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- J?

 

 

ftr/W‘fi" )

 

 

 

Establishing and Measuring

A Base Line

A Thesis Submitted to
The Faculty of
KICHIGAH STATE COLLEGE
of

AGhICULTUhE £39 REPLIED SCIEKCB

fir if) . By39
6‘4 ‘L ., - - 3; If; 1‘LL. " .‘ ‘1-
H.H; Girardln F.Ai ipeeler ‘ EZTQHQtachel

Candidates for the Degree of

Bachelor of Science

June 1934

TH
79!?

at
b
2’
« i

 

Table of Contents

Foreword

Definition of Base Line

Location of Base Line

Sketch of Base Line

Description of Base Line Monuments
Description of Astronomical Monuments
Measuring the Base Line

Determination of Latitude
Determination of Azimuth

Data and Results

Sample Computations for Base Line Measurement
Computation for Latitude

Computation for Azimuth

94759

10

Page

domfiffimr‘

- 20
21
22
25

FOhfidor-LD

de chose the subject of "Establishing a Base Line” for
our thesis because we wished to learn more about United
States Coast & Geodetic Survey methods of obtaining their
great accuracy in measuring distances. Je first met with
this subject in a Geodesj class at Michigan State College.
we believe that the practice obtained in performing the
work necessary for the completion of this thesis has given
us exPerience that we otherwise would not have obtained.
we wish to thank the Civil Engineering Department for
supplying the necessary equipment, to thank Professor C.M.
Cade for his aid, advice and criticism, and to thank.fir.
3.3. VanAtta and Mr. D.H. Barnes for the elevations with
which they provided us. in connection with their thesis.
we believe that the college will derive some benefit
from this thesis because the base line is permanent and can
be used in connection with courses given in Geodesy and
Astronomy.
Signed
Howard Girardin
Fred wheeler

Louis Stachel

Establishing and Measuring
A Base Line

A base line is the preliminary step in triangulation
work and therefore is a very important part. The length
of the base line must be determined by at least two com-
plete measurements with standardized tapes, with a resul-
tant accuracy of a probable error of 1 part in 1 million.
This measurement is used in triangulation work to compute
the sides of the original triangle by the method of ”Least
Squares". Then the computed sides are used to determine
the sides of other triangles. This procedure continues
and it can be seen that a slight error in the measurement
of the base line will accumulate as the work progresses.

The base line is located on the north side of the
road running East and west from Farm Lane, in front of the
Beef Cattle Barn, to South Harrison Road in front of the
Michigan State Police Barracks. It begins about 300 ft.
nest of the spur track and extends westward for approx-
imately 1000 ft. A sketch showing the location of the
base line in reference to the fence and road is on the

following page.

 

 

 

 

 

 

Iv
m _,
w. . m .. a. u...
3 M a M
f n / a
0 .. o M
a x... M r
.W k a m m W
1/ a
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h a W t
0 I 0 00 [WII F 0 I In L<r| a wulellxulawlfillll .1. b o b o (/0 . (VIII/”u
Illflllu lawl .l lllalblcllll lllllmflllcllnmlml lc\_ /e a a c a c4 a Is 1a a vvmwtwoiil- M

 

 

 

 

 

 

 

 

 

 

In order to make the

base line permanent the ‘
monuments were constructed 1
of concrete. The monument

at each end of the hassle {
15 in. square at the bottOI i
and is placed about 12 in.
under the surface of the

ground and projects about

8 in. above the surface.

 

They are reinforced with an

 

iron pipe the total length
of the monument. Securely End.uonunent

fastened in the top of the

pipe is a 3 in. diameter, standard 0.8.0.5 G.S. brass plate.
Each and monument is also fitted with a brass plate provid-
ing spaces for Latitude, Longitude and Elevation of the
mark in the center of the 3 in. diameter brass plate. The
monuments placed in between the two large monuments are the
standard U.S.C. & 6.8. monuments, placed at intervals of
approximately 100 ft. These monuments are 11 in. square

at the bottom and taper down to 7 in. square at the tep,
being 4 ft. 6 in. high. They are placed in the ground

with from 8 to 18 in. of the monument protruding above the
surface, depending upon the tepography of the ground be-

tween stations. Each monument is reinforced with an iron

pipe in which a brass plate is secured, as in the end
monuments.

