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parastaneja.blospo t.in (VOLUME I)

Dr. B.C. PUNM IA Formerly, Professor and Head, Deptt. of Civil Engineeri ng, & Dean, Faculty of Engineeri ng M.B.M. Engineeri ng College,

Jodhpur

Er. ASHOK KUMAR JAIN Director, Arihant Consultan ts, Jodhpur

Dr. ARUN KUMAR JAIN Assistant Professor M.B.M. Engineer ing College, Jodhpur

SIXTEENTH EDITIO N (Thoro ughly Revise d and Enlarg ed)

LAXMI PUBLICATIONS (P) LTD e GUWAHATI e HYDERABAD BANGALORE e CHENNAI e COCHIN e RANCHI e NEW DELHI MUMBAI e W LUCKNO e A KOLKAT e JALANDHAR INDIA e USA • GHANA e KENYA

......_

B.C. PUNMIA ASHOK KUMAR JAIN, ARUN KUMAR JAIN

; \

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MY FAT HER

Preface

I ,.'

This volwne is one of the two which offer a comprehensive course in those parts y used by of theory and practice of Plane and Geodetic surveying that are most commonl Degree. civil engineers. and are required by the students taking examination in surveying for surveying common more the chapters thirteen in Diploma and A.M.I.E. The first volume covers operations. , Each topic introduced is thoroughly describOd, the theory is rigorously developed General n. applicatio its illustrate to and. a ~rge DUIJ?ber of numerical examples are included invariably given by practical s~atements of important principles and methods are almost to illustrations. A large number of problems are available at the end of each chapter, stage~ illustrate theory and practice and to enable the student to test his reading at differem of his srudies. Apan from illustrations of old and conventional instruments, emphasis has been placed good deal on new or improved instruments both for ordinary as well as precise work. A al geometric the of discussion thorough a with ts of space has been given to instrumental adjustmen principles in each case. Metric system of units has been used throughout the text, and, wherever possible, since the the various formulae used in texc have been derived in metric units. However, g engineerin the ted in all cha~ge\ over to metric system has still nor been fully implemen gi\'C!": system, hdxe ~!so beer: ;;;~:~~Jtirr:~ i;~ •JUr conntiy, a fe·,~- examples in F.P.S. to I should lik.e to express my thanks to M/s. Vickers Instruments Ltd. (successors .. Ltd Watci M/s. Cooke, Troughton & Simm's), M/s. Wild Heerbrugg Ltd., M/s Hilger & ns from and M/s. W.F. Stanley & Co. Ltd. for permitting me to use certain illustratio es Universiti various to due also are thanks My hs. their catalogues or providing special photograp of some reproduce to me pennitting for and exami~g bodies of professional institution the questions from their examination papers. lnspite of every care taken to check. the numerical work. some errors may remain. and I shall be obliged for any intimation of theses readers may discover. JODHPUR 1st July, 1965

B.C. PUNMIA

Jl(

PREFACE TO THE THIRD EDITION

PREFACE TO THE NINTH EDITION

In this edition, the subject-matter has been revised thoroughly and the chapters have been rearranged. Two new chapters on "Simple Circular Curves' and 'Trigonometrical Levelling (plane)" have been added. Latest Indian Standards on 'Scales', 'Chains' and 'Levelling Staff have been included. A two-colour plate on the folding type 4 m Levelling Staff, conforming to IS 1779 : 1%1 has been given. In order to make the book more useful to the ~tudents appearing at A.M.l.E. Examination in Elementary Surveying, questions from the examination papers of Section A. from May 1962 to Nov. 1970 have been given Appendix 2. Account has been taken throughout of the suggestions offered by the many users of the book, and grateful acknowledgement is made to them. Futther suggestions will be greatly appreciated.

JODHPUR 1st Feb.. 1972

B.C. PUNMIA

PREFACE TO THE FOURTH EDITION In this edition, the subjec1-matter has been revised and updated. An appendix on 'Measurement of Distance by Electronic Methods' has been added. JODHPUR 15-10-1973

B.C. PUNMIA

In the Ninth Edition. the subject-matter has been revised and updated. B.C. PUNMIA

JODHPUR 1st Nov., 1984

PREFACE TO THE TENTH EDITION In the Tenth Edition, the book has been completely rewritten, and all the diagrams have been redrawn. Many new articles and diagrams/illustrations have been added. New

instruments, such as precise levels. precise theodolites, precise plane table equipment, automatic levels. new types of compasses and clinometers etc. have been introduced. Two chapters on 'Setting Out Works' and 'Special Instruments' bav~ been added at the end of the book. Knowledge about special instruments, such as site square , transit-level, Brunton's universal pocket transit, mountain compass-transit, autom.nic le~~ls, etc. will be very much useful to the field engineers. Account has been taken througho~t of the suggestions offered by the many users of the book, and grateful acknowledgement is made to them. Further suggestions will be greatly appreciated. B.C. PUNMIA A.K. JAIN

JODHPUR lOth July, 1987

PREFACE TO THE TWELFTH EDITION PREFACE TO THE FIFTH EDmON In the Fifth Edition. the suhiect-matter ha!< on SI units bas been added.

thnrnnQ:hly rP:vic:.,-1

JODHPUR

In the Twelfth Edition, the subject-matter has been revised and updated. An

Appenrli'~'

B.C. PUNMJA

25-4-1978

PREFACE TO THE SIXTH EDmON In the Sixth Edition of the book, the subject-matter bas been thoroughly revised and updated. JODHPUR 2nd Jan., 1980

B.C. PUNMIA

JOlJHPUR 30th March, 1990

B.C. PUNMIA A.K. JAIN

PREFACE TO THE THIRTEENTH.EDITION In the Thirteenth Edition of the book, the subject mauer has been thoroughly revised and updated. Many new articles and solved examples have ·been added. The entire book bas been typeset using laser printer. The authors are thankful to Shri Moo! singb Galtlot for the fine laser typesetting done by him. JODHPUR 15th Aug. 1994

