Topographic
Survey for Installation of
Swimming
Pool on Old Main Lawn,
The
PSM
Surveyors, L.L.C.
CE 209.01,
Group #6
Stephanie
Rea
Melissa
Herder
Mr.
Dan Luther
105
Sackett Building
Re:
Proposal for Surveying Services
Old Main Lawn Swimming Pool Installation
Dear
Mr. Luther:
We
appreciate the opportunity to submit this proposal for the topographic survey
located in
- Provide a topographic
survey of Traverse 63-23-83 (Location of Future Swimming Pool
Installation)
- Prepare a Topographic
Map, based on assumed elevation datum of the lot surveyed showing existing
monuments, sidewalks, and trees.
- Contour interval
shall be 0.25m
We
propose to perform the above Scope of Services in accordance with current
hourly rates. The fee for these services
(including expenses) is estimated at $700.00.
The Estimated Hourly Fee shall be billed monthly as work
progresses. Any additional surveying
services (as requested by the Client or the Client’s representative) not
included in the scope of services noted above shall be performed in accordance
with the attached hourly rates.
If
you find that this Scope of Services does not meet your needs, please contact
me and we will make the necessary modifications based on your input.
Sincerely,
Bean-O,
P.L.S.
Surveying
Manager
Table of Contents
Introduction 5
Pace
Calibration/ Traverse Pacing 7
Differential
Leveling and Level Circuit Adjustment 8
Horizontal
Distance and Interior Angle Measurement 10
Topographic
Map Preparation and Radial Traverse 12
Office
Computation Methods 13
Conclusions 18
Appendix
A: Calculations
Pace Calibration and Traverse
Pacing Data A2
Differential Leveling and
Level Circuit Analysis Data A3
Horizontal Distance and
Interior Angle Measurement Data A4
Raw Topographic Data A5
Traverse Computation
Tables A6
Traverse Sample
Calculations A8
Appendix
B: CAD Drawings
Lab #2 B2
Lab #3 B3
Lab #4 B4
Lab #6 B5
Summary of Figures, Tables, and Calculations
Figure 1. Layout of Traverse Points 4
Table 1. Pace Calibration Data and Calculations A2
Table 2. Traverse Pacing Raw Data and Adjusted
Azimuths A2
Table 3. Differential Leveling and Level Circuit
Analysis Raw Data A3
Office Computations for Differential Leveling A3
Table 4. Tabulation of Differential Error
Adjustments A3
Table 5. Raw Data for Measurements of Horizontal
Distances by
Total Station A4
Table 6. Raw Data for Interior Angle Measurement A4
Adjusted Interior Angle Computations A4
Table 7. Adjusted Angle Measurement A4
Table 8. Summary of Field (Unadjusted Data) 15
Table 9. Summary of Adjusted Data 15
Table 10. Raw topographic data from data collector
A5
Table 11. Tabulated Calculation of Azimuths for
Traverse Points A6
Table 12. Summary of Calculations for Latitude and
Departure Corrections A6
Table 13. Summary of Northing and Easting
Calculations A6
Table 14. Adjusted Traverse Distances and Azimuth
calculations A7
#83 #23 #63
Figure 1. Plan view of Old Main Law
and Traverse. The team surveying points are shown.
Introduction
Surveying
is defined by Wolf and Ghilani as, “the science, art, and technology of
determining the relative positions of points above, on, or beneath the earth’s
surface, or establishing such points.”
More generally, surveying provides a means of gathering data regarding
the boundaries and site features for an area of land. MPS Surveyors, L.L.C. has been contracted by
the department of Civil Engineering to conduct a series of surveys of Old Main
Lawn on the
The
intended purpose of this of series of surveys was to produce a relatively
accurate topographical map with key site features correctly located. The four intended surveys were used to
establish a basis for determining the overall accuracy of the survey and act as
a control group within the context of each individual survey. An obvious beginning point in order to get a
“feel” for the site and spatial orientation was to establish a pacing length
for each member of the surveying crew.
