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THESIS
MICHIGAN
AGRICULTURAL COLLEGE
CAMPUS TOPOGRAPHY
c. M. Stover D. K. Robinson
1921
THESIS

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MICHIGAN AGRICULTURAL COLLEGE
CAMPUS TOPOGRAPHY

A Thesis Submitted to
The Faculty of
MICHIGAN AGRICULTURAL COLLEGE

By
D. K. Robinson | C. M. Stover
Candidates for the Degree of
Bachelor of Science

June 1921.
 

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THESIS
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Introduction. .cccccccccrcscccccccccsccses erage 2

Apparatus Used... ..cccccccvcccnvecsccsceces
The Preliminary Work... ..ccccccccvcsccessees
The TYaveree...ccccccccccccvccccscccscsene
TOPOMTAPHY.. .crcccccvcsccccccssevsccccvecer
CONCLUBLON. .. wc cccccvccrcerccccsccvevcsece
Witnesses Of Stations... c.cccccccccrcseces
Data
Check Traver8@.....cccccccccccsccccevece
Cloped TraverBescccccccccccccscccccccces
Level Notes... ccccrccccccccscccesecsccsece
Computed CoordinateB...cccccccccscvecccs
Sample Computations... ccccsersccccveseces
Sample Unit Sheet... ccccccccccccccccces
Given Coordinates.....ssesee-+-eeee Back
Triangulation Map... cccccccccceccece "

Unit SHEeCtScccccvcccsccccsccccecccceces

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INTRODUCTION

A topographical survey, if based on a system of tri-
angulation, is mapped by first plotting the triangulation
points. If the area is small, the convergence of the mer-
idians may be neglected and the triangulation points plot-
ted by means of their rectangular coordinates. The draw-
ing for this purpose is ruled off into large scuares,

The topography includes the shape of the ground and the
location of all objects such as houses, walls, fences, water
courses, catchbasins, trees, manholes, edges of travelled
ways, poles, hydrants, monuments, and in fact, any object
that occurs within the limits of the survey.

This thesis deals with the extension of the topograph-
ical survey of the M. A. C. Campus which includes complet-
ing a secondary traverse control and adjusting between known
points, and the taking of topography by means of the plane
table.

~Lea
APPARATUS USED
I, Instruments:
1. Transit, reading to 30"
2. Plane Table, tripod, telescopic and sight alidade.
3. Wye level.
Il. Flags or range poles.
III, Tapes: 100° standard steel tape.
100° standard metallic tape.
THE PRELIMINARY WORK

From triangulation data previously completed, witnesses
and descriptions of the following triangulation points were
obtained: 9, 11, KE, Jj, 1, h, FOl, FO2, q, r, 8s, t, u, x,
CXN5, CXN6, CXN7, GPl and GP2. In each case, the point was
located, the witnesses verified or corrected (See page 10).
with the exception of the point "q". From the witnesses and
descriptions given for this point, nothing was discovered,
no doubt due to the fact that the field in which said point
was supposedly located had been recently plowed and several
trees in the vicinity removed. Another point "q" was es-
tablished for this particular survey.

THE TRAVERSE

4 traverse is run with a transit by setting up the in-
strument over the intersection of the sides of the traverse
and measuring the angles at the intersection or by orienting
on a given point and measuring the aximuth of the forward
line. The side lengths or distances from point to point are
measured with the tape. If a traverse is laid out so that
the point of ending is coincident with the point of begin-
ning, it is called a closed traverse.

In any case, if the point of ending is not coincident
with the point of beginning, there is an error of closure,
Since, in our case the traverse work was laid out with trans-

it and tape, the error is due more to the measurements with

the tape than to angular measurements. The error is there-
fore distributed throughout the various sides forming the
traverse s0 that only the lengths will be corrected. fhe
traverse is referenced to two coordinate axes at right angles
to each other. One of the axes may be a meridian or a line
in the traverse. This traverse was referenced to the base
line of the Campus triangulation system. The projection of
any line in a traverse on the meridian axis is called its
latitude: its projection on the other axis is called its de-
parture. The rule for distributing the error of closure is
as follows: The correction in latitude or departure of any
course i8 to the total error in latitude or departure as the
latitude or departure of the course is to the arithmetical
sum of the latitudes or departures..

