1 i^W
f
1 9 1 1:
tr.T.iiivaxs
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.