At the east end of the base smaller monuments are
placed at intervals of 10 ft., to be used in connection
with the field work of the astronomy classes given by the
Civil Engineering Department. These monuments are 6 in.
square and 5 ft. long containing a brass plate and rein-
forced in the same manner as the other monuments.

After the sites of the terminal stations were select-
ed, the first step was to place the transit on one end of
the line and sight on a range pole of target accurately
placed on the other end of the line. The stakes to mark
the points to place the monuments were accurately set on
line at intervals of approximately 100 ft. The line was
then cleared of brush so that the tape would hang free
when under tension. ‘

The intermediate and astronomical monuments were made
in the concrete laboratory, making use of the forms provid-
ed by the U.S.C. & G.S. They were made of concrete of a
1:4:2 mix and of a consistency so that the mixture could
be easily tamped. After setting for a week the monuments
were transported to the site of the base line. The end
monuments were poured in the field, using a standard form
provided by the U.S.C. & 6.8. After secondary stakes were
set and strings stretched to mark the point already mark-
ed on the preliminary stakes, holes were dug and the con-

crete monuments placed directly under the intersection of

-5-

the strings. The monuments provided for the astronomy
class were placed in the ground directly on line and ap-
proximately 10 ft. apart. A mark was scratched on the
brass plate directly on line to be of aid in lining the
tape. Also a mark was scratched perpendicular to the first
one as a reference when the distance was measured.

The measuring of the base was done with tapes which
were standardized at the Bureau of Standards at sashington
0.0. All measurements of the line were run once forward
and once backward with each tape and under varying weather
conditions. Tape-stretchers and a standardized scale were
employed to get the required tension on each tape for every
measurement.. Dividers and a steel scale, divided into
1/100 of an inch, were used to obtain the slight variations
over or under 100.000 ft.

The rear tape-man
stretched the tape with

a tape-stretcher and

 

accurately placed the
zero of the tape on the 1
mark on the center of ‘
the brass plate at the

zero station. The front

 

l
I
man stretched the tape to l

the required tension and L

kept it thus until the Bear Tape-man

-5-

third man had measured , h... ;. ,"__
the slight deviation
from exactly 100.000
ft., by means of the
dividers. dhen the
third man had measur-

ed it with the divid-

 

ers, he then used the L
scale and found out hOW‘ '~- - ~-- - m ~—+«-—r——~~——w-——
many 1/100 of an inch Front tape-man and third man

it was over or under

100.000 ft. He recorded this as (+) when over and (-J when
under and while he did this the front man read and recorded
the temperature on a standardized thermometer which was
'eupported on the tape so that the exact temperature of the
tape could be known. This procedure was repeated between
each station until the end of the line was reached. Then
the tape was turned around and another measurement was

made in the same manner going back to the sero station.

The lengths of the tapes and the pounds of tension to
apply varied with each tape. This information along with
the temperature at which the tape was standardized was
sent from Washington. D.C. when the tapes were returned
after they were standardized.

In finding the latitude of one end of the base line,

and the azimuth of the line, observations on Polaris were

taken. These obscIVations were taken at night along with
the astronomy class. A theodolits, a chronometer and a
step watch were used in taking the readings. The theodo-
lite Was set over the point on one end monument and the
plates set on zero. The cross hairs were sighted on the
Capitol hational Bank tower in Lansing and an angle of
approximately 90 degrees turned off. The telescOpe was
elevated to an angle of chest 42 degrees and when this
was done, Polaris could be seen in the telescOpe lens.
The cross hairs were set horizontally and vertically on
Polaris and the stop watch syncronized with the chrono-
meter. when the instrument-man had the cross hairs ex-
actly on the star he called "take" and the step watch was
stopped. The time to a tenth of a second was noted and
recorded. The horizontal and vertical angles were read
and recorded. Three readings were taken in this manner
and then the cross hairs were sighted again on the tower
and the horizontal angle read to serve as a check on the
readings. The teles00pe was inverted and the same pro-
cedure followed to take three more readings with the
telesc0pe in this position to take care of any error in
the instrument. After these were taken the cross hairs
hairs again centered on the tower and the mark checked.