As has been said, one of the axes may be a meridian line.
Distances measured @long the meridian axis are known as
ordinates or "y" distances and the distances along the other
axis as abscissas or "x" distances. It is well to choose
the base axes so that there will be no negative values for
the coordinates of any point. The coordinates of an unknown
point can be calculated from those of a known point if the
‘angie and distance to the unknown point from the known point

are measured.

Check traverses were run from CAN6 to CXN?7 by orient-
ing on GPl, the azimuth of which was determined from coord-
inates given us; also from CXN6 to FO1, from FOl to CXN5, h,

9, and FO2, from FO2 to x, §j, 11, and i.
& closed traverse was run beginning at CXN6 and orient-
ing as before, through points r, q, 8, t, u, CP2, GP1l, and
CxXN6. The error of closure in degrees was 0 1' 12" which was

distributed in proportion to the distance between the re-
spective points. From the field data obtained, the x and y
coordinates were computed (see computations pagel9 ). The
error due to unavoidable causes in the x coordinates amount-
ed to .25' while that of the y coordinates was 0.06'. The
true azimuths of all points was then computed from the cor-
rected coordinates for each point.

fhe elevation of each triangulation point was deter-
mined by precise leveling. Precise leveling differs from
the ordinary leveling in the instruments employed and the
care and refinement used in doing the work. The level may
be either of the wye or dumpy type, the former type being
used on this survey. The allowable error in thiga class of
work according to the U. S. Coast and Geodetic Survey is
0.016 feet per mile. Since the distance around our traverse
was 2782 feet, our allowable error ip 0.008 feet. However,
our actual error was 0.001 feet. the elevations of the
triangulation points of this traverse as determined by the

above method of leveling are found in the notes on pagel’.

~6<
TOPOGRAPHY

There are three general methods of taking topography,
namely, transit and tape topographical survey, sight alidade
plane table survey, and telescopic alidade plane table sur-
vey.

In taking flat topography, which included the location
of all objects such as houses, walls, fences, watercourses,
catch basins, trees, monuments, edges of the travelled ways,
poles, hydrants, manholes, and in fact any object that oc-
curred within the limits of the survey, both the telescopic
and the sight alidade were used. However, the sight alidade
proved to be much better adapted for this class of work be-
gause of the greater ease and rapidity of locating objects
through the sights.

Fhe method pursued in the taking of the flat topography
was as follows: A sheet of drawing paper kmown as a unit
sheet, upon which were plotted two or more of the known con-
trol points, was attached to the board, which was mounted
on a tripod. Each unit sheet was ruled into one inch squares
containing 2500 square feet of area, that is, 1" = 50', ‘The
sheets were made continuous by numbering every one hundred
foot division consecutively from the base axes. The control
points were then plotted on these sheets from the coordinates
previously determined by the traverse. The tripod and board
Was set over one of the plotted control points and the
board levelled and oriented. In order to explain this method
Clearly an example will be worked out in detail. Refer to
page 20 and consider the plane table as set up over tri-
 

angulation point 4. To orient bring the edge of the miler

of the alidade in coincidence With the line AC, which joins
triangulation point A with triangulation point C, and move

the plane table board horizontally about its vertical axis
until triengulation point C on the ground is sighted. Clamp >
the board in this position. The board may be oriented in
this manner by sighting on any accessible control point

such as B, The objects can now be located by the intersection
method. To locate the house in this example the corners nm,

n, and o are sighted and the lines Am, An, and Ao, respective-
ly, are drawn approximately greater in length than the actual
distance to the object. In like manner, the lines from A

to objects within the scope of the instrument, such as Ay,

4x, and Ag are drawn. The next step is the selection of a
sub-station such as 1 from which most of the above points

can be seen. To locate station 1 on the map the alidade

is sighted on 1 and the line of sight Al is drawn. The dis-
tance from A to 1 is measured on the ground and the corres-
ponding distance is laid off to scale from A along the line
Al. This definitely locates Sta 1. The board is then set

up over Sta 1, levelled and oriented as explained above,
using point A as a backsight. The points y, n, x, 0, and s |
are then sighted and the lines ly, ln, 1x, lo, and ls respect-
ively drawn on the sheet. Each point is located definitely
by the intersection of the corresponding lines from Sta A

and Sta 1 to the point. In a like manner as many substations
as are necessary are established in order to completely

locate all the objects on the sheet.

