Unit 3: Compass survey.

Unit 3: Compass survey

Topics covered – Compass Surveying
Meridian & Bearing - true, magnetic and arbitrary Traverse - closed, open. System of bearing - whole circle bearing, Reduced bearing, fore bearing, and back bearing, conversion from one system to another. Angles from the bearing and vice versa. Prismatic, Surveyor, Silva and Bronton (introduction) compass Local attraction with numerical problems. Plotting of compass survey (Parallel meridian method in detail). Unit 5: Compass traversing & Traverse computation

Unit 5: Compass traversing & Traverse computation
Definition Limitation of chain surveying Angle or direction measurement must Azimuth, Bearing, interior angle, exterior angle, deflection angle B C A θ ß θ-ß C B A ß Φ E D γ α θ C B A ß Φ E D γ α θ C B A 220 L 250 R Unit 5: Compass traversing & Traverse computation

Compass surveying Compass used for measurement of direction of lines Precision obtained from compass is very limited Used for preliminary surveys, rough surveying Unit 5: Compass traversing & Traverse computation

5.1 Meridian, Bearing & Azimuths
Meridian: some reference direction based on which direction of line is measured True meridian ( Constant) Magnetic meridian ( Changing) Arbitrary meridian Source: Bearing: Horizontal angle between the meridian and one of the extremities of line True bearing Magnetic bearing Arbitrary bearing Unit 5: Compass traversing & Traverse computation

Contd… True meridian Line passing through geographic north and south pole and observer’s position Position is fixed Established by astronomical observations Used for large extent and accurate survey (land boundary) Observer’s position Geographic north pole Unit 5: Compass traversing & Traverse computation

Contd… Magnetic meridian Line passing through the direction shown by freely suspended magnetic needle Affected by many things i.e. magnetic substances Position varies with time (why? not found yet) Assumed meridian Line passing through the direction towards some permanent point of reference Used for survey of limited extent Disadvantage Meridian can’t be re-established if points lost. Unit 5: Compass traversing & Traverse computation

Reduced bearing A B NΦE N S E W Either from north or south either clockwise or anticlockwise as per convenience Value doesn’t exceed 900 Denoted as N ΦE or S Φ W The system of measuring this bearing is known as Reduced Bearing System (RB System) A SΦW S W E N B Unit 5: Compass traversing & Traverse computation

Whole circle bearing (Azimuth)
Always clockwise either from north or south end Mostly from north end Value varies from 00 – 3600 The system of measuring this bearing is known as Whole Circle Bearing System (WCB System) B A S W E N 450 B A S W E N 3000 Unit 5: Compass traversing & Traverse computation

5.2 Conversion from one system to other
Conversion of W.C.B. into R.B. ß D Φ B θ A α C W E o S Line W.C.B. between Rule for R.B. Quadrants OA OB OC OD 00 and 900 900 and 1800 1800 and 2700 2700 and 3600 R.B. = W.C.B. = θ R.B. = 1800 – W.C.B. = 1800 – Φ R.B. = W.C.B. – 1800 = α – 1800 R.B. = W.C.B. = ß. NθE SΦE SαE SßE Unit 5: Compass traversing & Traverse computation

5.2 Conversion from one system to other
Contd… N Conversion of R.B. into W.C.B. D ß θ A W E o Φ α B C S Line R.B. Rule for W.C.B. W.C.B. between OA OB OC OD NθE SΦE SαE SßE W.C.B. = R.B. W.C.B. = 1800 – R.B. W.C.B. = R.B. W.C.B. = R.B. 00 and 900 900 and 1800 1800 and 2700 and 3600 Unit 5: Compass traversing & Traverse computation

5.2 Fore & back bearing Each survey line has F.B. & B.B. In case of line AB, F.B. is the bearing from A to B B.B. is the bearing from B to A Relationship between F.B. & B.B. in W.C.B. B.B. = F.B. ± 1800 Use + sign if F.B. < 1800 & use – sign if F.B.>1 1800 θ ß C B θ ß A D Unit 5: Compass traversing & Traverse computation