This completed the observations.

The same observations were used to find the azimuth

-8-

of the line as those to find the Latitude of the point.
The azimuth of the star was computed and the horizontnl
angle that was read on the theodolite when each reading
was made was added to the azimdth of the star. This
yielded the azimuth of the imaginsry line from the point
to the tower. The angle from the tower to the base line
was turned off and added to the azimuth of the imaginary
line from the point to the tower. This addition yielded

the reqxircd azimuth of the line preper.

-9-

Conclusion

In concluding this thesis we hepe to have conveyed
to the reader a definite and clear ides of how e base line,
suitable for 3.8.8. & G.S. work is measured and how the
Latitude_of a point and the azimuth of s line may be com-
puted from a series of observations on a pole star. Upon
examining the data it is very plainly seen that the best
resdlts in measuring were obtained when the temperature
remained nearly constant because the variation due to a
few degrees change in the temperature of the tape causes
a considerable error in the meesurement of the line.
Therefore the best time for measuring a line is on a

cloudy, misty day or else at night.

The following data was obtained in measuring the base
line with tape Ko. 8.5. 4415 on a cloudy day.
Supported at 0 5 100 ft. at 68°F, 10 lbs. tension
Length - 99.940 ft.
Sts. Temperstire Dist.(+)or(-) Diff. in Ste. Elev.

No. Degrees F. ft. e1ev. ft. Ho.
0-1 70 +0.07917 0.040 0 849.1998
1-2 69 -0.05500 0.155 1 849.2598
2-5 69 +0.04250 1.585 2 849.5727
5-4 72 +0.00917 1.482 5 847.7877
4-5 72 -0.02917 0.089 4 846.5057
5-6 71 +0.01085 0.255 5 846.2165
6-7 70 +0.08250 0.585 6 846.4715
7-8 69 -0.04085 2.568 7 847.0565
8-9 70 -0.00585 0.758 8 849.6243
9-10 70 -0.01855 0.505 9 850.5825
10 849.8875
10 849.8875
10-9 70 -0.01855 0.505 9 850.5825
9-8 70 -0.00585 0.758 8 849.6243
8-7 70 -0.05917 2.568 7 847.0565
7-6 70 +0.08167 0.585 6 846.4715
6-6 70 +0.01167 0.255 5 846.2165
5-4 70 -0.05000 0.089 4 846.5057
4-5 69 +0.01167 1.482 5 847.7877
3-2 67 +0.04417 1.585 2 849.3727
2-1 66 -0.03853 0.155 1 849.2398
1-0 68 +0.08167 0.040 0 849.1998

were obtained.

Sta.
No.

0-1

10-9
9-8

Hess.

ft.
100.01917
99.91500
99.98250
99.94917
99.91083
99.9508

()1

100.02250
99.89917
99.95417
99.92167

99.92167
99.93417
99.90083
100.02167
99.95167
99.91000
99.95167
99.98407
99.90167
100.02167

dist.

-17-

By using the date on page 16,

Temp.
corr.

+0.00129
+0.00005
+0.00065
+0.00253
+0.00258
+0.00194
+0.00129
+0.00055
+0.00129
+0.00129

+0.00129
+0.00129
+0.00129
+0.00129
+0.00129
+0.00129
+0.00065
—0.00065
-0.00129

0.00000

True inc.
length

100.02046
99.91565
99.98515
99.95175
99.91341
99.95277

1

C)
O

379

b.

.0‘
99.89982
.9

10
‘D

()3
U1
01

‘4
9

7")
m
Or

99.9:

99.92296
99.93546
99.90212
100.02296
99.95296
99.91129
99.95232
99.98542
99.90038
100.0216?

