CE 111 Circular Curve Lab
Spring 2005
Objective: Develop skills in determining positions of circular curves for field layout using standard
taping techniques and off-curve EDM measurements. Apply knowledge of spreadsheet
development learned in traverse laboratories to compute circular curve coordinate and layout data
for field survey.
Data
PI Station = 32+ 30.30 with coordinates of 170.34E, 284.51N (your coordinate values and
distances only need to be shown to the nearest 0.01 foot).
Azimuth of BC to PI tangent = 30O 00’ 00”
Delta = 36O 00’ 00” and the curve is to the right
D = 8O 00’ 00
Computations required
1) Complete sufficient manual computations of the circular curve to identify the following:
 BC and EC stations around the curve, as well as the EC station coming along the tangent.
 Deflection angle from BC to station 34+00
 Coordinates of Station 34+00
The answers are included in the following table, although the individual calculations to develop
them are not included here
In the hand computations they were only asked to complete a small portion of the table below.
The BC and EC stations, the deflection angles and the Coordinates of Station 34 are shown in the
table. The only element not shown there is the EC station coming along the tangent from the PI
Station EC from PI = 32+30.30 + T = 32+30.30 + 2+32.71 = 34+63.01
In the table EC around the curve was found to be 34+ 47.49
.
Sheet3
Simple Circular curves
revised 1/2/03
(Spiral length is 0 for simple circular curves)
Given R, Delta, PI sta and coordinates, azimuth from PC to PI
Place needed data in shaded cells
Distances may be m or ft.
deg
8
716.1975
Givens:
spirallen =
0
PI Sta =
3230.30 m
X coord
Y coord
Delta =
36 deg
PI =
170.348 284.507
PC or TS
53.99
82.98
Azi PC to PI =
30 deg
PT or ST
382.94
379.16
Radius =
716.197 m
Radius pt.
164.47
-275.12 of CC
Curve to :
mid pt cc
195.01
317.38
Right =+1
1
Back AZ=
210.00 deg
Left = -1
L of Cir C
450.00
Tangent =
232.71
L.C. of cc
442.63
mid ord =
35.05
Ext. =
36.86
Increment =
50
Partial Chords:
Nominal length =
true chord =
mid ord
=
50.00
49.99
0.44
arc dist
defl angle DEFLECTION ANGLE
STA
Sta (m) from PC from PC degrees
min
BC or SC
2997.59
0
0
0.00
0.00
30
3000
2.41 0.096264
0.00
5.00
30.5
3050
52.41 2.096264
2.00
5.00
31
3100
102.41 4.096264
4.00
5.00
31.5
3150
152.41 6.096264
6.00
5.00
32
3200
202.41 8.096264
8.00
5.00
32.5
3250
252.41 10.09626
10.00
5.00
33
3300
302.41 12.09626
12.00
5.00
33.5
3350
352.41 14.09626
14.00
5.00
34
3400
402.41 16.09626
16.00
5.00
CS or EC
3447.59
450.00
18
18.00
0.00
chord
from PC X Coord Y Coord
0
0.00
53.99
82.98
47
2.41
55.20
85.06
47
52.39
81.83
127.36
47
102.32
111.35
167.71
47
152.12
143.61
205.89
47
201.73
178.46
241.74
47
251.10
215.72
275.06
47
300.17
255.22
305.71
47
348.86
296.76
333.52
47
397.13
340.13
358.37
0
442.63
382.94
379.16
2) General spreadsheet
A basic spreadsheet layout with initial computations will be provided by the instructor
The results of the spreadsheet are included on the previous page
3) Angle and distance measurements for EDM
The surveyor found a convenient location in the field to use to set out the curve from a
single point that was not on the curve. The following measurements were made from this position
to two control points A and B, with the instrument at I.
Page 1
Instrument at I. Distance IA = 477.86 feet, Distance IB = 499.26 feet. Points A and B were
both west of the instrument. The angle AIB was 75O 59’ 00”.
a)
In the office the coordinates of the control points were found to be:
A: 398.44 E, 215.65 N
B: 432.66 E, 877.13 N.
Calculate the position the surveyor plans to occupy by using two strategies:
1. Use the measured distance data in conjunction with the calculated AB distance
2. Use distance AI and the measured angle.
B
I
A
1) Find length and azimuth of A B using basic inversing equations learned in the traverse
programming:
Length = 662.36 Azimuth = 20 57’ 41”
2) Strategy 1: Find coordinate of I using only the distances
Cosine law can be applied to determine Angle I and the Sine law or Cosine Law can be used
to determine the other two angles: The values are shown in Table 1 along with the solutions using
the measured angle, the control line and one of the measured field distances.
Strategy 2: Find coordinate of I using Angle AIB, and distances AB and AI
Sine law can be used for all remaining unknowns.