5.2 Fore & back bearing Contd… Relationship between F.B. & B.B. in R.B. system B.B.=F.B. Magnitude is same just the sign changes i.e. cardinal points changes to opposite. B D NΦE NßW SßE SΦW A C Unit 5: Compass traversing & Traverse computation

5.2 Calculation of angles from bearing and vice versa
In W.C.B.system ( Angle from bearing) Easy & no mistake when diagram is drawn Use of relationship between F.B. & B.B. Knowledge of basic geometry ß θ C A B ß B Θ ß θ θ-ß C A Unit 5: Compass traversing & Traverse computation

5.2 Calculation of angles from bearing and vice versa
Contd… In R.B. system (Angle from Bearing) Easy & no mistake when diagram is drawn Knowledge of basic geometry C A B NθE SßE B C A SßE SθW 1800-(θ+ß) Θ+ß Unit 5: Compass traversing & Traverse computation

5.2 Calculation of bearing from angle
Normally in traverse, included angles are measured if that has to be plotted by co-ordinate methods, we need to know the bearing of line Bearing of one line must be measured Play with the basic geometry Diagram is your good friend always Ø ? ? ? ? Unit 5: Compass traversing & Traverse computation

Contd… =?  Bearing of line AB = θ1 Back Bearing of line AB = θ1 Fore Bearing of line BC =θ2 = α –  = α -[3600 –( θ1) ] = α+ θ  = 3600 – BB of line AB = ( θ1)  is also = alternate angle of (1800 – θ1) = (1800 – θ1) Unit 5: Compass traversing & Traverse computation

Contd… =?  Bearing of line BC = θ2 Back Bearing of line BC = θ2 Fore Bearing of line CD = θ3 = ß –  = ß -[3600 –( θ2) ] = ß+ θ  = 3600 – BB of line BC = ( θ2) Unit 5: Compass traversing & Traverse computation

Contd… ? Ø  Bearing of line CD= θ3 ? Back Bearing of line CD = θ3  = 3600 – BB of line CD = ( θ3) Fore Bearing of line DE = θ4 = γ –  = γ -[3600 –( θ3) ] = γ+ θ Unit 5: Compass traversing & Traverse computation

Contd… Ø =? Bearing of line DE= θ4 Back Bearing of line DE = θ4 Fore Bearing of line EF = θ5 = BB of line DE + Ø = θ4 + Ø Unit 5: Compass traversing & Traverse computation

5.2 Numerical on angle & bearing
What would be the bearing of line FG if the following angles and bearing of line AB were observed as follows: (Angles were observed in clockwise direction in traverse) EFG = DEF = CDE = BCD = ABC = ’ ’ 950 15’ ’ ’ Bearing of line AB = ’ Unit 5: Compass traversing & Traverse computation

EFG = DEF = CDE = BCD = ABC = ’ ’ 950 15’ ’ ’ Bearing of line AB = ’ A ’ B ’ ’ D ’ E ’ F G ’ C F G ’ ? A ’ E ’ B ’ D ’ C ’ Unit 5: Compass traversing & Traverse computation

’ A ’ B FB of line BC = ( ’- 1800) ’ = ’ C B ’ ’ D FB of line CD = ( ’- 1800) ’ = ’ Unit 5: Compass traversing & Traverse computation

’ D ’ E FB of line DE = ’ - ( ’) = ’ D ’ E ’ F FB of line EF = (840 15’+1800) ’ = ’ Unit 5: Compass traversing & Traverse computation

FB of line FG = ’ - {1800+(BB of line EF)} FB of line FG = ’ - {(1800 +(00 30’)} = ’ A ’ B ’ ’ D ’ E ’ F G ’ C E ’ F G ’ Unit 5: Compass traversing & Traverse computation

Contd… From the given data, compute the missing bearings of lines in closed traverse ABCD. A = 810 16’ Bearing of line CD = N270 50’E Bearing of line AB = ? 360 42’ B = D C B A Bearing of line BC = ? ’ D = Unit 5: Compass traversing & Traverse computation

Contd… For the figure shown, compute the following. The deflection angle at B The bearing of CD The north azimuth of DE The interior angle at E The interior angle at F B S550 26’E N ’E C A 790 16’ N120 58’W D S120 47’E F E S860 48’W Unit 5: Compass traversing & Traverse computation