B.C. PUNMIA ASHOK K. JAJN ARUN K. JAIN

Jl(

PREFACE TO THE THIRD EDITION

PREFACE TO THE NINTH EDITION

JODHPUR 1st Feb.. 1972

B.C. PUNMIA

PREFACE TO THE FOURTH EDITION In this edition, the subjec1-matter has been revised and updated. An appendix on 'Measurement of Distance by Electronic Methods' has been added. JODHPUR 15-10-1973

B.C. PUNMIA

In the Ninth Edition. the subject-matter has been revised and updated. B.C. PUNMIA

JODHPUR 1st Nov., 1984

PREFACE TO THE TENTH EDITION In the Tenth Edition, the book has been completely rewritten, and all the diagrams have been redrawn. Many new articles and diagrams/illustrations have been added. New

JODHPUR lOth July, 1987

PREFACE TO THE TWELFTH EDITION PREFACE TO THE FIFTH EDmON In the Fifth Edition. the suhiect-matter ha!< on SI units bas been added.

thnrnnQ:hly rP:vic:.,-1

JODHPUR

In the Twelfth Edition, the subject-matter has been revised and updated. An

Appenrli'~'

B.C. PUNMJA

25-4-1978

PREFACE TO THE SIXTH EDmON In the Sixth Edition of the book, the subject-matter bas been thoroughly revised and updated. JODHPUR 2nd Jan., 1980

B.C. PUNMIA

JOlJHPUR 30th March, 1990

B.C. PUNMIA A.K. JAIN

B.C. PUNMIA ASHOK K. JAJN ARUN K. JAIN

fl! - I:!

i SI

Contents

PREFACE TO TilE SIXTEENTH EDITION In !he Sixteenth Edition, !he subject matter has been thoroughly revised, updated and rearranged. In each chapter, many new articles have been added. ·Three new Chapters have been added at !he end of !he book : Chapter 22 on 'Tacheomelric Surveying'. Chapter 13 on 'Electronic Theodolites' and Chapter 24 on 'Electro-magnetic Disrance Measurement (EDM)'. All !he diagrams have been redrawn using computer graphics and !he book has been computer type-set in bigger fonnat keeping in pace with the modern trend. Account has been taken throughout of !he suggestions offered by many users of !he book and grateful acknowledgement is made to !hem. The authors are thankful to Shri M.S. Gahlot for !he fine Laser type setting done by him. The Authors are also thankful Shri R.K. Gupta. Managing Director Laxmi Publications. for laking keen interest in publication of !he book and bringing it out nicely and quickly. Jodhpur Mabaveer Jayanti lsi July, 2005

B.C. PUNMIA ASHOK K. JAIN ARUN K. JAIN

CHAYI'ER

FUNDAMENTAL DEFINITIONS AND CONCEPTS I

1.1.

SURV~YING : OBJECT

1.2.

PRIMARY

1.3. 1.4. 1.5.

CLASSIFiCATION PRINCIPLES OF SURVEYING UNITS OF MEASUREMENTS

1.6.

PLANS

1.7. 1.8. 1.9.

SCALES PLAIN SCALE DIAGONAL SCALE

1.10.

THE VERNIER

1.11.

MICROMETER

1.12 1.13

SCALE ERROR

1.14.

SHRUNK

1.15.

SURVEYING -

CIIAYI'ER

DIVISIONS

AND

12 18

MICROSCOPES

OF CHORDS DUE TO USE

19 OF

CHAPTER 3.1. 3.2. 3.3.

3.7. 3.8. 3.9.

3.10. 3.11.

~~~ 4.1.

COMPUI'ED

'1:1 '1:1 28 29 PERMISSmLE

ERROR

RESULTS

3()

LINEAR MEASUREMENTS 37 37 38 46

DIFFERENT METHODS DIRECT MEASUREMENTS INSTRUMENTS FOR CHAINING OL-;

S0RVEY

U.NJ;.s

CIWNING MEASUREMENT OF LENGfH WITH TilE HELP OF A TAPE ERROR DUE TO INCORRECI' CHAJN. CHAINING ON UNEVEN OR SLOPING GROUND

ERRORS IN CHAlNING TAPE CORRECTIONS DEGREE OF ACCURACY IN CHAINING PRECISE UNEAR MEASUREMENTS

so so S4

60 70

CHAIN SURVEYING 8S

4.2.

CHAIN TRIANGULATION SURVEY STATIONS

4.3.

SURVEY LINES

"' I .___

21 22

ACCURACY AND ERRORS

RA..'IJG!t-;G

3.5. 3.6.

SCALE

CHARACI'ER OF WORK

ERRORS

2.4.

WRONG

SCALE

2.6.

2.3.

s .8 10

2..5.

2.2.

MAPS

GENERAL SOURCES OF ERRORS KINDS OF ERRORS TIIEORY OF PROBABILITY ACCURACY IN SURVEYING

2.1.

SURVEY

fl! - I:!

i SI

Contents

B.C. PUNMIA ASHOK K. JAIN ARUN K. JAIN

CHAYI'ER

FUNDAMENTAL DEFINITIONS AND CONCEPTS I

1.1.

SURV~YING : OBJECT

1.2.

PRIMARY

1.3. 1.4. 1.5.

CLASSIFiCATION PRINCIPLES OF SURVEYING UNITS OF MEASUREMENTS

1.6.

PLANS

1.7. 1.8. 1.9.

SCALES PLAIN SCALE DIAGONAL SCALE

1.10.

THE VERNIER

1.11.

MICROMETER

1.12 1.13

SCALE ERROR

1.14.

SHRUNK

1.15.

SURVEYING -

CIIAYI'ER

DIVISIONS

AND

12 18

MICROSCOPES

OF CHORDS DUE TO USE

19 OF

CHAPTER 3.1. 3.2. 3.3.

3.7. 3.8. 3.9.

3.10. 3.11.

~~~ 4.1.

COMPUI'ED

'1:1 '1:1 28 29 PERMISSmLE

ERROR

RESULTS

3()

LINEAR MEASUREMENTS 37 37 38 46

DIFFERENT METHODS DIRECT MEASUREMENTS INSTRUMENTS FOR CHAINING OL-;

S0RVEY

U.NJ;.s

CIWNING MEASUREMENT OF LENGfH WITH TilE HELP OF A TAPE ERROR DUE TO INCORRECI' CHAJN. CHAINING ON UNEVEN OR SLOPING GROUND

ERRORS IN CHAlNING TAPE CORRECTIONS DEGREE OF ACCURACY IN CHAINING PRECISE UNEAR MEASUREMENTS

so so S4

60 70

CHAIN SURVEYING 8S

4.2.