The results are shown in Table 1 and Table 2.
Strategy 3: Although not required, the calculated coordinates using line IB, AB and angle AIB
are also shown.
(Note: the process of computing the coordinates of an occupied point using field measurements is
referred to as “resection”. Many modern total stations have the software to do this for the user. Not
all total stations in our laboratory have this capability).
Strategy 1 requires application of the cosine law to find the first angle, then cosine law or sine law
can be used The three angles should be:
A = 48 d
44’
11”
B = 45d 58’ 48”
I = 85d 19’ 01”
The coordinates of I can be found by using the coordinates of A and the knowledge that the
Azimuth to I must be 20 57’ 41” + 480 44’ 11
Strategy 2 can begin with the sine law to find Angle B (using angle I plus the distances IA and AB.
All results are shown in Tables 1 and 2 below.
Only Strategy 1 and 2 were asked for in the lab instructions.
Table 1 Computed angles and sides for Instrument location
Distance or Angle
Strategy 1
Strategy 2
IA
477.86’ (measured)
477.86’ (measured)
IB
499.26’ (measured)
499.33’
Angle A
480 41’ 56”
480 41’ 28”
Angle B
450 58’ 34”
450 58’ 37”
0
Angle I
85 19’ 30”
850 89’00”(meas’rd)
Table 2 Coordinates of Total Station (I)
Strategy
Easting
Strategy 1
773.25
Strategy 2
773.29
Strategy 3
773.31
Average
773.28
Strategy 3
477.94’
499.26’ (measured)
480 41’ 53”
450 59’ 07”
850 19’00” (meas’rd)
Northing
512.08
512.02
512.13
512.08
Relying on distance measurements produced a calculated angle 30 seconds less than the measured
angle. This difference would be considered very large for an instrument that apparently can
measure to the nearest second. Of course, the angle may have been correct and the difference is
due to errors in the distance measurements. Fortunately, because the triangle was a reasonably
strong triangle, the coordinates were reasonably consistent. (Small angles, especially those less
than 20 degrees when the sine of the angle is needed in computations, are undesirable). Even in
our situation, the computed Northing differed by over 0.10 feet, dependent on the data used to
compute the coordinate.
b)
Using the coordinates from part a, establish a table to show the azimuth and distance from
the instrument to points A and B and all the curve points including the PI, BC, EC, and every half
station along the curve.
If coordinates of I are taken to be 773.28E, 512.08N the Azimuth to point A (398.44 E, 215.65 N )
is
Azi = 2700 – Atan( (215.65-512.08)/(398.44- 773.28) = 2310 39’ 45”
Dist = sqrt(deltax^2 + deltaY^2) =
477.89’
All other distances and azimuths from I could be calculated in a similar manner. Since the students
had already written a program to inverse coordinates to distances and azimuths, I would expect
most of them to copy segments of that program to make a spreadsheet that would work here.
Table 3 Distance and Azimuth data for Circular curve from Total Station
Coordinates
STATION
INSTRUMENT
E
N
773.28
512.08
398.44
215.65
53.99
82.98
30.00
55.19
85.06
30.50
81.83
127.37
31.00
111.35
167.71
31.50
143.61
205.90
32.00
178.45
241.74
32.50
215.72
275.06
33
255.21
305.71
33.5
296.75
333.52
34
340.12
358.37
EC
382.93
379.16
PI
170.34
284.51
Contrl point
BC
Sta.
delta E
to next
sta
delta N
374.840
719.293
718.087
691.454
661.935
629.673
594.827
557.565
518.069
476.532
433.156
390.352
602.940
296.430
429.100
427.018
384.713
344.369
306.183
270.340
237.016
206.371
178.557
153.708
132.920
227.570
dist to
nex sta
Azimuth
Azimuths
point
(radians)
degrees
minutes
sec
477.89
4.043272
231
39
45
837.56
4.174505
239
10
53
835.46
4.175905
239
15
42
791.27
4.204658
240
54
33
746.16
4.232675
242
30
52
700.17
4.259796
244
4
6
653.38
4.285811
245
33
32
605.85
4.310441
246
58
12
557.66
4.333308
248
16
49
508.89
4.353881
249
27
32
459.62
4.371395
250
27
45
412.36
4.384191
251
11
44
644.46
4.351486
249
19
18
Summary
The spreadsheet programs took time to develop, but the principles used were those learned
from previous activity. Similar problems encountered in the future (class project and other) will be
easily addressed. In reviewing the final layout problem, the surveyor may need to re-consider the
setup location as several distances are long; sighting the point may be difficult unless the optics of
the instrument are good. In any event, to verify the correctness of the layout the points will need to
be checked from another location or by a different method.