Contd… Deflection Angle at B = (410 07’ ’) = ’ R C N ’E 790 16’ A B D E F S550 26’E S120 47’E S860 48’W N120 58’W Bearing of line CD = (790 16’ ’) = S ’ W North Azimuth of line DE = ’ = ’ Interior Angle E = 1800 – (120 47’ ’) = ’ Interior Angle F = (120 58’ ’) = ’ Unit 5: Compass traversing & Traverse computation

5.4 Error in compass survey (Local attraction & observational error)
Local attraction is the influence that prevents magnetic needle pointing to magnetic north pole Unavoidable substance that affect are Magnetic ore Underground iron pipes High voltage transmission line Electric pole etc. Influence caused by avoidable magnetic substance doesn’t come under local attraction such as instrument, watch wrist, key etc Unit 5: Compass traversing & Traverse computation

5.4 Local attractions Let Station A be affected by local attraction Observed bearing of AB = θ1 Computed angle B = θ – ß would not be right. ß B θ θ1 C A Unit 5: Compass traversing & Traverse computation

5.4 Local attractions Detection of Local attraction By observing the both bearings of line (F.B. & B.B.) and noting the difference (1800 in case of W.C.B. & equal magnitude in case of R.B.) We confirm the local attraction only if the difference is not due to observational errors. If detected, that has to be eliminated Two methods of elimination First method Second method Unit 5: Compass traversing & Traverse computation

5.4 Local attractions First method Difference of B.B. & F.B. of each lines of traverse is checked to not if they differ by correctly or not. The one having correct difference means that bearing measured in those stations are free from local attraction Correction are accordingly applied to rest of station. If none of the lines have correct difference between F.B. & B.B., the one with minimum error is balanced and repeat the similar procedure. Diagram is good friend again to solve the numerical problem. Pls. go through the numerical examples of your text book. Unit 5: Compass traversing & Traverse computation

5.4 Local attractions Second method Based on the fact that the interior angle measured on the affected station is right. All the interior angles are measured Check of interior angle – sum of interior angles = (2n-4) right angle, where n is number of traverse side Errors are distributed and bearing of lines are calculated with the corrected angles from the lines with unaffected station. Pls. go through the numerical examples of your text book. Unit 5: Compass traversing & Traverse computation

5.5 Traverse, types, compass & chain traversing
A control survey that consists of series of established stations tied together by angle and distance Angles measured by compass/transits/ theodolites Distances measured by tape/EDM/Stadia/Subtense bar C B A E D a1 e1 c1 b1 b2 c2 Unit 5: Compass traversing & Traverse computation

5.5 Traverse, types, compass & chain traversing
Use of traverse Locate details, topographic details Lay out engineering works Types of Traverse Open Traverse Closed Traverse C B A ß Φ E D γ α θ Unit 5: Compass traversing & Traverse computation

5.5 Types of traverse Open traverse Geometrically don’t close No geometric verification Measuring technique must be refined Use – route survey (road, irrigation, coast line etc..) C B A 220 L 250 R Unit 5: Compass traversing & Traverse computation

5.5 Types of traverse Contd… Close traverse Geometrically close (begins and close at same point)-loop traverse Start from the points of known position and ends to the point of known position – may not geometrically close – connecting traverse Can be geometrically verified Use – boundary survey, lake survey, forest survey etc.. C B A ß Φ E D γ α θ C B A 220 L 250 R D Co-ordinate of A &D is already known Unit 5: Compass traversing & Traverse computation

5.5 Methods of traversing Methods of traversing Chain traversing (Not chain surveying) Chain & compass traversing (Compass surveying) Transit tape traversing (Theodolite Surveying) Plane-table traversing (Plane Table Surveying) Aa22 + Aa12 - a2a12 cosA 2×Aa2×Aa1 = C B A D b1 b2 a2 a1 c1 c2 C B A b2 b1 c2 c1 Unit 5: Compass traversing & Traverse computation

5.5 Methods of traversing Contd… Chain & compass traversing (Free or loose needle method) Bearing measured by compass & distance measured by tape/chain Bearing is measured independently at each station Not accurate as transit – tape traversing A C B D E F length Unit 5: Compass traversing & Traverse computation