CHAIN TRIANGULATION SURVEY STATIONS

4.3.

SURVEY LINES

"' I .___

21 22

ACCURACY AND ERRORS

RA..'IJG!t-;G

3.5. 3.6.

SCALE

CHARACI'ER OF WORK

ERRORS

2.4.

WRONG

SCALE

2.6.

2.3.

s .8 10

2..5.

2.2.

MAPS

GENERAL SOURCES OF ERRORS KINDS OF ERRORS TIIEORY OF PROBABILITY ACCURACY IN SURVEYING

2.1.

SURVEY

XIII

_;{4 4.5.

LOCATING GROUND FEATURES : OFFSETS FIELD BOOK

4.6.

FIELD WORK

4.7. 4.8.

4.10.

4.11.

VCH APTE R

5.4.

THE

5.5.

S.6.

THE SURVEYOR'S COMPASS WILD 83 PRECISION COMPASS

5.1.

MAGNETIC

5.8.

LOCAL

/~R 6.1. 6.2.

6.3. 6.4.

6.l. {

6.6. 6.7.

6.8. 6.9.

CHAPTER

PRISMATIC

COMPASS

7.2.

CHAIN

7.5. 7.6. 7.7. 7.8.

7.9.

7.10. 7.11. 7.12.

CHAPTER 8.1.

8.2.

9.3. 9.4.

116

9.5. 9.6.

124

9.8.

!25

9.9.

142

OMITIED MEASUREMENTS

AND DEPARTURE CONSECUTIVE CO-ORDINATES : LATITUDE OMITfED MEASUREMENTS

144

9.18.

ISO ISS ll6

161

9.21.

METIIOD

162 162

164 16l 167

168 169

CONTOURING

-196 197 201

204 211

213 21l

216 216

222

226 230

233 23"? 238 240

244 2"48 2l2

257

10.2. 10.3. 10.4. IO.S.

CONTOUR INTERVAL CHARAcrERISTICS OF CONTOURS METHODS OF LOCATING CONTOURS INTERPOLATION OF COtiTOURS

10.6.

CONTOUR GRADIENT USES OF CONTOUR

10~7.

\.QHAPTER 11

172

11.2.

177

11.3.

183

244

10.1.

171

ISO

182

243

UE.i>it:RA.i..

11.1.

179

182

HYPSOMETRY

161

LEVELLING PRECISION

THE LEVEL TUBE SENSITIVENESS OF BUBBLE TIJBE BAROMETRIC LEVELLING

9.19. 9.20.

Ill

ERRORS DEGREE

9.17.

181 182

19l

9.11. ~ CURVATURE AND REFRAcriON 9.13. RECIPROCAL LEVELLING AL SECfiONJNG) 9.14. PROALE LEVELLING (LONGITUDIN 9.15. CROSS-SECTIONING 9.16. LEVELLING PROBLEMS

137

PROCEDURE

LEVELLING

DIFFERENTIAL LEVELLING HAND SIGNALS DURING OBSERVATIONS BOOKING AND REDUCING LEVELS BALANCING BACKSIGIITS AND FORESimiTS

'-)kf'(

141

TRAVERSING FREE OR LOOSE NEEDLE COMPASS TRAVERSING AND CHAIN TRAVERSING BY FAST NEEDLE METHOD ANGLES TRAVERSING BY DIRECT OBSERVATION OF TAPE AND IT TRANS WITH LS DETAI LOCATING CHECKS IN CLOSED TRAVERSE PLOTIING A TRAVERSE SURVEY LATmJDE AND DEPARTURE CONSECUTlVE CO-ORDINATES ERROR G CLOSIN BALANCING TilE TRAVERSE DEGREE OF ACCURACY IN TRAVERSING

_fl

137

THEODOLITE

TRAVERSE SURVEYING

!!'l'TP0!"!U':'T!0!'J'

7.3.

SURVEY

DEANIDONS METHODS OF LEVELLING LEVELLING INSTRUMENTS LEVELLING STAFF THE SURVEYING TELESCOPE TEMPORARY ADJUSTMENTS OF' A LEVEL ING) THEORY OF D!RECT LEVELLING (SPIRIT LEVEL

9.1.

133

THE ESSENTIALS OF THE TRANSIT DEFINITIONS AND TERMS TEMPORARY ADJUSTMENTS GENERAL S MEASUREMENT OF HORlZONTAL ANGLE S MEASUREMENT OF VERTICAL ANGLE OLITE MISCELLANEOUS OPERATIONS WITH THEOD RElATIONS D DESIRE AND LINES FUNDAMENTAL WORK OLITE TI!EOD IN ERROR OF SOURCES

109

127

GENERAL

8.7.

110

120

THE THEODOLITE

7.4.

COMPASS

DECUNATION IN

9S 98 100

8.l. 8.6.

118

ATTRACTION

ERRORS

8.4.

106

THE COMPASS

5.3.

5.2.

lOS

CROSS STAFF SURVEY PLO'ITING A CHAIN SURVEY

INTRODUCfiON BEAIUNGS AND ANGLES mE 'I'HEORY OF MAGNETIC COMPASS

5.1.

S INSTRUMENTS FOR SEITING OUT RIGJIT ANGLE ING CHAIN BASIC PROBLEMS IN OBSTACLES IN CHAINING

G CASE I ' BEARING. OR LENGTH, OR BEARIN ED OMIIT SIDE ONE AND LENGTH OF G OF ANOTF.HR SIDE OMmE D CASE D : LENGTH OF ONE SIDE AND BEARIN ED CASE m ' LENGTHS OF TWO SIDES OMIIT OMmE D CASE IV : BEARING OF TWO SIDES SIDES ARE NOT ADJACENT CASE II, m, IV : WHEN THE AFFECTED

8.3.

