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THE RELATIVE EFFICIENCY OF LAND-SURVEYING METHODS

BY

Martin Francis Conneli^y

THESISFOR THE

degree of

Bachelor of Sc ience

IN

CIVIL KNOINEERING

IN THE

COLLEGE OF ENGINEERING

UNIVERSITY OF ILLINOIS

1911

UlTIVERSITY OF ILLINOIS

May 25, 1911

I recorriiDenci tnat the thesis prepared unaer my supervision

by MARTIN FRANCIS CONNELLY entitled The Relative Efficiency of

Land-Surveylng Methods be approved as fulfilling this part of the

reiiuirements for the degree of Bachelor of Science in Civil Engi-

neering.

Recommendation approved:

Head of the Department of Civil Engineering*

1975S1

o

C IT T E K T; S

INTRODUCTION

1. TRAVERSE !ffiTHOD

DISCUSSION

EZAIIPLES. FIELD NOTES. COIiPUTATIONS.

2. RjlDIATION IIETHOD

DISCUSSION

EZAIvIPLES. FIELD NOTES. COI^IPUTATIONS.

3. INTERSECTION liEETHOD

DISCUSSION

4. CONCLUSION

Digitized by the Internet Archive

in 2013

http://archive.org/details/relativeefficienOOconn

1

IITTROL'UGTIOiL

7/hen called upon uo survey a farrn. the majority of

surveyors v/ill from force of habit use the traverse method.

Seldor;,if ever, do uhey even consider the advantages to ho gained,

both in the field and in the off ice. by the use of some other method.

'vVhen asked for reasons for the use of the traverse method they ansv:er

triat it is the only practical one; else v/hy would it be used in

preference to all others? But does the mere fact that it is very

V7idely, perhaps almost alv:ays , used in making farm surveys prove

that it is the most efficient method? If it is not the best, vzhafc

is?

The only v;ay to furnish conclusive evidence as to the

efficiency of any method is to compare it v;ith others, employing

each under practically similar conditions . w'ith this in viev/ two

fields, one containing about oG acres, anc^ the othor about 200 acres,

77ere chosen and surveyed by both the traverse and radiation methods.

T:.e intersection method is not loractical for farm surveying hence

it is not included in this comparison, although it can be used

occaoionally and is more accurate than the other methods. Conclusions

'.vere based upon the time taken for each successive step for esidh

method, the num.ber of steps required , and the accuracy of the work.

2

t:-is relative eltigieicy o? laitd^sltrveyiiig methods.

~Tien a large tract of land is to be subdivided into

smaller farms, or v/hen the area of a farm is desired the services

of a surveyor are required. He may employ any number of methods to

make the survey but the lollov/ing are the three principal ones now

used and these only 7/ill be discussed, - ey ar- ;

1, The Traverse liethod,

2, The Radiation Llethod.

3, The Intersection method.

The t -"averse and radiation methods are used more often

ir farm surveying? than the intersection method, and hence 7/ill be

more fully discussed. Surveys oi tro "ields ';7ere made by

each of these methods and repeated, in order to check the accuracy

of the v;ork and the time used for the different operations. Because

of the infrequent use of the intersection method, no surveys v/ere

made by it, Jor a small fari.!, hovrever, of thirty or forty acres,

v;here the base line is entirely within the field it is a ver;/ good

method to use. The method most widely used is the traverse and it

will receive first discussion,

1, TRAVERSE :iET-10D.

The principal method now in use xor ob'^aining the area

of a field is the Traverse :..ethod. This consists of reading the

angles formed ^^y the sides of the far.-:;, measuring the sides, and from

these jomputing the area.

3

The different steps taken in this survey are ; (1) drivinp: stakes at

each corner of the field, (2) making offsets, (3) setting up trans-

it, (4) placing flagpoles at corners adjacent to set-ups, (5)

reading interior angles, and (6) computing the content.

The old corners should he located if possible. If not

nev/ ones r;:ust he estahlislied hy driving stakes in each corner of the

field. Offsets large enough to clear an;/ obstruction tc t -e line

of sight should be taken. The driving of stakes for these offsets

take up considerable time and tends to decrease the efficiency of

this method. Having established the corners and offset stakes,

the transit is set up at each hub and sights taken on the flagpoles

on the adjacent corners. The interior angles are read tv/ice as

a check and the mean taken as the required angles. VThen each side

has been chained the field v/ork is comnleted and the notes are ready

for the office. The area is then computed by the method of

latitudes and departures.