5.5 Methods of traversing Contd… Transit tape traversing Traversing can be done in many ways by transit or theodolite By observing bearing By observing interior angle By observing exterior angle By observing deflection angle Unit 5: Compass traversing & Traverse computation

5.5 Methods of traversing Contd… By observing bearing A C B D E F length Unit 5: Compass traversing & Traverse computation

5.5 Methods of traversing Contd… By observing interior angle Always rotate the theodolite to clockwise direction as the graduation of cirle increaes to clockwise Progress of work in anticlockwise direction measures directly interior angle Bearing of one line must be measured if the traverse is to plot by coordinate method A E F D C B length Unit 5: Compass traversing & Traverse computation

5.5 Methods of traversing Contd… By observing exterior angle Progress of work in clockwise direction measures directly exterior angle Bearing of one line must be measured if the traverse is to plot by coordinate method A E F D C B length Unit 5: Compass traversing & Traverse computation

5.5 Methods of traversing Contd… By observing deflection angle Angle made by survey line with prolongation of preceding line Should be recorded as right ( R ) or left ( L ) accordingly C B A 220 L 250 R D Unit 5: Compass traversing & Traverse computation

5.5 Locating the details in traverse
By observing angle and distance from one station By observing angles from two stations Unit 5: Compass traversing & Traverse computation

5.5 Locating the details in traverse
By observing distance from one station and angle from one station By observing distances from two points on traverse line Unit 5: Compass traversing & Traverse computation

5.5 Checks in traverse Checks in closed Traverse Errors in traverse is contributed by both angle and distance measurement Checks are available for angle measurement but There is no check for distance measurement For precise survey, distance is measured twice, reverse direction second time Unit 5: Compass traversing & Traverse computation

5.5 Checks in traverse Contd… Checks for angular error are available Interior angle, sum of interior angles = (2n-4) right angle, where n is number of traverse side Exterior angle, sum of exterior angles = (2n+4) right angle, where n is number of traverse side C B A ß Φ E D γ α θ C B A ß Φ E D γ α θ Unit 5: Compass traversing & Traverse computation

5.5 Checks in traverse Contd… Deflection angle – algebric sum of the deflection angle should be 00 or 3600. Bearing – The fore bearing of the last line should be equal to its back bearing ± 1800 measured at the initial station. C B A ß E D θ C B A ß should be = θ Unit 5: Compass traversing & Traverse computation

5.5 Checks in traverse Contd… Checks in open traverse No direct check of angular measurement is available Indirect checks Measure the bearing of line AD from A and bearing of DA from D Take the bearing to prominent points P & Q from consecutive station and check in plotting. C B A E D C B A E D Q P Unit 5: Compass traversing & Traverse computation E

5.6 Field work and field book
Field work consists of following steps Steps Reconnaissance Marking and Fixing survey station First Compass traversing then only detailing Bearing measurement & distance measurement Bearing verification should be done if possible Details measurement Offsetting Bearing and distance Bearings from two points Bearing from one points and distance from other point Unit 5: Compass traversing & Traverse computation

5.6 Field work and field book
Contd… Line Bearing Distance Remarks AB AE BA BC CB CD DC DE ED EA Field book Make a sketch of field with all details and traverse in large size C B E D A b1 b3 b4 b2 w1 w2 Line Bearing Distance Remarks Bw1 Cw2 Db2 Db3 Eb4 Eb1 Unit 5: Compass traversing & Traverse computation

5.7 Computation & plotting a traverse
Methods of plotting a traverse Angle and distance method Coordinate method LATITUDE AXIS E (74.795, ) D (26.879, ) C ( , ) B( , ) A ( , ) DEPARTURE AXIS (0,0) Unit 5: Compass traversing & Traverse computation

Contd… Angle and distance method Suitable for small survey Inferior quality in terms of accuracy of plotting Different methods under this By protractor By the tangent of angle By the chord of the angle Unit 5: Compass traversing & Traverse computation

Contd… By protractor Ordinary protractor with minimum graduation 10’ or 15’ Unit 5: Compass traversing & Traverse computation