'-" 2S9 260 264 266 267

MAPS

PLANE TABLE-SURVEYING

271

ACCESSORIES GENERAL WORKING OPERATIONS PRECISE PLANE TABLE EQUIPMENT METHODS (SYSTEMS) OF PLANE TAD LING INTERSECTION (GRAPHIC TRIANGULATION)

273

TRAVERSING RESECITON

278

27S 27l

276

XIII

_;{4 4.5.

LOCATING GROUND FEATURES : OFFSETS FIELD BOOK

4.6.

FIELD WORK

4.7. 4.8.

4.10.

4.11.

VCH APTE R

5.4.

THE

5.5.

S.6.

THE SURVEYOR'S COMPASS WILD 83 PRECISION COMPASS

5.1.

MAGNETIC

5.8.

LOCAL

/~R 6.1. 6.2.

6.3. 6.4.

6.l. {

6.6. 6.7.

6.8. 6.9.

CHAPTER

PRISMATIC

COMPASS

7.2.

CHAIN

7.5. 7.6. 7.7. 7.8.

7.9.

7.10. 7.11. 7.12.

CHAPTER 8.1.

8.2.

9.3. 9.4.

116

9.5. 9.6.

124

9.8.

!25

9.9.

142

OMITIED MEASUREMENTS

AND DEPARTURE CONSECUTIVE CO-ORDINATES : LATITUDE OMITfED MEASUREMENTS

144

9.18.

ISO ISS ll6

161

9.21.

METIIOD

162 162

164 16l 167

168 169

CONTOURING

-196 197 201

204 211

213 21l

216 216

222

226 230

233 23"? 238 240

244 2"48 2l2

257

10.2. 10.3. 10.4. IO.S.

CONTOUR INTERVAL CHARAcrERISTICS OF CONTOURS METHODS OF LOCATING CONTOURS INTERPOLATION OF COtiTOURS

10.6.

CONTOUR GRADIENT USES OF CONTOUR

10~7.

\.QHAPTER 11

172

11.2.

177

11.3.

183

244

10.1.

171

ISO

182

243

UE.i>it:RA.i..

11.1.

179

182

HYPSOMETRY

161

LEVELLING PRECISION

THE LEVEL TUBE SENSITIVENESS OF BUBBLE TIJBE BAROMETRIC LEVELLING

9.19. 9.20.

Ill

ERRORS DEGREE

9.17.

181 182

19l

9.11. ~ CURVATURE AND REFRAcriON 9.13. RECIPROCAL LEVELLING AL SECfiONJNG) 9.14. PROALE LEVELLING (LONGITUDIN 9.15. CROSS-SECTIONING 9.16. LEVELLING PROBLEMS

137

PROCEDURE

LEVELLING

DIFFERENTIAL LEVELLING HAND SIGNALS DURING OBSERVATIONS BOOKING AND REDUCING LEVELS BALANCING BACKSIGIITS AND FORESimiTS

'-)kf'(

141

_fl

137

THEODOLITE

TRAVERSE SURVEYING

!!'l'TP0!"!U':'T!0!'J'

7.3.

SURVEY

DEANIDONS METHODS OF LEVELLING LEVELLING INSTRUMENTS LEVELLING STAFF THE SURVEYING TELESCOPE TEMPORARY ADJUSTMENTS OF' A LEVEL ING) THEORY OF D!RECT LEVELLING (SPIRIT LEVEL

9.1.

133

109

127

GENERAL

8.7.

110

120

THE THEODOLITE

7.4.

COMPASS

DECUNATION IN

9S 98 100

8.l. 8.6.

118

ATTRACTION

ERRORS

8.4.

106

THE COMPASS

5.3.

5.2.

lOS

CROSS STAFF SURVEY PLO'ITING A CHAIN SURVEY

INTRODUCfiON BEAIUNGS AND ANGLES mE 'I'HEORY OF MAGNETIC COMPASS

5.1.

S INSTRUMENTS FOR SEITING OUT RIGJIT ANGLE ING CHAIN BASIC PROBLEMS IN OBSTACLES IN CHAINING

8.3.

'-" 2S9 260 264 266 267

MAPS

PLANE TABLE-SURVEYING

271

ACCESSORIES GENERAL WORKING OPERATIONS PRECISE PLANE TABLE EQUIPMENT METHODS (SYSTEMS) OF PLANE TAD LING INTERSECTION (GRAPHIC TRIANGULATION)

273

TRAVERSING RESECITON

278

27S 27l

276

11.8.

THE

THREE-POINT

PROBLEM:- .

11.9 TWO POINT PROBLEM 11.10. ERRORS IN PLANE TABLING 11.11. ADVANTAGES AND DISADVANTAGES

r/CIIAPI'E R 12

""' 279

285

PLANE TABLING

CALCULATION OF AREA

12.1. 12.2.

GENERAL GENERAL METHODS OF DETERMINING AREAS 12.3. AREAS COMPIJTED BY SUB-OMSION IJ'IITO TRIANGLES ~ AREAS FROM OFFSETS TO A BASE LINE : OFFSETS AT REGULAR INTERVALS OFFSETS AT IRREGUlAR INTERVALS ~ AREA BY DOUBLE MERIDIAN DISTANCES 12.7. AREA BY CO-ORDINATES 12.8. AREA COMPUTED FROM MAP MEASUREMENTS

vz.5.

_/ -~--9.

AREA

._,.£HAYfER 13 13.1

PLANIMETER

.JYI'/

TRAPEZOIDAL FORMULA (AVERAGE END AREA THE PRISMOIDAL CORRECTION THE CURVATURE CORRECTION VOLUME FROM SPOT LEVELS VOLUME FROM CONTOUR PLAN

__!)1

FIG. 3.27. IIYPOTENUSAL ALLOWANCE.