This allowed the crew to evaluate data produced by the other three, more
sophisticated, means of surveying. The
pace lengths determined by the crew enabled the members to locate appropriate
intermediate points to set up the automatic level for initial elevation
readings based on known benchmarks.
Prominent site features were then located using horizontal distance
measurements between the established points of control, traverse points #23,
#63, and #83, and calculating the interior angles of those points. Finally, the horizontal and vertical
locations of key features and other points of elevation interest were
determined using the method of radial traversing.
Surveying
plays a key role in engineering, construction, and transportation, and
consequently, the degree of accuracy and precision are of great
importance. Properly establishing
boundaries, property lines, site features, and elevations are crucial to
successful completion of projects. It is
of the utmost importance that all sources of error be identified if possible
and dealt with accordingly to validate the survey. Such sources of error include systematic
errors and random errors. Systematic
errors are biases on the part of the observer, environment or instrument. Systematic errors can be eliminated through
mathematical means if the conditions producing the errors remain constant. Random errors on the other hand are caused by
factors beyond the observer’s control, but obey the laws of probability. Random errors can be eliminated most of the
time by an adjustment procedure known as least
squares. Fortunately, random errors,
by their very nature, tend to cancel each other out.
Finally,
benchmarks, as mentioned above, play a key part in the validity of a
survey. Benchmarks provide a point of
known elevation and location as determined by a previous survey such as GPS
(global positioning system) surveying.
Benchmarks are usually permanent features or monuments. The accuracy of these points enables control
points to be established for the area to be surveyed and also provides a system
of verifying the consistency of points within a traverse. A useful source of information for locating
benchmarks is the Land Surveying and Geomatics: On-line Resource, which
references the North American Vertical Datum of 1988 (NAVD88). The benchmarks used during this surveying
exercise were located on the steps of the Old Main and Sackett buildings on the
Lab #2: Pacing Calibration and Traverse Pacing
Date:
Weather: Sunny and calm, 80º F
Location: Old Main Lawn, The
Equipment: Fiberglass tape, range poles, compass
Purpose:
§
To
calibrate the pace length of each student
§
To
understand the basic concepts of measurement statistics
§
To
become oriented to the traverse (63,23,83) that is the assignment for the
semester
§
To
learn a coarse method for measuring lengths and directions of lines
Procedure:
The two activities performed in this lab were pace
calibration and traverse pacing.
During pace calibration, we used range poles and
fiberglass tape; each group member paced 30 meters 10 times and recorded the number
of paces for each 30 meter length. The averaged pace was calculated from this
data and used as a basis for comparison with other surveying methods.
During traverse pacing, we used the pacing
calibration as discussed above to measure the length of each leg of our
traverse. Each traverse leg was paced twice by the same person to avoid
blunders and help ensure accuracy; the two distances were averaged to determine
the actual paced distance. Using the compass, we measured the azimuth angles,
and then corrected it for the 11º west declination. To minimize error, we also
measured the back azimuth and subtracted 180º if appropriate to compare with
the azimuth.
Field Computations:
Field computations include determining the average
length of pace for each group member, averaging the distances paced for each
traverse leg, correcting the azimuth for 11º west declination, and subtracting
180º from the back azimuth if appropriate in order for averaging with the
azimuth.
Reference drawings for
Lab: See Appendix
B, page 1
Error Statement:
Our compass reading was calculated to the nearest
1º. Therefore, error allowance for the compass reading is
Lab #3: Differential Leveling and Level Circuit Adjustment
Date:
Weather: Partly cloudy with light wind, 78º F
Location: Old Main Lawn, The
Equipment: Automatic level, fiberglass level rod, rod level, turning point
Purpose:
§
To
determine the adjusted elevation of the stations of the traverse (63,23,83)
§
To
become familiar with mathematical adjustment procedure for a single level loop
Procedure:
The automatic level was set up at the approximate
mid point between the Old Main benchmark and traverse point 23. The foresight and back sight readings were
taken. The level was then moved to a
point half way between traverse point 23 and an arbitrary turning point between
traverse points 23 and 63. Foresight and
back sight readings were once again taken.