Grsie
OOII‘.
t»)
0.00000
0.00009
0.01256
0.01099
0.00000
0.00033
0.00172
0.03502
0.00287
0.00127

0.00127
0.00287
0.03301
0.00173
0.00033
0.00000
0.01098
0.01257
0.00009
0.00000

the following results

True hor.
length

100.02046
99.91556
99.97059
99.94076
99.91341
99.95244

100.02207
99.86680
9

1f:

(0
()3
H3

.59

9

(C

(O
m

. 169
99.92169
99.93259
99.86911

100.02123
99.95263
99.91129
99.94134
99.97085
99.90029

100.0216?

-12-

The following data was obtained in m0&suring the base
line with tape KO. G2155 on a cloudy, misty day.
Supported at 0 & 100 ft. at 68°F, 22 lbs. tension
Length - 99.998 ft.

Sta. Temperature Dist.(+)or(-) Diff. Sta. Elev.
No. Degrees F. ft. elev. 30.
0-1 52 +0.08249 0.040 0 849.1998
1-2 53 -0.0358O 0.133 1 849.2398
2-3 54 +0.03540 1.585 2 849.3727
3-4 54 -0.00299 1.482 3 847.7877
4-5 54 -0.07583 0.089 4 846.3057
5-6 54 +0.00458 0.255 5 846.2163
6-7 54 +0.08291 0.585 6 846.4713
7-8 54 -0.08333 2.568 7 847.0563
8-9 56 -0.00166 0.758 8 849.6243
9-10 58 -0.02166 0.505 9 850.3823
10 849.8873
10 849.8873
10-9 51 -0.02416 0.505 9 850.3823
9-8 51 -0.00166 0.758 8 849.6243
8-7 51 -0.08208 2.568 7 847.0563
7-6 52 +0.08541 0.585 6 846.4713
6-5 52 +0.00499 0.255 5 846.2163
5-4 52 -0.07374 0.089 4 846.3057
4-3 52 -0.00208 1.482 3 847.7877
3-2 52 +0.03624 1.585 2 849.3727
2-1 52 -0.03416 0.133 1 849.2398
1-0 52 +0.08333 0.040 0 849.1998

were obtained.

Stu.
No.

0-1

'9-10

10-9
9-8
8-7

7-6

171833.

ft.
100.08049
99.96220
100.03340
99.99501
99.92217
100.00258
100.08091
99.91467
99.99034
99.97654

99.97584
99.99634
99.91592
100.08341
100.00299
99.92426
99.99592
100.03424
99.96384
100.08135

diet.

By using the data on page 12, th-

Temp.
corr.
(-)

0.01032
0.00908
0.00903
0.00903
0.00903
0.00903
0.00903
0.00903
0.00774

0.00645

0.01097
0.01097
0.01097
0.01032
0.01032
0.01052
0.01032
0.01032
0.01052
0.01052

0

True inc.
length

100.07017
99.98253
100.02437
99.98598
99.91314
99.99355
100.07188
99.90584
99.98860
99.98989

99.90287
99.98537
99.90495
100.07309
99.99267
99.91394
99.98560
100.02592
99.95352
100.07101

Grade
eorr.
0.85500
0.00008
0.01258
0.01099
0.00000
0.00032
0.00171
0.03303
0.00286
0.00128

0.00127
0.00285
0.03302
0.00173
0.00032
0.00000
0.01094
0.01238
0.00009
0.00000

following results

True hor.
length

100.07017
99.95244
100.97499
99.97499
99.91314
99.99323
100.0701?
99.87261
99.98574
99.96801

99.96

H
O

99.98252
99.87193
100.07136
99.99235
99.91594
99.97466
100.01136
99.95343
100.07101

-14...