-8~
CONCLUSION.

The information obtained from this plane table survey
Shows that the sight alidade is best adapted for this par-
ticular clase of work. When the objects to be located are
s0 situated that well defined intersections of the lines of
sight from two or more setups are obtainable, one topographer
is all that is required. However, in locating objects or
buildings which are very close to each other, and angling
roads, paths and streams, two topographers are required, one
to chain distances and the other to plot the points. Of
course, one topographer could do this alone but greater speed

is obtained with a party of two.
 

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CHECK TRAVERSE

 

 

 

was | to | “MeTared | Sgmputes
cxye | GP1 | 3° 10" 41" | 3° 10" 41"
CXN7 | 290°25" 15"
Fol | 108°54' 00" | 108°54* 28"
Fez 71°48" 15"
r 103°38' 45"
@ 71°42" 35"
Fol CXN6 | 288°54" 00"
FO2 359°27' 00" | 359°29' 25"
CXN5 | 112°47' 20"
Ag 47°O7' 30"
h 358°33" 45"
Fo2 FOl | 179°29' 25"
x 0°31' 45"
j 9°31' 30"
FOS 3°39" 06"
FOS FO4 $57 ° 09" 13"
GP1 GP2 1°42' 17"

 

 

 

 

~15—<

 

 
 

CLOSED TRAVERSE
K at to Azimuth Distance (ft)

 

 

CxXN6 | GP1 3°10" 41"

2 103° 38" 45" 4231.65
r q 48°51' 15" 588.20
q s 559° 48' 00" 281.00
e t 0°55" Zo" 664.70
t u £270°09' 15" 580.15
a GP2 270.01' 45" 437.50
GP2 GP1 181° 43" 45"
GP1 cxne | 13°12" 15"

dane FRM RK a > ME a ak

FO2 FO. | 179°29" 25"
x 0°31" 30" 702.80
j 9°31" 45" 263.80

 

 

 

 

~16-

 
 

 

 

LEVEL |NOTES
B.8.| H.I. F.3. Elev. Sta.
857.860 CXN6
5.403 | 861.263
22555 | 858,950 r
10.838 | 850.425 q
32660 | 854.085
1.451 | 852.654 8
9.171 | 844.914
6.715 | 847,372 u
1.897 | 849.269
11.288 | 837,981 GP2
848.650 For
1.742 | 850.392
4.428 | 845.964 5
9.020 | 841.372 x

 

 

 

 

 

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-18-
SAKPLE COMPUTATIONS

Y of CXN6G = 7596.80 | dy of r * 4401.80
This dy is found as follows:

Distance from r to CXN6 = 4231.65'

Sine (103 38’ 45" - 90) # ,23592

then, dy (r) = 451.65 x .22592 # 4101.80
X of CXN6 = $3471.90 dx of r 2-419.50
This dx ig found as follows:

Distance from r to CXN6 #® 431.65'

cos (103 38' 45" - 90) = .97177

then, ax (r) = 431.65 x .97177 = «419.50
Correction:

Total distance around traverse is 2783.2

Distanoe from r to CXN6 is 431.65'

Total error of closure is 0.25'

Amount of correction = 'Dist/Total dist) x error
(431.65/2783.2) x 0.25 = .04

Computed dx (r) # 419.50

Corrected ax (r) = 419.50 - .04 = 419,46"

 

 

 

 

 

Coordinates:
(Y) (xX)
- 696.80 + 3471.90
$+ 101.81 - 419,46
- 687.01 = 443.00
- 280.98 + 361,01
- 664,60 - 10,67
- 1827.58 + 2599.78
- __1.01 + 380.18
- 1828.59 4 2979.96
- O.21 4 437,54
- 1828.80 + 3417.50

~19-
 

 

 

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Coordizele Data
Tria ngulation 1797
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