The level was then moved halfway between the turning point and traverse
point 63 in order to complete that leg of the traverse by taking another
foresight and back sight reading. The
level was repositioned midway between traverse point 63 and another arbitrarily
chosen turning point along the line of traverse points 63 and 83. Foresight and back sight readings were
taken. That leg of the traverse was
completed by moving the automatic level half way between the turning point and
traverse point 83 and taking foresight and back sight readings. The level was then moved to a point between
traverse point 83 and a final arbitrarily chosen turning point. Foresight and back sight readings were once
again taken. The final leg of the
traverse was completed by repositioning the level midway between the turning
point and the
Field Computations:
Field computations include adding the back sight
to the previously determined elevation, then subtracting the foresight reading
from this value to obtain the elevation for the next leg of the traverse. The total back sight readings were summed, as
were the foresight readings. A page
check was performed by adding the back sight summation to the elevation of the
Old Main benchmark and then subtracting the foresight summation. This value was then compared to the elevation
of the
Reference drawings for
Lab: See
Appendix B, page 2
Error Statement:
Error of closure was determined using the equation:
Callow = 12√k, where k =
the total distance of the traverse divided by 1000.
Cactual was compared to Callow and found to be within
tolerances. (3 mm < 7.339 mm)
The actual error realized over the course of our
traverse was -0.003 m. This error can be
attributed to slight user errors in keeping the rod level while the reading was
being taken. Additional errors include
set up and leveling of the automatic level and the random errors associated
with reading foresight and back sight errors to the nearest 5mm. Overall, our traverse was well within the
range of acceptable error; therefore, the survey is acceptable.
Lab #5: Horizontal Distance and Angle Measurement Using the Total
Station
Date:
Weather: Sunny and cool, 65º F
Location: Old Main Lawn, The
Equipment: Total Station, Prism Pole, Plumb Bob
Purpose:
§
To
determine the length of the sides of a traverse using a Total Station
§
To
determine the adjusted interior horizontal angles of a geometrically closed
traverse using a Total Station
§
To
become familiar with the procedure for horizontal distance measurement by EDM
§
To
become familiar with the IDR method for horizontal angle measurement
Procedure:
During this lab, we learned to properly set up and
care for a total station instrument, and used it to measure distances and
horizontal angles.
The total station had to be set up over each
traverse point in order to measure the distances between them. To set up the total station instrument, it
first was screwed onto the tripod and rough leveled. It was then centered precisely over the traverse
point and fine leveled. The machine was
checked for battery power and corrected for atmospheric conditions and
parallax, and then zeroed.
To measure the horizontal distance of the traverse
legs, the total station was set up over the first point (#63), and the prism
pole held vertically over the back sight (#23).
Using levels for precision, the distance between these points was shot
by sighting the prism pole reflector.
The prism pole was then moved to the fore sight (#83) and the distance
was shot with the total station. This
process was repeated for all three stations.
This method allowed us to double check each distance for accuracy.
To measure the interior horizontal angles of the
traverse, the theodolite mode of the instrument was utilized. The back sight from station #63 to station
#23 was chosen as 0º00’00”, and then the 1DR (once direct, once reversed)
method was used to double check our numbers for accuracy. This involved shooting from the back sight to
the fore sight, returning to the original location, and then shooting again and
dividing by two. Plumb bobs were used to
center the sight over the back sights and fore sights. This process was repeated for all three
stations.
Field Computations:
Field computations include averaging the distances
and angles read from the total station instrument, adjusting the angles using
the average correction method, and calculating the allowable and actual
misclosures for error comparison.