The first field under consideration is a five-sided

farm of about 80 acres and typifies the average farm. The time taken

for each operation, i.e., driving stakes, chaining, setting up

instrument, and making computations, '.vas taken and recorded in the

field 01 office.

Stakes were driven at each of the five corners and suit-

able offsets taken as shovzs in Fig, 1. The poles v;ere set up at each

offset stake and the inferior angles read, the mean of tlie two

readings being taken as the required angle. Five transit stations

were required, one over each offset stake. Jpon the completion

SURVEY OF FELD BY TRAl/FRSF MFThOD.3ta. I

Sra.3

Fig. /

STAT/ONOCCUPJED

STAT/ONS/O/iT^D

DOUBLE.ANGLE

.. . .

ANGLE D/STANCEFEET Notes

/ S March //, /9JI

Z /

i7a''Zz:-oo" S9-//''00" /W.FConne//y .- Insf^

F. /</Fche.r- - Rod.3 /ai"- 3&'-oo" /(b03. 3 Tennj:?.

W/nc/y, c/ouc/y3 &

^ 179'-0(b'- OO" 8e''-35'-oo Z<o/b.4-

3s S.(35°-4S.'-00" /3^-S/'-Oo" /SOV.^

/ a7S°- 18 - 00'/37-33-od /33.3

Check 8^''-//'-oo"

Tata/ ^4 O* - OO- OO

5

of the instrtunent work, the sides of the field were measured, re-

corded, and the area computed,

as follows :-

The time spent in the field was

Date

Uar. 3, 1911

Kind of Work

Offset stakes

Instrument

Chaining

Time of Day Hours

10:35-11:40 1-05

1:55- 4:00 £-05

1:00- 5:40 1-40

Total Time

4hrs,-50 min.

The same method of procedure was used in the second

survey of this field. In this case the ground had heen recently

plowed, which fact made the chaining more difficult. The time taken

was as follows :-

Date

Uar. 11, 1911

Kind of Work

offset stakes

Instrument

Chaining

Time of Day

10:30-11:30

l:E5-3:25

3:35-5:05

Hours Total Time

1-00

2-00

1-40

4 hrs,-40 min.

The second field contained ah out 200 acres and was sur-

veyed in the same manner as the first one with one exception, A

small knoll on the south side of the field so obstructed the line of

sight as to make one additional set-up necessary. This was made on

top of the knoll as shown in Fig, 2, The time taken for this survey

was as follows:-

6

F/G. ZSURVEY OFF/ELD BF TF/iVEF^F MEFFOD.

A

E

Sca/e /i'/7= /ooo^.

STAT/OAJCCCUP/EP 5/GHre.o AA/<5JLE.

AA/0J.£

A

O

£

C

B

D

ET

cEBC

/!

33- oo"

/r9- 33 -00

89- /6,'-ao'

3///. 6

^f.F:'Ce>/^/^<s//y Rat/.

a/r Jbi;/'//'/7^. 7e/n^ 7S'

3aS3'- /6'-3o"

/ 33 '-"

^/^ - yg'- oo"

7

COMPUTATIONS FOR AREA OFR/ELD Qpj

A-3

/oo. /at

/&o3.3

8. /S'3 9oy

/o^. c^e.^. 3.^0 ^9 T/

departctre. /60 3.

'5 oo'-oSW

o.aooa o

/S'07. /39. 8S'

3. /rsz^a

/3. /S"

9^0a '^7 ^9 39S3a. 36'8ss/ 3. / yy^ //

4?. /^3-<i> & ^^.SCSC To0/^33 /5

/03 .3^

/? /^6'6& ^

' A 37^^/0 /

Noo- oo£.

0.00 -/-^. 7S

1

8

® @ @

^.^6S.S(>S S.'^^^^if/Arsa =- /83/8 Area = ^^gy Ar7sa^'^8 9r

@ ©• ©

/a^./atr ^ /a^ /at =/.//? 070 /a^ /at =J-'^/yro^-Z^^.c/ejo- = /."^ 74-/ o I /o^ dsjC?. ^AT7j±^o/_ /o^. ^(p. ^ 3. ^a4-9 7/

3,^&7'=^o3 3.092/77 <;>.L^Z^7S~AheCi ^dG>^ Area ^ /^J^ Area =

= ^ . S^. /¥:

^ €>(^. AS'J acres.

9

Date Zind of '7ork Time of Day Hours TotallUne

-lay 29,1011 Offsets 9:00-11:00 £-00

Inst.