Thus,

BA = 100 sec 9 links BA' = 100 links

Hence

AA' = 100 see e- 100 links = 100 (sec

Now sec 9=1+2+24+ ..... . (were h

Tfh:

FIG. 3.26 Method 3. Hypoteousal allowance chain length and at every ar field the In this method, a correction is applied in the intermediate surveying or locating in facilitates This changes. slope the every point where pr-int!i Vlhen the chain is strerched on th~ slope, the A arrow is not put at the end of the chain but is placed in advance of the end, by of an amount which allows for the slope correction. In Fig. 3.27, BA' is one chain length on slope. The arrow is not put at A' but is put at A, the distance AA • being of such magnirude that the tl{ '''f'Jh...a ..J horizontal equivalent of BA is equal to 1 chain . The distance AA' is sometimes called lzypotenusal allowmzr.e.

e' se•

14----D,-->j

FIG. 3.24.

LINEAR MEASUREMENTS

e- I)

(3.5)

links 2 ··.

e ' . . d" l . 1 "~"2! e IsmraJaDI::ll_

SURVEYING

AA'= 100 ( I +2-!Jiinks AA' =50 9' links If. however. 8 is in degrees, we have

AA'=~O'

100

Thus. if

2 - I ]links ~9 • 10.000 ... (3.5 b).

in n. meaning

0 =.!. radians n AA'

=50 a'= 50 ,,;

... 13.5 c)

Thus. if !he slope is I in 10, ~)~

The distance M' is ao allowance ;vhich must be made for each chain lenglb measured on !he slope. As each chain lenglb is measured on !he slope. !he arrow is set forward by .. Ibis amount. In !he record book, !he horizontal distance between 8 and A is directly recorded as I chain. Thus, !he slope is allowed for as !he work proceeds. Example 3.7. TilE distance between the points measured along a slope is 428 m. Final the lwriwntal distance bern~en them if (a) tiJe angle of slope benveen the points is 8 •. (b) the difference in level is 62 m (c) tile slope is 1 in 4 .

Solution. Let . (a)

(b)

I It

Hypotenusal allowance (il) Slope is 4 min 20m Hence from Eq. 3.5 (c),

~1'-h'=..j (428)2 -

tan 9 =.!.4 = 0.25

L =I cos 9 = 428 cos 14' 2' = 415.Z3 m. Example 3.8. Find the hypotenusal allowance per chain of 20 m --g

... (3.24)

Solution. Volume of tape per metre run = 0.08 x 100 = 8 em' Weight of the tape per metre run= 8 x 0.078 = 0.624 N :. Total weight of the tape suspended between two supports = W = 8 x 0.078 x 10 = 6.24 N ,-_

~~uw

~..:orrecnon

2 '1f:(•P!.) 1 r:!!W 2 3 ~- J0 Y (6.2!") -. = 0.004H7 m. - -2 = = or sag= Ls = - - 24 (100)2 24 P 24 P2

Example 3.12. A steel tape 20 m long standardised at 55' F with a pull of 10 kg was used for measuring a base line. Find the correction per tape length. if the temperature ar the time of measurement was 80 'F and the pull exened was I6 kg. Weight of I cubic em of steel = 7.86 g, Wt. of rape= 0.8 kg and E = 2.I09 x IO' kg/em'. Coefficient of expansion of tape per I'F=6.2xio-•. Solution. Correction for temperature= 20 x 6.2 x 10 - 6(80 - 55) = 0.0031 m {additive) (P- Po)L . AE Correcuon for pull3 Now, weight of tape= A (20 x 100)(7 .86 x 10- ) kg = 0.8 kg (given) 8 A= _°6 x = .0.051 sq. em 78 2

. 'I'

[ ,,

1_'1

' :il :11

:I 1

I ,

"'i·.I !1

:'I

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II" ~! •ii,,6

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I 'I

I I

II !r

SURVEYING

Then

UNEAR MEASUREMENTS

A tape 20m long of standard length a1 84 'F was used to measure a line, the mean temperature during measurement being 65°. The measured distance was 882.10 metres, the following being the slopes : for IOO m 2 ' 10' for I 50 m 4'12' for 50 m I ' 6' for 200 m 7' 48' for 300 m 3'0' for 82.10 m 5 ' 10' of expansion is 65 X 10- 'per I' F. co-efficient the if line the Find the true length of

L D 9=-=--

Example 3.10.

R+h

Lh h =L-R h )-' =C ( I-R ( I+R R D=L R+h=L

:. Correction (Cm,,) = L- D = ~h (subtractive)

8. Correction to measurement in vertical plane Some-times, as in case of measurements in mining shafts, it is required to make measurements in vertical plane, by suspending a metal tape vertically. When a metal tape AB, of length I, is freely suspended vertically, it will lengthen by value s due to gravitational pull on the mass ml of the tape. In other words, the tape will be subjected to a tensile force, the value of which will be zero at bcttom point (B) of the tape, and maximum value of mgl at the fixed point A, where m is the mass of the tape per unit length. Let a mass M be attached to the tape at its lower end B. Consider a section C, distant x from the fixed point A. It we consider a small length Bx of the tape, its small increment Ss.f in length is given by Hooke's law p (8x) OSx=AE , where P =pull at point C, the

value of which is given by,

... (3.22)

Solution. Correction for temperature of the whole length = C, 7 =La (Tm ~To)= 882.1 X 65 X 10- (65- 84) = 0.109 m (Subtractive) Correction for slope= J:/(1 - cos 9) = !00 (I -cos 2' 10') + !50 (I -cos 4' 12') +50 (I -cos I' 6') + 200 (I -cos 7' 48') + 300 (I - cos 3') + 82.10 (I - cos 5' 10') = 0.071 + 0.403 + 0.009 + 1.850 + 0.411 + 0.334 = 3.078 (m) (subtractive) Total correction= 0.109 + 3.078 = 3.187 (subtractive) :. Corrected length= 882.1- 3.187 = 878.913 m.

"+1' 1

B..,

Mass M

FIG. 3.35

Example 3.11. (SI Units). Calculflte the sag correction for a 30 m steel under a pull of IOO N in three equal spans of 10 m each. Weight of one cubic em of steel =0.078 N. Area of cross-section of tape =0.08 sq. em.

P=Mg +mg (1-x) Substituting this value, we get I os, -mgx AE-=Mg+mg ox

mor 2

Integrating, AE s, = Mg x + mglx - "-'=- + C 2 Whot:-n r.,... n :!!"!~ ~ ,... " ~ril::? -,,:::: t.:.·. _ ,. .

s,=~ [M +-2 m (21-x)]

... (3.23 a)

s=~[ M+~]

... (3.23 b)

lfx=l, When M=O,

_ mgl 2 S-

... (3.23)

2AE

Taking into account the standardisation tension factor, a negative exrensi~n must be 'allowed ,initially a< the tape is not tensioned up to standard tension or pull {P0).