Reference drawings for
Lab: See
Appendix B, page 3
Error Statement:
The least count of the Sokkia SET5A is 5”, and the
smallest increment of angle measurement is 2.5”. The error in our measurements was calculated
by comparing the allowable misclosure:
CALLOW =
1.5(L.C.) √n = 12.99” ≈ 13”
with the actual misclosure:
CACTUAL = (Mean
Angle Sum)/180º = 0º00’02”
Since 2” < 13”, the survey measurements are
OK.
Lab #6: Topographic Map Preparation and Radial Traverse
Date:
Weather: Sunny and cool, 50º F
Location: Old Main Lawn, The
Equipment: Total station, prism pole, cloth tape, spikes, plumb bob
Purpose:
§
To
perform a radial survey from a known baseline to determine horizontal and
vertical locations (x,y,z) of various points
§
To
collect topographic map information within a defined area
Procedure:
First, the total station was set up at the first
traverse point, #63, and leveled using the methods we had previously learned. The
prism height was set and measured to the nearest, as well as the height of the
total station. The baseline azimuth was set using the THEO mode. One group
member walked to another traverse point (either #23 or #83), and used a leveler
to hold the prism pole straight. The total station button “Sdist” (in EDM mode)
was pressed in order to measure the slope, vertical angle, and horizontal angle
to the prism pole, while the data collector displayed the prism height and the
horizontal distance.
Following measurements of data for the traverse
points, information was collected for various random points and landmarks, such
as trees, sidewalks, and flagpoles. Each group member took 10 shots each to
collect this information. Sidewalks required three shots, two to determine the
line of the sidewalk, and one to determine sidewalk width. Trees required two
shots, one to determine the slope distance, and one to determine the angles.
After taking 10 shots, we would return to the traverse point to measure again,
in order to check that the baseline azimuth had not been reset.
Field Computations:
Field computations including double-checking the
angles the total station and data collector gave us. Equations used include H=
Ssinq
and V=Scosq,
where S is the slope distance and q is the vertical angle. We
also used EB = EA + hi +V – prism height to check
elevations. See Appendix B for sample calculations.
Reference drawings for
Lab: See
Appendix B, page 4
Error Statement:
All field notes with horizontal distances were
recorded to the nearest 1 cm. Since total linear error was calculated to be
0.005 m and the distance was 239.77 m, the precision was 1:48129. Since total
station error should range between 1:5000 and 1:100000, our error is acceptable.
Sources of error would include not holding the prism pole vertically level, not
holding the rod with the same pressure at each point (i.e. the rod could be in
the ground on grass, but just resting on the aluminum disks), and
unintentionally resetting the baseline.
Office Computation
Methods Based on Raw Data
Collection
Introduction
to Office Methods
Field Data Summary:
Raw data was collected in the field to determine
elevations, interior angles, and distances between points. Following the
gathering of this information, a data collector and total station was used to
determine the topographic points. This section is broken into two parts that
discuss each of these areas.
First, the determination of elevations, interior
angles, and distances as they related to the first three labs and procedures
will be discussed. An explanation of the errors found and resulting adjustments
to the field data will be included, as well as a reference to both tabulated
raw data and tabulated adjusted data (found in Appendix A).
The second part of this section will address the
topographic map raw data and explain how points on the map were determined. An
explanation of errors, tabulated adjusted values, and references for each will
be given.
Points Provided by
Instructor:
The instructor provided the back azimuth for line
63-83 as 305º26’00”. Also provided were the Northing (X) as 966.305 m and
Easting (Y) as 983.751 m. This allowed us to determine the topographic map for
the area in question.
Determination
of Elevations, Interior Angles, and Distances
Pace Calibration and
Traverse Pacing:
For pace calibration, each surveyor paced a 30 m
length 10 times, recording the number of paces for each leg. The average
distance per pace was then calculated. Sample calculations for one surveyor can
be found in Appendix A, Table 1.