Chaining 3.45-6:15 2-30

7 ]irs.-45 min

The above fields are fair representations of the averaf^e

farm and rIyo an idea of the work required to get the areas by tlE

traverse method. The principal objections to this method are that

the surveyor as no check or. himself untJl the entire survey is

completed, the time taken for the numerous set-ups and the dis-

tances that must be chained. This objection increases V7hen the

field to le i-<urveyed is of a sv/ampy or marshy nature.

10

E- -^ADIATIOII IIETMCD.

Although not in v/ide use at present, the applicahility

of the radiation method to farm surveying renders it valuable to

the surveyor. In a field of small area or v/here the corners are

all visible from one point,only one set-up is necessary. In a

long narrov/ field tv70 transit-points, or three at the mo^:^ , are

required, shov7ing the marked advantage of this method over any

other. The chaining is greatly reduced, since only the radiating

lines need to be measured. In making a survey v/ith the radiation

method the steps ts-ken are:- (1) S3tting corner stakes, (2) driving

hubs for transit, (3) setuing flag-poles at each corner, (4) reading

the angles, (5) chaining distances from transit point to corners

of field, and (6) computing the area.

The corner stakes are driven at each corner of the field

and at such points as m.ay be chosen for transit points. Flag-poles

are set behind each corner stake, and sometimes at intermediate

points in the boundary line , and a sight taken on each to obtain the

angle between the lines radiating from the transit-point to the

corners. The sum of the angles around each transit-point should

be equal to 360? These lines are then measured and the area of

each triangle computed by the f orraula , Area- -|- b c sdn A.

T/hen tv;o transit-points are required, flag-polos may be

placed in each corner of the field and at points in the boundary

lines, can readily be seen from the transit-point as shov/n in _ig.

F/G. 3.

In case point 2 can not be seen from 1, flag-poles are

placed at points B and E, in the boundary lines of the field. With

the transit set over 1, the angles about that transit-point and the

lines, A-1, B-1, E-1, and F-1 are measured. This operation is re-

peated using E, as a transit-point. The entire area is then com-

puted. Or in case 2 can be seen from 1, flag-poles are placed at

A, 1, and P, and the angles around 1, measured. With 2 as a transit

point and flags at 1, G, and D this operation is repeated so as to

obtain the angles around 2, The only lines rov^uired to be measured

are A-1, F-1, 1-2, 2-G, and 2-D. This greatly reduces the chaining

and makes the accurac3^ of the survey dependent upon the angular

measurements. Since the transit man has a checl: upon the angles

around any point, and since angular measurement is m.ore accurate

than linear measurement, greater accuracy may be obtained with the

radiation method than ?;ith the traverse method.

For sake of comparison, the same fields 7/ere taken, as

v/ere used for the traverse method. The first, a five-sided field

of about 80 acres was surveyed under conditions similar to those

existing at the time the traverse was made. Two positions for

12

transit-points were chosen as shown in Pig. 4. Stakes v/ere driven

at each of these positions and at each corner of the field* V/ith

the transit at the north transit-point and flag poles at the northat the

corners of the field and^ couth hub, sights were taken to obtain

the angles between the lines radiating from the transit-points to

the flag-poles. Throe readings were recorded and the mean was

taken as the required angle, The distances to the flag-poles

having boon measured, the transit was removed to the next transit-

point. Flag-poles were set at the hub just vacated and at the re-

maining corners and the angles and lines measured as before. The

area of the entire field v/as then computed. The time taken was as

follows :-

Date Kind of 'iVork

Mar. 25,1911 Driving stakes andSetting flag-poles

Instrument

Chaining

Time of Day Hours Total Time

10:30-11:45 1-15

12:30- 2:00 1-30

2:00- 3:00 1-00

3 hrs.-45 min

The same field was used for the second survey in order to

obtain a check on the first. The time taken was as follows :-

Date Kind of Work Time of Day

Mar. 31, 1911 Driving Stakes etc. 9:30-10:35

Instrument 10:35-12:00

Chaining 1:15-2:25

Hours Total Time

1-05

1-25

1-10

3 hrs.-40 min

13

r/G. 4-

SUR\/EY or r/ELD BY RADIATION METHOD

STAT/ON STAT/OA/ TR/PLE ANGLE D/STANCE NOTESOCC(/P/ED SIGHTED ANGL.E FEET====

/ C

D 3/3"- S./'- CO" /04-£7'-00'' //ES.