Thus,

the general equation for precise measuremems is

gx[ M+ t m(21 s,= AE 2 See example 3.19 for illustration.

Po] -x>--g

... (3.24)

~~uw

~..:orrecnon

2 '1f:(•P!.) 1 r:!!W 2 3 ~- J0 Y (6.2!") -. = 0.004H7 m. - -2 = = or sag= Ls = - - 24 (100)2 24 P 24 P2

. 'I'

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UNEAR MEASUREMENTS

SURVEYING

20 = 0.00112 (additive) Hence, 0.05! X 2.JQ9 X 106 2 ' 20 Correction for sag= l,(wl,y = 1 is thus continued till a a'~ of length ''" (IQ' X 5 + 5 X 6") =52' 6" '' '' '' is .measured at a time with ' '\ : the help of 5 bars and teel b1 !!.fR=ib•' 2 frameworks. The work is thus continued till the end of the base is reached.

3. 4. .

A steel tape for spacing the tripods or stakes. Six thermometers : four for measuring the temP.,ature of the field and two for standardising the four thermometers. A sensitive and accurate spring balance.

The F1eld Work The field work for the measurement of base line is carried out by two parties (I) The setting ow pany consisting of two surveyors and a number of porters, have the duty to place the measuring tripods in alignment in advance of the measurement, and

l ·"imetallic thermometer. Example : The Eimbeck Duplex Apparatus (U.S. Coast and Geodetic Survey), Borda's Rod (French system) and Bessel's Apparatus (German system). (iir) Monometallic base bars, in which the temperature is either kept constant at melting point of ice, or is otherwise ascertained. Example : The Woodward Iced Bar Apparatus and Struve's Bar (Russian system). The Colby Apparntus (Fig. 3.36). This is compensating and optical type rigid bar apparatus designed by Maj-Gen. Colby to eliminate the effect of changes of temperature upon the measuring appliance. The apparatus was employed in the Ordinance Survey and the Indian Surveys. All the ten bases of G.T. Survey of India were measured with Colby Apparatus. The apparatus (Fig. 3.36) consistS of two bars, one of steel and the other of brass, each 10 ft. long and riveted together at the centre of their length. The ratio of co-efficientS of linear expansion of these metals baving been determined as 3 : 5. Near each end of the compound bar, a metal tongue is supported by double conical pivotS held in forked ends of the bars. The tongue projectS on the side away from the brass rod. On the extremities of these tongues, two minute marks q and a' are put, the distance between them being exactly equal to 10' 0". The distance ab (or (a' b') to the junction with the steel is kept ~ ths of distance ac (or a' c') to the brass junction. Due to cbange in temperature, if the distance bb' of steel change to b, b,' by an amount x, the distance cc' of brass will change to c1c,' by an amount ~ x, thus unahen'ng the positions of dots a and a'. The brass is coated with a special preparation in order to render it equally susceptible to change of temperature as the steel. The compound bar is held in the box at the middle of itS length. A spirit level is also placed on the bar. In India, five compound bars were simultaneously employed in the field. The gap between the forward mark of one bar and the rear bar of the next was kept .constant equal to 6" by means of a framework based on the same principles as that of the 10' compound bar. The framework consists of two microscopes, the distance between the cross-wires of which was kept exactly equal to 6". To stan with. the cross-wires of the first microscope of the framework was brought (il)

;!"....., !:'"~!1~~1e~':'~

•.·.. :~~ the

plarlr,~~

':!0!, ~"'~ lr:~c

the centre cf the ::me

e~treT.ity

l")f the

base line. The platinum dot a of the first compound bar was brought into the coincidence

with the cross-hairs of second microscope. The cross-hairs of the first microscope of the second framework (consisting two microscopes 6" apan) is then set over the end a' of the first rod. The work 14----- --to·o·- ------> 1 is thus continued till a a'~ of length ''" (IQ' X 5 + 5 X 6") =52' 6" '' '' '' is .measured at a time with ' '\ : the help of 5 bars and teel b1 !!.fR=ib•' 2 frameworks. The work is thus continued till the end of the base is reached.

3. 4. .

l ·"llfed, the bearings of the lines can be calculated provided the bearing of

one line is also measured. Referring to Fig. 5.7, let a..~.y.li, be ~.included angles measured clockwise from back srations and 9 1 be lhe measured. bearing of the line

AB.

---M-

./"I ""'-

hJ_/e,

FIG. 5.7. CALCULATION OF BEARINGS FROM ANGLES.

~I'

CALCULATION OF ANGLES FROM BEARINGS Knowing the bearing of two lines, the angle between the two can very easily be calculated with the help of a diagram, Ref. to Fig. 5.5 (a), the in cludc;d angle a. between the lines c· ACandAB = e,- 9 1 = F.B. of one A, line- F.B. of the other line, both bearings being measured from a common point A, Ref. to Fig. c angle the (b) (b), 5. 5 (a) a= (180' +-e,}- e, =B. B. of BEARINGS. FROM FIG. 5.5 CALCULATION OF ANGLES previous line- F.B. of next line. Let us consider the quadrantal bearing. Referring to Fig. 5.6 (a) in which both the bearings have been measured to the same side of common meridian, the included angle a.= e,- e,. In Fig. 5.6 (b), both the bearings have been measured to the opposite sides

Similarly, referring to Fig. 5.2, the conversion of R.B. into W.C.B. can be expressed int the following Table ··; TABLE 5.2. CONVERSION OF R.B. INTO W.C.B. line

AC AD

I I

AFj

Rule for W.C.B.

R.B.

•

W.C.B. between

0° and 90°

NaE

W.C.B. = R.B.

S~ E

W.C.B. = 180°- R.B.

90" and 180°

saw

W .C. B.

=180° + R.B.

180° and 270°

NoW

W.C.B. = 360'- R.B.

