudes and epartures - ample Recall the results of our eample problem Latitudes and epartures - ample Recall the results of our eample problem ide earing Length (ft) Latitude eparture ide earing Length (ft) Latitude eparture alancing Latitudes and epartures Latitude (89.53 ft.)cos(6 5') ft. orrection in Lat L 6 5 L ft. LL orrection in Lat orrection in Lat ft ft ft ft. alancing Latitudes and epartures eparture (89.53 ft.)sin(6 5') 0.63 ft. orrection in ep L ft. orrection in ep L orrection in ep 0.63 ft ft ft ft.

6 IVL alculations 6/3 alancing Latitudes and epartures alancing Latitudes and epartures Latitude eparture 75.8 ft orrection in Lat (75.8 ft.)cos(9 38') 5.7 ft. orrection in Lat L L L L orrection in Lat ft ft ft ft ft orrection in ep (75.8 ft.)sin(9 38') 86.6 ft. orrection in ep L L orrection in ep 0.63 ft ft ft ft. alancing Latitudes and epartures alancing Latitudes and epartures orrections alanced Length (ft.) Latitude eparture Latitude eparture Latitude eparture orrections alanced Length (ft.) Latitude eparture Latitude eparture Latitude eparture orrections computed on previous slides orrected latitudes and departures alancing Latitudes and epartures orrections alanced Length (ft.) Latitude eparture Latitude eparture Latitude eparture alancing Latitudes and epartures ombining the latitude and departure calculations with corrections gives: orrections alanced earing ide Length (ft.) Latitude eparture Latitude eparture Latitude eparture o error in corrected latitudes and departures

7 IVL alculations 7/3 Group ample Problem alance the latitudes and departures for the following traverse. Group ample Problem 3 In the surve of our assign site in Project #3, ou will have to balance data collected in the following form: orrections alanced Length (ft) Latitude eparture Latitude eparture Latitude eparture ft ft ft ft. Group ample Problem 3 In the surve of our assign site in Project #3, ou will have to balance data collected in the following form: orrections alanced earing ide Length (ft.) Latitude eparture Latitude eparture Latitude eparture closure = ft. alculating Traverse rea The best-known procedure for calculating land areas is the double meridian distance (M) method The meridian distance of a line is the east west distance from the midpoint of the line to the reference meridian The meridian distance is positive () to the east and negative (-) to the west Precision = alculating Traverse rea alculating Traverse rea Reference Meridian ft ft ft ft ft. 8 8 The most westerl and easterl points of a traverse ma be found using the departures of the traverse egin b establishing a arbitrar reference line and using the departure values of each point in the traverse to determine the far westerl point

8 IVL alculations 8/3 alculating Traverse rea alculating Traverse rea orrections alanced Length (ft.) Latitude eparture Latitude eparture Latitude eparture Point is the farthest to the west Reference Meridian ft ft ft ft ft. 8 8 M alculations Reference Meridian The meridian distance of line is: M of line is the departure of line M alculations Meridian distance of line The meridian distance of line is equal to: the meridian distance of ½ the departure of line ½ departure of The M of line is twice the meridian distance of line M alculations M alculations Meridian distance of line The M of an side is equal to the M of the last side plus the departure of the last side plus the departure of the present side alanced M The M of line is departure of line

9 IVL alculations 9/3 M alculations M alculations alanced M alanced M The M of line is M of line departure of line the departure of line The M of line is M of line departure of line the departure of line M alculations alanced M The M of line is M of line departure of line the departure of line M alculations alanced M The M of line is M of line departure of line the departure of line M alculations alanced M otice that the M values can be positive or negative Traverse rea - ouble rea The sum of the products of each points M and latitude alanced M ouble reas , The double area for line equals M of line times the latitude of line

10 IVL alculations 0/3 Traverse rea - ouble rea The sum of the products of each points M and latitude alanced M ouble reas , , The double area for line equals M of line times the latitude of line Traverse rea - ouble rea The sum of the products of each points M and latitude alanced M ouble reas , , , The double area for line equals M of line times the latitude of line Traverse rea - ouble rea The sum of the products of each points M and latitude alanced M ouble reas , , , , The double area for line equals M of line times the latitude of line Traverse rea - ouble rea The sum of the products of each points M and latitude alanced M ouble reas , , , , ,456 The double area for line equals M of line times the latitude of line Traverse rea - ouble rea The sum of the products of each points M and latitude alanced M ouble reas , , , , ,456 rea = -7,64 36,30 ft. acre = 43,560 ft. rea = acre Traverse rea - ouble rea The sum of the products of each points M and latitude alanced M ouble reas , , , , ,456 rea = -7,64 36,30 ft. acre = 43,560 ft. rea = acre