/ De: sd^-za'-oo" 7Z/. 9 n/ectfTjer c/€a/~ o/^t/

/ E3S5-09'-ao" /3/ - 43 - Oo" 7^3.

1

/

c 333°-/^ -OO" //^'-4-4'-00" &047.9

360"- oo'- oc"

& A3 sad'' 33'-00'^ 173"- 3l'-00'' 77G.4-

8/ ^^j'-oo'-oo" ^7^- 40'-00"

/

A S3'- ^^'-oo' ^047. e

1

3(}0'''00'- Oo"

1

14

COMPOTXIT/OA/S F0/<' OF F/FLD ^(hj

A CID

/\r<£a = ^ be SinA

/o^. = 3.C6

A IS. A

H i/Of 7^/. 3

/o<^ 7^ 3J

i/a^ ^04-7-9

/o^ T76 '4-

e. ^^S97 -/o

9. -/O

-f. 66 O i>0

5>.C9S 97-/03. 3 //J /

£. 8900^^ 9/ -/o

A

J.

5/n /73~3/

/o ansa.

- e>.<i>9 8e7 -/o- ^.8'^ 00 <^

= ^-9/387=r OS"^ 7S'~/0- S(i 06 8

- 3. 2f J3 /

area.

/^r-<sa = c36,3 6£~ s^. /j^

/irea, = S*4/,S8o s^. A^.

15

3/0 ^v"- : :.' s/y7 3/^ : S^9.a

^ C/3 = (//^"--^f-^'J ~ (^/^- /^-J^ 3/"- 3^'-00"

/o^ - = 3,G93^V - /o

/o^ //5~S' - 3.c6as-s^ ClB /ojr ^3/a.(. = 3.3&3 V3 Ar-aa = /. 333, '^00 S^.

= ^047- S^-^ 77(b. 4-^ - ZX ^c^Y/i X 77-^. ^ COS -'

/A - ^/9S. ^ 7^

S/'n S3'- 4-9' : S/S^.^ 3/'n A/^ : 77^.. 4-

^ A/^ = AO "-So - 00 "

£M = (/J/ ^5y~ {zo "-s-a J~ //o° -£-3 oc

/o^ 7Z3,f - ^.SS-92.a

/Oi^ sm //O °~ S3' = '9-9 7<^ -^9 ~ /c

/r?^ i^rdo. = STs G 7 6 'f-

Tbta./ ar-<sa ~ -t^ /e>3, 7^6 y

16

On making the third survoy, a 200 acre field v/as chosen,

The same method was used as in the previous surveys with the ex-

ception that the set-ups were taken on a line joining the north and

south corners as shown in Fig. 5, The time for this survey was

as follows :-

Date Kind of V/ork Time of Day Hours Total Time

Apr. 22, 1911 Driving stakes etc. 8:30- 9:05 1-35

Instrument 9:05-11:40 2-35

Chaining 1:15- 3:10 1-55

6 hrs,-5 min

A comparison of the time taken in these surveys with those

of the traverse method will clearly show the advantages of the

radiation method. In case of any error in reading the angles ahout

any transit-point it can he detected immediately since the sum

should equal 360°. The distance to be chained was very much less

and consequently much time was saved with smaller chances for

error. Only two set-ups were required, whereas with the traverse

method five were necessary in all cases. In the survey of marshy

ground this method is superior to any other since the area can be

obtained without entering the field. In hilly country one set-up

on a prominent hill v/ould be all that 7;ould be required for the

survey. The advantages of this method are therefore:- (1) minimum

number of set-ups, (2) minimum amount of chaining, and (3) work

readily checked as it progresses. Stadia readings should always

be taken when using the radiation method, as a check on the

measured distances.

17

r/G. sSURVEY OF FIELD BY RADMT/ON MFT/iOD

F A

\

1

1

£\1

1

B

D

cSTATIONOCCUP/£D

STAT/OAy/SJG/^TED

P/STy^A/CBFEET Notes

E Br? zrz'-oo'-oo" 40"- 40-oo"

D F-Kirch er~

F /so'-^o'- oo" //6T. ^ lVea-^/n£/— c/ear cr/^t^

E. FA 38"' 4-o'- ao" /4-^/. 8

coo/ . Te/y?^

^^to"- oo'~nri>

3 cE. ^66^- oe)'.oo"

B C.