270° and 360°

FORE AND BACK BEARING The bearing of line, whether expressed in W.C.B. sySiem or in Q.B. system, differs according as the observation is made from. one end of the line or from the other. If the bearing of a line AB is measured from A towards B. it is known as forward bearl;:;-g A, or Fore Bearing (f. B). It the bearmg of the line Ali is measured from B towards bacKward in measured is it smce itls kiiown as backward bearing or Back Bearing (B.B.), " direction. Considering first the W.C.B. system and referring to Fig. 5.3 (a}, the back bearing of line AB is $ and fore bearing of AB is e . Evidently $ = 180 • +e. Simi(b) (a) larly, from Fig. 5.3 (b), the back bearing fore and $ is CD of bearing FIG. 5.3 FORE AND BACK BEARINGS. e. hence. $ = e- 180 '. Thus, in general, it can be stated that B. B.= F.b. :r: idu~, usmg ptus sign when r.D. 1s u:,),) wur1 JbV uiid itWU4,J .J'O" rvii.C.i1

F.IJ. is greater than 18{)

•

ond E for W ond vice versa, the numerical value of the bearing remaining the same.

l· .·-1-.

...

(a)

(b)

FIG. 5.4. FORE AND BACK BEARINGS.

c '

(d)

FIG. 5.6 CALCULATION OF ANGLES FROM BEARINGS.

::·t:

¥ '•

(o)

(b)

1•1

•

Again, considering the Q.B.· system and referring to Fig. 5.4 (a), the fore bearing of line AB is NeE and, therefore, the back bearing is equal to sew. Similarly. from Fig. 5.4 (b), the fore bearing of the line CD is sew and back bearing is equal to NeE. Thus, it con be srated thar ro conven the fore bearing to back bearing, it is only necessary to change the cardinal poinrs by substituting N for S,

~·

•

113

TilE COMPASS

SURVEYING

112

of. the common meridian, and included angle a.= e, + 92 • In Fig. 5.6 (c) both the bearings angle have been measured to the same side of different meridi~ns and the included ·~ ... .... - .. .:..v

\."'2 ' "IJ•

......... 'b'

.. '..

.... ~

,_,,

. .. •-------c- --· --··· --------•--

-------~..>

~~-

TP·-:-~fr('

sides of differet!l meridians, and angle a.= 180 •- (e, - 9,). CALCULATION OF BEARINGS FROM ANGLES In the case of a traverse in which incLuded angles between successive lines have any been mea>llfed, the bearings of the lines can be calculated provided the bearing of

one line is also measured. Referring to Fig. 5.7, let a..~.y.li, be ~.included angles measured clockwise from back srations and 9 1 be lhe measured. bearing of the line

AB.

---M-

./"I ""'-

hJ_/e,

FIG. 5.7. CALCULATION OF BEARINGS FROM ANGLES.

ll4

SURVEYING

The bearing of the next line BC = e, = e, + a - 180' ... (1) The bearing of the next line CD = a, = a, + ~ - 180' ... (2) The bearing of the next line DE= a, = a, + y - 180' ... (3) The bearing of the next line EF =a,= e, + 1i + 180' ... (4) As is evident from Fig. 5.7, (a,+ a), (a,+~). and (a,+ y) are more than !80' while (a,+ li) is Jess than 180'. Hence in order to calculate the bearing of the next line, the following statement can be made : "Add the measured clockwise angles to the bearing of the previous line. If the sum is more than 180°1 deduct 180°. If the sum is less than 180°, add 180° ". In a closed traverse, clockwise angles will be obtained if we proceed round the traverse in the anti-clockwise direction. E~LES ON ANGLES AND BEARINGS c.A(xample 5.1. (a) Convert the following whole circle bearings to quadrantal bearings: (i) 22' 30' (ir) 1700 12' (iir) 211' 54' (iv) 327' 24'. (b) Convert the following quadrantal bearing to whole circle bearings : (i)Nl2'24'E (ir)S31'36'E (ii1)S68'6'W (iv)N5'42'W . Solution. (a) Ref. 10 Fig. 5.1 and Table 5.1 we have (1) R.B.= W.C.B. = 22' 30' = N 22' 30' E. (ir) R.B.= 180'- W. C. B . = 180'-170' 12' = S 9' 48' E. (iii) R.B.= W. C. B.- 180' = 211' 54 -180' = S 31' 54' W. (iv) R.B.= 360'- W.C.B. = 360'- 327' 24' = N 32' 36' W. (b) Ref. 10 Fig. 5.2 and Table 5.5 we have (1) W.C.B.= R.B.= 12' 24' (ir) W.C.B.= 180'- R.B.= 180'- 31' 36' = 148' 24' (iir) W.C.B.= 180' + R.B.= !80' + 68' 6' = 248' 6' (iv)/ W.C.B.= 360'- R.B. = 3UO'- 5' 42' = 354' 18' _;EXample 5.2. The following are observed fore-bearings of the lines (1) AB 12' 24' (ii) BC 119' 48' (iir) CD 266' 30' (iv) DE 354' 18' (v) PQ N 18' 0' E (vi) QR Sl2' 24' E (vii) RSS59' 18'W (viii) ST N86' 12'W. Find their back bearings. Solution : 8.8.= F. B.± 180', using+ sign when F.B. is Jess than 180' ,and- sign when it is more than 180°. (r) B.B. of AB = 12' 24' + !80' = 192' 24'. (ii) B.B. of BC = 119' 48' + 180' = 299' 48' (iii) B. B. of CD= 266' 30'- 180' = 86' 30' (iv) B.B. of DE= 354' 18' - 180' = 174' 18' (v) B.B. of PQ =S 18' 0' W fvl) B. B. of QR = N 12' 24' W (vii) B.B. of RS = N 59' 18' E (viii) B.B. of ST = S 86' 12" E

115

THE COMPASS

Axample 5.3. The following bearings were observed with a compass. Calculale the

interior angles. Fore Bearing Line 60' 30' AB 122' 0' BC 46° 0' CD 205' 30' DE 300" 0'. EA Solution. Fig. 5.8 shows the plotted traverse. .. ,122°0'

~...'205°30'

\,Jj/ FIG. 5.8.