Contd… By the tangent of angle Trignometrical method Use the property of right angle triangle, perpendicular =base × tanθ A B 600 5cm 5cm×tan600 cm D θ b P = b× tanθ B A D Unit 5: Compass traversing & Traverse computation

Contd… By the chord of the angle Geometrical method of laying off an angle A 450 5cm (2×5×sin 450/2)cm D B r B A D θ Chord r’ = 2rsinθ/2 rsinθ/2 θ/2 Unit 5: Compass traversing & Traverse computation

Contd… Coordinate method Survey station are plotted by their co-ordinates. Very accurate method of plotting Closing error is balanced prior to plotting-Biggest advantage C B A D E C B A D C’ B’ A’ D’ E’ E e’ Unit 5: Compass traversing & Traverse computation

Contd… What is co-ordinates Latitude Co-ordinate length parallel to meridian +ve for northing, -ve for southing Magnitude = length of line× cos(bearing angle) Departure Co-ordinate length perpendicular to meridian +ve for easting, -ve for westing Magnitude = length of line× sin(bearing angle) (-,-) ( +,-) A θ B L = l×cosθ D = l×sinθ I (-, +) IV III II l (+,+) Unit 5: Compass traversing & Traverse computation

Contd… Consecutive co-ordinate Co-ordinate of points with reference to preceding point Equals to latitude or departure of line joining the preceding point and point under consideration If length and bearing of line AB is l and θ, then consecutive co-ordinates (latitude, departure) is given by Latitude co-ordinate of point B = l×cos θ Departure co-ordinate of point B = l×sin θ A θ B l Unit 5: Compass traversing & Traverse computation

Contd… Total co-ordinate Co-ordinate of points with reference to common origin Equals to algebric sum of latitudes or departures of lines between the origin and the point The origin is chosen such that two reference axis pass through most westerly If A is assumed to be origin, total co-ordinates (latitude, departure) of point D is given by Latitude co-ordinate = (Latitude coordinate of A+ ∑latitude of AB, BC, CD) Departure co-ordinate = (Departure coordinate of A+ ∑Departure of AB, BC, CD) C B A D Unit 5: Compass traversing & Traverse computation

Contd… For a traverse to be closed Algebric sum of latitude and departure should be zero. Dep. DA (+) C B A D Lat. DA(+) Lat. AB(+) Dep. AB (-) Dep. BC (-) Dep. CD Lat. CD(+) Lat. BC(-) Unit 5: Compass traversing & Traverse computation

Contd… Dep. DA’ C B A D A’ Lat. DA’ Lat. AB Dep. AB Dep. BC Lat. CD Lat. BC Dep. CD Real fact is that there is always error Both angle & distance Traverse never close Error of closure can be computed mathematically ∑lat ∑dep A A’ θ Closing Error (A’A) =√(∑Lat2+ ∑dep2 ) Bearing of A’A = tan-1 ∑dep/∑lat Unit 5: Compass traversing & Traverse computation

Contd… Error of closure is used to compute the accuracy ratio Accuracy ratio = e/P, where P is perimeter of traverse This fraction is expressed so that numerator is 1 and denominator is rounded to closest of 100 units. This ratio determines the permissible value of error. S.N. Types of traverse Permissible value of total linear error of closure 4 5 Minor theodolite traverse for detailing Compass traverse 1 in 3,000 1 in 300 to 1 in 600 Unit 5: Compass traversing & Traverse computation

Contd… What to do if the accuracy ratio is unsatisfactory than that required Double check all computation Double check all field book entries Compute the bearing of error of closure Check any traverse leg with similar bearing (±50) Remeasure the sides of traverse beginning with a course having a similar bearing to the error of closure Unit 5: Compass traversing & Traverse computation

Contd… Balancing the traverse (Traverse adjustment) Applying the correction to latitude and departure so that algebric sum is zero Methods Compass rule (Bowditch) When both angle and distance are measured with same precision Transit rule When angle are measured precisely than the length Graphical method Unit 5: Compass traversing & Traverse computation