A ' 9/'- /S'-OO" 3)Zi>.S

B AC S'^"- C6> - oo" /6o'-a^'-oo" /4S3. 7

560'- ao'-oo"

18

3 . lilTERSECTIOU -JETHGD,

The intersection r,ethod is seldom if ever used in farm

surveying. It consists of measuring-oii a "base line 01 convenient

length, inside or outside of the field, and reading the angles

f crnied by lines radiating from each end of the base line to the

corners of the field. The base line nust be chosen so as to have

all corners of the field visible from its ends. The succeDsive

steps taken up in this surve;/ are; (1) driving shakes at each

corner of the field ai, at; both ends of the base line, (2) rieasuring

the angles, (3) measuring tho base line, and (4) computing the

content. This is the most accurate of all methods of farm surveying

and it should be used v/hen possible. The principal disadvantages

of the intersection method are ,1) the inability to obtain a line,

in the surve;/ of the average field, from each end of v/hich all

corners of the field can bo seen, (2) the error that is produced

by a slight inaccuracy in the measurement of the base line, and

, .

(3) the angles should not be less than 50 not i:iore than 120

for accurate v;ork.

19TABLE I

Re3ujf>3 o-^ ySurv&ys by Rac//af/on and Traverse A//e-/'hod^

.

No. ofSurvey

Meihod Durance.Chamec/ln Rtt

No. SetupsRe<^uired. for Purvey

AREj4cre.5.

ia.

lb.

Tfaver-jG

Hadiat/onS3SE. O6Z 7s5". O 2

^ hrj.- 4S min.

3hr.s.- 4.5min.4jJ34j 743 95. Z9

96. 3 i

Za.Zb.

Traverse,fiadiafion

33SI. /^r

Z4 hrj.- 40 miri.

3hrj.--40 m'ln.

4, ie3^ 734-

4j I93j767 eh. 23

3 a.

3 b.

Tfaver^e/^adiai'ion

S2

7hrj. - 4Strt'in.

&hrs - e>S min.9, (.94j zno

4 a.

4 b.

Tfa i^er-j^

f^adia-hionII95Z. OS80O.4

J-

Z7hr.s. - 3o rMjn.

Shr.s.'Ssmin9J S93, 4Z9 EZZ. S3

GOiiOL'JoIOil.

The results of the several surveys, as shov.Ti in the above

tahle, sriov; conclusively that the radiation method although not

extensively used at present is a time saver as coaparcd ";ith the

traverse method. It is a very difficult matter to convince surveyors

that the traverse mcthotl is not the best or that there is any r<ethod

as good as it. hey are loath to give it up or to experiment v/ith

any other method. In the earliest stages of farm survej/ing, v;hen

surveys vrere made V7ith the compass, the traverse method v/as undoubt-

ly the best. But nov; that v;e have much more accurate instrument to

measure anfcles and lengths of lines, T7hy should the eld method,

used 77hen farm surveying was in its infancy, be still employed to the

exclusions of all other met'-.ods?

In making a survey, the surveyor plans to obtain the most

accurate results with as little time in the field as is possible.

Expenses in the field, occasioned by the services of rodmen and axeme]:.

amount oo considerable and malvO a decided inroad upon uhe profits

of the v/ork. Therefore it is mone;. in the surveyors pocket to use

the method that will give accurate results and that requires the

least time in the field.

so

With the traverse method as shown "by Table 1, more transit'

points must be taken. In the fields under discussions the number of

stations required by the radiation method was but 40% of that re-

quired by the traverse method. The distances that were measured in

the radiation method were about 75% as great as those required for

the traverse method. This reduces the time spent in the field from

ZOfo to S5% and increases the profits of the surveyor proportinnally.

The radiation method requires more office work, but the saving in

the field work more than compensates for this. As only one man is

required to compute the area of the field, the increased expenditure

of money is little.

Angular measurement is more accurate than linear measure-

ment, therefore the radiation method is more accurate than the

traverse method. The angles in the radiation method can be checked

at any station before the transit is removed, but in the traverse

method any error at a transit-point can not be detected until the

entire survey has been finished.

In the traverse method the error of closure will show

the accuracy of the work and check any blunder made in chaining.

This is the principal advajitage to be gained in using the traverse

method, but even this becomes of minor importance if stadia readings

are taken after each line has been measured in the radiation method.

The errors due to chaining are; fl) omitting of entire chain length,

and (2) reading the wrong fraction of a chain length at the end of

the line, and these errors may be eliminated by taking stadia

readir gs.

21

From the alDove results the writer's conoliision is, that

the radiation method of farm surveying is just as efficient as the

traverse method. It is tho most profitahle method to use "because

it requires less time and fewer men than the traverse method.