Included angle = Bearing of previous line- Bearing of next line LA = Bearing of AE - Bearing of AB = (300' - 180')- 60' 30' = 59' 30'' /D

. 0".,,.;..,,..

,....~

-q.,. .... ;..,., ,..,; rJr

= (60' 30' + 180')- 122' = ll8' 30'. L C = Bearing of CB - Bearing of CD

= (122' + 180')- 46' = 256' LD = Bearing of DC - Bearing of DE = (46' + 180') - 205' 30' = 20' 30'. LE = Bearing of ED - Bearing of EA = (205' 30' - 180') - 300'+ 360' = 85' 30' Sum = 540' 00'.

Check :

(2n - 4) 90' = (10 - 4) 90' = 540'.

~xam.ple 5.4. The following interior angles were measured with a se.aanr in a closed traverse. The bearing of the line AB was measured as 60° 00' with prismaJic compass.

ll4

SURVEYING

115

THE COMPASS

Axample 5.3. The following bearings were observed with a compass. Calculale the

interior angles. Fore Bearing Line 60' 30' AB 122' 0' BC 46° 0' CD 205' 30' DE 300" 0'. EA Solution. Fig. 5.8 shows the plotted traverse. .. ,122°0'

~...'205°30'

\,Jj/ FIG. 5.8.

Included angle = Bearing of previous line- Bearing of next line LA = Bearing of AE - Bearing of AB = (300' - 180')- 60' 30' = 59' 30'' /D

. 0".,,.;..,,..

,....~

-q.,. .... ;..,., ,..,; rJr

= (60' 30' + 180')- 122' = ll8' 30'. L C = Bearing of CB - Bearing of CD

= (122' + 180')- 46' = 256' LD = Bearing of DC - Bearing of DE = (46' + 180') - 205' 30' = 20' 30'. LE = Bearing of ED - Bearing of EA = (205' 30' - 180') - 300'+ 360' = 85' 30' Sum = 540' 00'.

Check :

(2n - 4) 90' = (10 - 4) 90' = 540'.

~xam.ple 5.4. The following interior angles were measured with a se.aanr in a closed traverse. The bearing of the line AB was measured as 60° 00' with prismaJic compass.

117

THE COMPASS

SURVEYING

116

Calculate the bearings of all other line LD ~ 69' 20~ Solution. Fig. 5.9 shows the plotted ttaverse. To fmd the bearing of a line, add the measured clockwise angle to the bearing of the previous line. If the sum is more than 180', deduct 180'. If the sum is less than 180', add 180'. Clockwise angles will he obtained

if we proceed in the anticlockwise direction round the traverse. Starting with A and proceeding to-

if LA ~ 140' 10'; LB ~ 99' 8';

(l) Surveyor's compass (2) Prismatic compass (3) Transit or Level Compass. Earth 's Magnetic Field and Dip

. "' 0 J:/)., 9o ' 0' to 360' with zero at vernier C. For angle of elevation wilh (b) (a) face left, vernier C reads GRADUATION. CIRCLE VERTICAL OF FIG. 6.11. EXAMPLES 30' while D reads 210' . In !his system, therefore, 180' are to be deducted from vernier D to get the correct reading. However, it is always advisable to talte full reading (i.e., degrees, minutes and seconds) on one vernier and pan reading (i.e., minutes and seconds) of the other.

corrected values for !he first set. Several such sets may be taken by setting !he initial angle on !he vernier to different values. The number of sets (or positions, as is sometimes called) depends on !he accuracy required. For first order triangulation, sixteen such sets are required with a !" direction lheodolite, while for second order triangulation, four and for third order triangulation two.

I i

!he horizontal. It may be an angle of elevation or angle of depression depending upon wbelher !he object is above or below the horiwntal plane passing through the trunnion axis of the instrument. To measure a vertical angle, the instrument should be levelled with reference to !he altitude bubble. When the altitude bubble is on the index frame, proceed

as follows :

&oB&> .......

(!) Level the instrument wilh reference to !he plate level, as already explained.

I 0

angle of elevation as positive

circle is moved with telescope, it is easy to see how the readings are taken.

ANGLES

----·

Fate: Ri•ht

] ~

Angle

Mean

. . .. .

•

4(l

Vertical Angle

Average Vertical

Angle

.. ..

12 20 -5 12 30 00 40 +2 25 so 7 38 20 7 38 25 +2 26 00

-5 12

A -5 12 20 12 00 -5 12 10 25 20 +2 25 30 7 37

.. . .•

4(l

Mean

4(l

6.7. MISCELLANEOUS OPERATIONS WITH THEODOLITE 1. TO MEASURE MAGNETIC BEARING OF A LINE In order to measure !he magnetic bearing of a line, the thendolite should be provided wilh eilher a tubular compass or trough compass. The following are the steps (Fig. 6.12):

these operalions.

the algebraic difference betWeen the cwo readings taking

B +2 25

!he vertical circle. Similar observation may be made wilh anolher face. The average of !he two will give the required angle. Note. It is assumed that the altitude level is in adjustmenl and that index error has been eliminaled by permanenl adjristmems. The clip screw shauld nat be touched during

•

Vertical

the object. Use vertical circle tangent screw .for accurate bisection. (4) Read both verniers (i.e. C and D) of vertical circle. The mean of the two gives

and angle of depression as negative. Table 6.4 illustrates the melhod of recording the ·observations. Graduations on Vertical Circle Fig. 6.11 shows two examples of vertical circle graduations. In Fig. 6.1l.(a). the circle has been divided into four quadrants. Remembering !hat !he vernier is fixed while

... ~

Fate:un

(2) Keep !he altitude level parallel to any two foot screws and bring the bubble central. Rotate !he telescope through 90' till the altitude bubble is on the third screw. Bring !he bubble to !he centre with !he third food screw. Repeat the procedure till !he bubble is central in both !he positions. If !he bubble is in adjustment it will remain central for all paintings of !he telescope. (3) Loose !he vertical circle clamp and rotate the telescope in vertical plane to sight

In some instruments, the altitude bubble is provided both on index frame as well as on the telescope. Tn such c~H~~-~, the !n~tn~m

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References