The following date was obtained
line with tape H0. 02155 at night.
Supported at 0 & 100 ft. at 68°F, 22
Length - 99.998 ft.

in measuring the base

lbs. tension

Sta. Temperature Diet.(+)or(-) Diff. Ste. filev.
No. Degrees F. ft. elev. n .
0-1 60 +0.08416 0.040 0 849.1998
1-2 60 -0.05585 0.133 1 849.2598
2-3 60 +0.03585 1.585 2 849.5727
5-4 60 -0.05355 1.482 5 847.7877
4-5 60 -0.07750 0.089 4 846.5057
5-6 60 +0.00416 0.255 5 846.2165
6-7 60 +0.09583 0.585 6 846.4715
7-8 59 -0.08416 2.568 7 847.0563
8-9 59 -0.00085 0.758 8 849.6245
9-10 59 -0.01166 0.505 9 850.5825
10 849.8873
10 849.8873
10-9 58 -0.01450 0.505 9 850.5825
9-8 58 -0.00166 0.758 8 849.6245
8-7 58 -0.08585 2.568 7 847.0563
7-6 58 +0.09555 0.585 6 846.4713
6-5 58 +0.00166 0.255 5 846.2165
5-4 58 -0.07250 0.089 4 846.5057
4-5 58 -0.00250 1.482 5 847.7877
5-2 58 +0.03416 1.585 2 849.5727
2-1 58 -0.03500 0.133 1 849.2393
1-0 58 +0.08442 0.040 0 849.1998

were obtained.

Ste.
No.

0-1
1-2
2-5
5-4
4-5
5-6
6-7
7-8
8-9
9-10

10-9-

9-8
8-7
7-6

6-5

113328. air-Lt.

ft.
100.05219
99.99217
100.05393
99.96466
99.92050
100.00215
100.09585
99.91584
99.99717

99.98654

99.98550
99.99654
99.91217
100.09135
99.99966
99.92550
99.99550
100.0321?
99.96500
100.08241

Temp.
corr.
(-)
0.00616
0.00516
0.00516
0.00516
0.00516
0.00516
0.00516
0.00581
0.00581

0.00581

0.00645
0.00645
0.00645
0.00645
0.00645
0.00645
0.00645
0.00645
0.00645

0.00645

True inc.
length

100.07700

(1"

u
VII.

‘0

5701
100.

O

2867
99.95950
99.91554
99.99700

100.0886?
99.90805
99.99126

99.98053

99.97705
99.98989
99.90572
100.08488
99.99521
99.91905
99.98905
100.02572
99.95655

100.07596

Grade
corr.
{-)
0.00000
0.00007
0.01257
0.01096
0.00000
0.00034
0.00175
0.05502
0.00287
0.00127

0.00125
0.00286
0.05501
0.00172
0.00052
0.00000
0.01099
0.01255
0.00009

0.00000

By ueing the date on page 14, the following results

True hor.
length

100.07700
99.956S4
100.01610
99.94854
99.91554
99.99666
100.08694
99.87501
99.98859

99.97925

99.97580
99.98705
99.87271
100.08516
99.99289
99.91905
.99°97806
100.0131?
99.95645

100.07596

were obtained.

Sta.

,0
.170 o

0-1

10-9
9-8

fieas 0

ft.
100.02667
99.91167
99.98167
99.95583
99.9125
99.95667
100.02667
99.90675
99.94167

99.92833

99.92750
99.94333
99.90167
100.02750
99.95917
99.91500
99.95583
99.98000
99.91085

100.02500

dist.

-19-

Temp.
corr.

+0.00258
+0.00129
+0.00129
+0.00129
+0.00129
+0.00005
+0.00065

0.00000

0.00000

0.00000

0.00000
0.00000
0.00000
0.00000
-0.00129
-0.00129
-0.00065
-0.00065
-0.00065
-0.00065

True inc.
length

100.02925
99.91296
99.98276
99.90712
99.91579
99.95792

100.02792
99.90676
99.90167

99.92855

99.92750
99.94353
99.90167
100.02750
99.95788
99.91371
99.95518
99.98635
99.91018
100.02435

Grade
001T.
{-)
0.00000
0.00008
0.01956
0.01098
0.00000
0.00033
0.00171
0.03302
0.00286

0.00127

0.00130
0.00239
0.03301
0.00171
0.00053
0.00000
0.01096
0.01255
0.00008
0.00000

By using the data on page 18,_the following results

True hor.
length

100.02925
99.91288
99.97020
99.94614
99.91379
99.95099

100.02561
99.87365
99.93881
99.99706

99.86866
100.02579
99.95755
99.91571
99.94422
99.97179
99.91010
100.02455

-go-

The values on pages 13 and 15 were given a weight of
2 and the values on pages 11,17 and 19 were given a weight
of 1. Then the arithmetical mean wee taken and the follow-

ing reeulte obtained.