During traverse pacing, each group member paced
one leg of the 63, 23, 83 traverse. The number of paces from the calibration
exercise was recorded and the distance determined. The azimuth and back azimuth
for each line was recorded. This raw data was adjusted for the 11o
west declination. Both the raw data and the adjusted angles can be found in
Appendix B, Table 2.
Differential Leveling and
Level Circuit Analysis:
Using the bench mark elevation (given by the
instructor) on Old Main of 356.121m and the BM for Sackett of 353.549 m, the
survey team collected raw data including the back sight, elevation, forward
sight, and the distance traversed. The distance traversed was determined using
the pacing calibration as previously discussed. Unadjusted
elevations were determined by adding the back
sight (BS) to the BM elevation to get the HI, and then by subtracting the
foresight (FS) to get the unadjusted elevation for a point. Both the raw field
data and the calculated unadjusted elevations can be found in Appendix A, Table
3.
Adjustments were made based on the closure error,
which was found to be -3mm by subtracting the final BM at Sackett from our
actual measured elevation. Although this closure error is about half of the
allowable error of 7.34 mm, error adjustments were calculated through ratios
and rounded to the nearest 5mm, and added to the unadjusted elevations to
determine the final values. Sample error and adjustment calculations for can be
found in Appendix A, page 2. Appendix A, Table 4 shows the tabulated error and
adjusted elevation values.
Horizontal Distance and
Interior Angle Measurement:
After determining the adjusted elevations for each
of the traverse points, the survey team measured the horizontal distance and
interior angles.
For horizontal distances between the traverse
points, the total station was used. Each distance was taken twice to avoid
blunders; the mean of these distances was taken as the final value. This raw
data can be seen in Appendix A, Table 5.
Interior angle measurements were also taken using
the total station. A direct and reverse angle reading was taken for each point
in order to avoid blunders. The unadjusted angle was then calculated by taking
the mean of the direct and one-half the reverse angle. See Appendix A, Table 6
for the raw field data and unadjusted values.
Allowable misclosure for the interior angles
measured was calculated using least count of the instrument being 5” and the
equation 1.5 L.C. Ö3. Allowable misclosure was found to be
13”; actual misclosure, determined by summing the mean interior angles and
subtracting 180º from this value, was found to be 2”. The survey was determined
acceptable because the actual misclosure was much greater than the allowable. Sample computations for
misclosure can be found in Appendix A, page 3.
Finally, angle adjustments to the interior angles
were calculated based on the 2” error found during misclosure calculations.
Using the average correction method, the average adjustment was 2”/3 legs, or
0.667”. Errors were rounded to the nearest 2.5” because this is the smallest
unit of angular measurement for the instrument. Because error is accumulated,
the total average correction was the sum of all corrections, which was then
used to determine successful differences between each point. The successive
differences were added to the unadjusted angles to arrive at the adjusted
angles. Table 7 in Appendix A shows a tabulation of the error and adjusted
angles.
Summary of
Raw and Adjusted Data for Determining Elevations, Interior Angles, and
Distances
The summary data shown in Tables 8 and 9 summarize
the material collected in the first three labs. Table 8 shows the unadjusted values;
Table 9 shows the adjusted values. Notice that, especially for elevations, our
values are the same. This is due to the fact that our error was very small.
Elevation values were obtained from differential leveling. Distance values were
obtained from measurements with the total station (the third lab listed); these
compared similarly with those from the traverse lab. Interior angles were
determined from the third lab using the total station.
Table 8. Summary of Field
(Unadjusted Data)
Table 9. Summary of
Adjusted Data
Topographic
Map Preparation/Radial Traverse
Collection of Unadjusted
Data
After gathering the previous information, the survey
team used a data collector and total station to map topographic points for the
determination of contours in the topographic map. Raw data collected includes
the slope distance, vertical angle, horizontal angle, horizontal distance, and
elevation of each point. To avoid blunders, the final information gathered was
compared with the material previously gathered and shown in Table 9 above. Raw
data from the data collector (including the ASCII file) can be found in
Appendix A, Table 10.