Contd… Where Clat & Cdep are correction to latitude and departure ∑L = Algebric sum of latitude ∑D = Algebric sum of departure l = length of traverse leg ∑l = Perimeter of traverse Bowditch rule Clat ∑L ∑l = l × Cdep ∑D ∑l = l × Where Clat & Cdep are correction to latitude and departure ∑L = Algebric sum of latitude ∑D = Algebric sum of departure L = Latitude of traverse leg LT = Arithmetic sum of Latitude Transit rule Provide the flow diagram for coordinate method plotting Clat ∑L LT = L × Cdep ∑D ∑DT = D × Unit 5: Compass traversing & Traverse computation

Contd… Graphical rule Used for rough survey Graphical version of bowditch rule without numerical computation Geometric closure should be satisfied before this. D’ C’ E’ D C E A’ B’ e’ B A A C’ B’ A’ D’ E’ e’ a e d c b Unit 5: Compass traversing & Traverse computation

5.7 Example of coordinate method
Plot the following compass traverse by coordinate method in scale of 1cm = 20 m. Line Length (m) Bearing AB S 880 E BC S 060 E CD S 400 W DE N 810 W EA N 480 E E B C D A Unit 5: Compass traversing & Traverse computation

Step 1: calculate the latitude & departure coordinate length of survey line and value of closing error Line Bearing Length (m) Latitude co ordinate Departure Coordinate AB BC CD DE EA S 880 E S 060 E S 400 W N 810 W N 480 E 130.00 158.00 145.00 308.00 337.00 -4.537 48.182 16.515 P = ∑l = m ∑L= 0.932 ∑D = Closing Error (e) =√ (∑L2+ ∑D2 ) Closing Error (e) = m Unit 5: Compass traversing & Traverse computation

Step 2: calculate the ratio of error of closure and total perimeter of traverse (Precision) Precision = e/P = 1.675/1078 = 1/643 which is okey with reference to permissible value (1 in 300 to 1 in 600) Step 3: Calculate the correction for the latitude and departure by Bowditch’s method Clat(AB) 0.932 1078 = 130 × = Cdep(AB) 0.536 1078 = 130 × = Unit 5: Compass traversing & Traverse computation

Step 4: Apply the correction worked out (balancing the traverse) Line Latitude coordinate Departure coordinate Correction to Latitude Correction to Departure Corrected Latitude co ordinate Corrected Departure Coordinate AB BC CD DE EA -4.537 48.182 16.515 -0.112 -0.137 -0.125 -0.226 -0.291 +0.065 +0.079 +0.072 +0.153 +0.168 ∑L= 0 ∑D = 0 Unit 5: Compass traversing & Traverse computation

Step 5: Calculate the total coordinate of stations Line Corrected Latitude co ordinate Corrected Departure Coordinate Stations Total Latitude Coordinate Total Departure Coordinate AB BC CD DE EA A B C D E (assumed) 26.879 74.795 (CHECK) 49.239 300.00(CHECK) Unit 5: Compass traversing & Traverse computation

B( , ) LATITUDE AXIS C ( , ) E (74.795, ) D (26.879, ) (0,0) DEPARTURE AXIS Unit 5: Compass traversing & Traverse computation

Degree of accuracy in traversing
The angular error of closure in traverse is expressed as equal to C√N Where C varies from 15” to 1’ and N is the number of angle measured S.N. Types of traverse Angular error of closure Total linear error of closure 1 2 3 4 5 First order traverse for horizontal control Second order traverse for horizontal control Third order traverse for survey of important boundaries Minor theodolite traverse for detailing Compass traverse 6”√N 15”√N 30”√N 1’N 15’√N 1 in 25,000 1 in 10,000 1 in 5,000 1 in 3,000 1 in 300 to 1 in 600 Unit 5: Compass traversing & Traverse computation

5.7 Tutorial Plot the traverse by co-ordinate method, where observed data are as follows Interior angles A = ’ 12” B = ’ 12” C = ’ 42” D = ’ 12” E = ’ 42” Side length AB = ’, BC = ’, CD = ’ DE = ’, EA = ’ Bearing of side AB = N ’ 00” E (Allowable precision is 1/3000) E B C D A Unit 5: Compass traversing & Traverse computation

Thank you for your attention! Any questions? Querries? Unit 5: Compass traversing & Traverse computation

Unit 3: Compass survey.

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