Lab 6 - Differential Leveling Assignment (1)
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301
Subject
Civil Engineering
Date
Dec 6, 2023
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Pages
5
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CE 301
–
Civil Engineering Systems
Lab 6
–
Differential Leveling
Page
1
of
5
Laboratory 6 - Differential Leveling
Background
Differential leveling is used to find the elevations of given points by taking measurements from a
reference value or benchmark.
The topography of a land surface must be known for a variety of
different projects, such as highway design, stormwater modeling, and building construction.
Automatic levels are used to measure the change in elevation between two points.
First, a
backsight
is
taken on a point of known elevation, such as a benchmark.
This allows us to calculate the elevation of
the instrument itself.
Next, the telescope is turned to face a point of unknown elevation and a
foresight
is measured there.
The elevation of the new point can be found by subtracting the measured foresight
from the elevation of the instrument.
The backsight tells us how far
above
the benchmark our instrument is.
The foresight tells us how far
below
our instrument point A is.
Thus:
?? = ?
?𝑀
+ ?𝑆
?
?
= ?? − ?𝑆
Where:
HI = height of instrument
E = elevation
BS = backsight
FS = foresight
Backsight
Foresight
Automatic
Level
Level
Rod
Level Rod
Benchmark
Point A
CE 301
–
Civil Engineering Systems
Lab 6
–
Differential Leveling
Page
2
of
5
Problem Statement
In major storms, the runoff of rain that cannot be absorbed by the land can cause flooding, particularly
on impermeable surfaces such as roads.
The Texas Department of Transportation has hired you to
determine whether the majority of water that falls on the plot of land being investigated flows onto San
Jacinto or Dean Keeton so they can design a suitable drainage system.
You set up a closed circuit of points on the corner of San Jacinto and Dean Keaton.
By finding the
elevation of each point, you will be able to draw a rough map of the area and estimate the flow of water
from the top of the hill onto the two streets.
Laboratory Experiment
We will use a simple level circuit to establish the elevations of a series of points on the tract of land at
the corner of San Jacinto and Dean Keeton.
By performing a closed circuit, we can also verify the
calibration of our level rods and our ability to use the equipment correctly.
Before starting your data collection, calculate the permissible misclosure for this circuit.
𝑃?????????? ?????????? = 0.02√?
Where:
n = the number of instrument setups
When you reach the end of the course, you must compare this value to your observed error.
If you are
outside of the acceptable range, you must repeat your measurements.
Data collection:
Draw a map of the points in relation to each other and the neighboring streets.
Set up the instrument between the benchmark and Point A.
Level your instrument using the
bulls-eye bubble level.
Place your level rod on the benchmark.
Focus the telescope on the automatic level and read the measurement off the level rod.
Record
this as your backsight on the benchmark.
Place your level rod on Point A.
Focus the telescope on the automatic level and read the measurement off the level rod.
Record
this as your foresight on Point A.
Move your automatic level to a spot between Point A and Point B.
Take a backsight of A and a
foresight of B.
Repeat this process at each point.
Close the loop by taking a backsight on Point E and a foresight on the benchmark.
This will allow
you to calculate an elevation for the benchmark.
CE 301
–
Civil Engineering Systems
Lab 6
–
Differential Leveling
Page
3
of
5
Tips for accurate readings:
Setting up the automatic level halfway between points will reduce errors due to the curvature of
the earth as discussed in your reading.
Pace between the two points you’re measuring to find a
midpoint and set your automatic level there.
Your level rod needs to be perfectly vertical to take a correct reading.
Sway your level rod back
and forth over the point while your teammates are looking through the automatic level.
The
lowest
value seen on the level rod is the correct reading.
Use a small square of wood to provide a firm, even surface to rest the level rod on at each point.
NEVER
move your automatic level before you have taken both a backsight and a foresight at a
point.
Calculations
Perform a page check when you finish your measurements to verify your calculations.
Page Check:
?
?𝑀
𝐾??𝑤?
+ ∑ ?𝑆 − ∑ ?𝑆 = ?
?𝑀
𝐹𝑖?𝑎𝑙
Find your loop misclosure by taking the difference between your final, calculated elevation of the
benchmark and the initial, known elevation of the benchmark.
𝐿??? ?????????? = ?
?𝑀
𝐹𝑖?𝑎𝑙
− ?
?𝑀
𝐾??𝑤?
= 𝛿
A simple adjustment procedure is used to cancel out the error accumulated during data collection.
The
total loop misclosure,
δ
, is divided by the number of times the instrument was set up, n.
This correction
value is applied to each elevation calculated in increasing proportion.
Thus:
???????? ????????? ?? ? = ????????? ?? ? − 1 ×
𝛿
?
???????? ????????? ?? ? = ????????? ?? ? − 2 ×
𝛿
?
Since the elevation of B was measured relative to the elevation of A, we assume that error has
accumulated through two instrument setups.
Thus, the elevation of E requires the most adjustment.
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Related Questions
FUNDAMENTALS OF SURVEYING 1, FIELD
1.) A backsight reading of 2.73m is taken to a point A and subsequently a foresight reading of 1.35m is taken on point B from a level station established midway between the two points.
a)What is the difference in elevation between points A and B?
b) If the elevation of A is 386.70m above sea level, what is the elevation of B?
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a. Draw the diagram
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c. the vertical stadia distance
d. the elevation on the point where the rod was held
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Surveying Question:
A differential leveling circuit starts at benchmark Concrete Benchmark (Elevation=232.051m) goes out to an unknown benchmark and then continues to a known control point (Elevation=227.975m). Two turning points are used with the measurements included in the attached table.
Determine the elevation of the unknown benchmark
Determine the order and class of the survey.
For First order Class 1:
Allowable Error= +/- 4(K)1/2
Range of Constant= m less than/equal to 4
For First Order Class 2:
Allowable error= +/- 5(K)1/2
Range of constant= m greater than/equal to 4, and m less than equal to 5 (between 4 and 5)
For Second Order Class 1:
Allowable error = +/- 6(K)1/2
Range of Constant = m greater than/equal to 5, and m less than equal to 6 (between 5 and 6)
For Second Order Class 2:
Allowable error = +/- 8(K)1/2
Range of Constant = m greater than/equal to 6, and m less than equal to 8 (between 6 and 8)
For Third Order, Any Class:
Allowable Error = +/-12(K)1/2
Range…
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Latitude
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A lake 280 m long had soundings taken at right angles to its length on ranges 60m, 120m, 200m from one end. The calculated approximate cross sectional areas at each range are: A0 =15 sqm, A60=190 sqm, A120=375 sqm
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RR = 1.95
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Unit: meter
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answer in two decimal places
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rod reading = 1.495m
lower stadia hair reading = 1.245m
stadia constant = 0.381m
stadia interval factor = 95.5
observed vertical angle = -15°30'
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Angle
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