Sta. mean hor. length
Ho. ft.
0-1 100.05676
1-2 99.94012
2-5 100.0000?
3-4 99.96185
4-5 ' 99.91436
5-6 99.98225
6-? 100.06108
7-8 99.87158
8—9 ' 99.97075

9-10 99.95526

Total length - 999.71341

Sample Calculations for Base Line

Date taken from page 10.
Tape 02155 Length - 99.998 ft. at 68°F and 22 lbs tension
measurement made from Sta. 1 to Pte 2.
Temperature - 54°F.
Increment under 100.00' I 0.04585'
fleas. length - 99.998 - 0.04583 - 99.95217
Temp. corr. - 0. 00000645 3 100A14 a -0. 00905
Tree inclined length - 99.95217 — 0.00908 = 99.94314'
Q\L2

0"
Crude correction - -(L - ~92“

where L a length and H - diff. in elev.

 

Grade correction - 49 9.94.514 «v 99.943142 - 0.1532 )

\

. -00 00009 '

'\

True her. length - 99.94314 - 0.00009 - 99.94505'

Date anl Calculations for Obtaining

Latitude and Azimuth of Line

Telesc0pe «etch time Vertical angle Horizontal angle
hevereed g0 29 48?6 41° 52' 00" 81° 2’ 40”
" 20 49 19.0 41° 51' 10” 81° 26' 20"
" 20 52 21.7 41° 50' 40" 81° 27' 30"
Direct 21 02 26.0 41° 53' 40”' 81° 30' 00"
” 21 05 35.1 41° 54' 40” 81° 51' 10”
° 21 08 8.6 41° 55' 00” 81° 32' 20"

AVerege 20 56 £0.55 41° 52' 51.67" 81‘ 28' 20"

h m 8
Average of watch readings . 20 56 20.53
Known watch and clock corr. s +18.00
Local civil time (T) - 20 56 58.55

Solar time (0) - 11h Elm 56.275 or 174° 9' 0.45"
63 83° 56' 58.32".
Coordinates of Polaris
06- 1h 57m 64.033

Hour angle (t) I 0 -<Xf8 9h 53m 52.248 or 148° 28' 5.6”

Reduction
0 - 11h 51m 56.273
06. 9h 53m 52.243
t - 12h 49m 3.68
h'- 41° 52' 51.67"
2" 48° 7' .23”
r . 0° 1' 8.04”

2 ' 48° 8' 10.97"

Reduction Con'd

ten F
cot<f

008 t - ~0.85248

cotd’coe t

0.01834

tun F ‘ -0.01503

F - -0° 52' 43.44"

ein(¢ + F) - 008 F 003 Z cec
008 F - 0.000885

cos 2 - 0.667558

oeccfflu 1.000170

ein(¢ + P) - 0.0073734

h? + F) - 41° 51' 51.82"

0- 42° 44' 35.26"

Sin A - ein t coed” . 0.52297 x 0.01853 , 0.0128714
313*? 0.72175

 

Azimuth of star (A) - 0° 44' 20.00"

Azimuth to tower : 97° 51' 40.00"

Angle from tower to line - 7° 55' 7"

Azimuth of line - 97° 51' 40.00" - 7° 55' 7"

7 " v . 89° 56' 33.00"

ROOM USE 2‘th

 

I

MICHIGAN STATE UNIVERSITY LIBRARiES

l. 3" WI I‘lil } ‘ H Hi I]

1
i
I

I

31293 030614543