In addition to comparisons with previous data, we
checked the unadjusted elevations and the horizontal and vertical distances for
each point. Elevations were determined by knowing the elevation at one certain
point. Since the team knew the elevation at 63 was
352.534, we could check the elevation at point 83
by using the equation Elev83 =
Elev63 +h.i. +V – prism height. For checking the horizontal
& vertical distances, the equations used were H=S cos q and V = S sin q, where S is the slope
distance and q is the vertical angle.
Sample calculations for topographic map preparation can be found beginning on
page A8.
Determination of Adjusted
Data
After gathering the traverse data, a known back
azimuth of line 63-83, 305º26’0” was used to calculate the azimuths for each of
the three traverse legs. Calculations were preformed by adding the field angle
to the back azimuth for each traverse leg to determine the azimuth. To
determine the back azimuth of the next leg, 180º was added if the azimuth was
less than 180º; 180º was subtracted if the value was greater than 180º, but
less than 360º. If the value of the azimuth was greater than 360º, 360º was
subtracted to arrive at the next back azimuth. Detailed calculations for this
data can be found in Table 11, Appendix A.
To adjust the azimuths found in the previous
steps, latitudes and departures were first determined, which allowed for
latitude and departure correction. It was determined that the overall latitude
correction needed was -0.00498m, and that the departure correction was -0.00009
seconds, both of which are very small values. The adjusted latitudes and
departures were found using the equations below.
Latitude = Distance * cosq, where q is the azimuth
Latitudecorrection = -∑Latitudes
* Distance/∑Distances
Adjusted Latitude = Latitude + Latitudecorrection
Departure = Distance * sinq, where q is the azimuth
Departurecorrection = -∑Departures
* Distance/∑Distances
Adjusted Departure = Departure + Departurecorrection
Azimuth corrections were then determined by taking
the cotangent of the adjusted departure/adjusted latitude, and then adjusting
that value based in if the signs of the adjusted latitudes and departures.
The Northing and Easting for each traverse point
by beginning with the known Northing and Easting for point 63, which was given
by the Instructor. To obtain the Northing for the next point, the adjusted
latitude was added to the previous elevation; to obtain the Easting, the
adjusted departure was added. Area of the traverse was obtained using the product
method. Northings and Eastings were
multiplied diagonally in each direction and summed. The sum obtained by
multiplying from left to right was subtracted from the sum
calculated from right to left, and the average
taken to determine the traverse area. Detailed calculations can be found in
Appendix A, page A10.
Finally, error and precision were determined. The
linear error of closure, which was found to be 0.00498 meters, was calculated
using LEC = (∑Latitudes2
+ ∑Departures2)1/2. Relative error of closure
was calculated by dividing the error by the distance traveled; our relative
error was extremely small, at 0.00002. See detailed calculations in Appendix A,
beginning on page A9.
Conclusions
We
here a MPS Surveyors, L.L.C. believe the accuracy of our work to be well within
tolerable error limitations. We have
been careful to ensure that enough surveys were conducted to be confident that
errors were eliminated or compensated for appropriately. The information provided by our work is of a
quality that will make the construction of the swimming pool and subsequent
landscaping able to proceed on schedule.
A
note on errors:
Errors
from one survey are capable of being transferred into the next survey,
compounding with the errors generated during the next survey. This phenomenon of error propagation may
result in surveying data that contains such gross errors as to invalidate the
survey. However, by conducting a sufficient
surveys and checking data to make sure it is reasonable before leaving the
site, the errors propagating from the first survey through the fourth survey
have little impact on the final accuracy of the report. Each individual survey contained sufficient
redundancy checks to validate the accuracy and precision of the other surveys.
MPS
Surveyors, L.L.C. also prides itself on being able to tell our clients that we
encountered no errors during this surveying exercise. Thank you for your business, and enjoy your
new recreational facility.