11 IVL alculations /3 Traverse rea - ouble rea The word "acre" is derived from Old nglish æcer (originall meaning "open field", cognate to wedish "åker", German acker, Latin ager and Greek αγρος (agros). The acre was selected as approimatel the amount of land tillable b one man behind an o in one da. This eplains one definition as the area of a rectangle with sides of length one chain (66 ft.) and one furlong (ten chains or 660 ft.). Traverse rea - ouble rea The word "acre" is derived from Old nglish æcer (originall meaning "open field", cognate to wedish "åker", German acker, Latin ager and Greek αγρος (agros). long narrow strip of land is more efficient to plough than a square plot, since the plough does not have to be turned so often. The word "furlong" itself derives from the fact that it is one furrow long. Traverse rea - ouble rea Traverse rea ample 4 The word "acre" is derived from Old nglish æcer (originall meaning "open field", cognate to wedish "åker", German acker, Latin ager and Greek αγρος (agros). Find the area enclosed b the following traverse alanced acre = 43,560 ft. M rea = rea = ouble reas ft. acre P alculations Rectangular oordinates The same procedure used for M can be used the double parallel distances (P) are multiplied b the balanced departures The parallel distance of a line is the distance from the midpoint of the line to the reference parallel or east west line Rectangular coordinates are the convenient method available for describing the horizontal position of surve points ith the application of computers, rectangular coordinates are used frequentl in engineering projects In the U, the ais corresponds to the east west direction and the ais to the north south direction

12 IVL alculations /3 Rectangular oordinates ample In this eample, the length of is 300 ft. and bearing is shown in the figure below. etermine the coordinates of point Latitude =300 ft. cos(430 ) =.83 ft. oordinates of Point (00, 300) 4 30 eparture =300 ft. sin(430 ) = ft. = = ft. = = 5.83 ft. Rectangular oordinates ample In this eample, it is assumed that the coordinates of points and are know and we want to calculate the latitude and departure for line oordinates of Point (00, 300) Latitude = Latitude = -400 ft. eparture = eparture = 0 ft. oordinates of Point (30, -00) Rectangular oordinates ample onsider our previous eample, determine the and coordinates of all the points alanced Rectangular oordinates ample alanced coordinates = 0 ft. = = ft. = 0.60 = ft. = = 6.0 ft. = = ft. = = 0 ft. Rectangular oordinates ample coordinates = 0 ft. = ft. = = ft. alanced = 7.67 = ft. Rectangular oordinates ample (59.974, ) (39.373, 5.53) (0.0, 69.03) = = 5.5 ft. = 5.5 = 0 ft. (30.55, 9.933) (6.00, 0.0)

13 IVL alculations 3/3 Group ample Problem 5 ompute the and coordinates from the following balanced. alanced oordinates ide earing Length (ft.) Latitude eparture Latitude eparture Points rea omputed b oordinates The area of a traverse can be computed b taking each coordinate multiplied b the difference in the two adjacent coordinates (using a sign convention of for net side and - for last side) rea omputed b oordinates (59.974, ) (39.373, 5.53) (0.0, 69.03) (30.55, 9.933) (6.00, 0.0) rea = acre Twice the area equals: = ( ) 5.53( ) 0.0( ) 9.933( ) 69.03( ) = 7, ft. rea = 36,30. ft. (0.0, 69.03) rea omputed b oordinates There is a simple variation of the coordinate method for area computation (30.55, 9.933) (59.974, ) (39.373, 5.53) (6.00, 0.0) Twice the area equals: = rea omputed b oordinates There is a simple variation of the coordinate method for area computation (59.974, ) Twice the area equals: nd of n Questions? (0.0, 69.03) (30.55, 9.933) (39.373, 5.53) (6.00, 0.0) (5.53) (0.0) 6.00(9.933) 30.55(69.03) 0.0( ) (39.373) 5.53(6.00) - 0.0(30.55) 9.933(0.0) 69.03(59.974) = -7,640 ft. rea = 36,30 ft.