CE 111 Lab 1
Basic Application of Mathematical Tools in Surveying
Objectives: Apply knowledge of geometry, statistics and spreadsheets to problems related to
surveying. Produce a report that demonstrates skills in engineering problem solution to meet
standards of CE 111.
Background
This laboratory contains several problems that are encountered in surveying practice.
The instructors’ primary goal in this laboratory is for you to use previously acquired skills to
develop solutions, and to present the solutions so they are easily understood and checked by
others. Guidance for laboratory reports and problem sets are available on the Web on the CE
111 homepage. Your organizational and problem solving strategies learned in CE 104, CE 160,
ENGR 160 and related courses will be applied. A third resource for general writing guidance is
the department’s Communication Guide which can be accessed from the CE website:
(http://www.cce.iastate.edu/student_rsrcs/commguide.pdf ).
Laboratory reports are presented in Chapter 5.
In this lab, a peer (fellow student) will be the first one to review your presentation to
check on the accuracy of the work, the clarity of your presentation and the attention to detail for
meeting requirements. Help that student out so he or she can return the report with a comment “Good job.”
Section 1: Highway Surveying Problem.
A) Point of intersection of survey lines.
Given: Line 1 has two points for which the coordinates are known.
X=135.50, Y =450.52 and X = 185.48, Y = 678.44
Line 2 is at an angle of 60O 00’ from the positive Y axis (or as we will learn for
surveying, Line 2 has an Azimuth of 60O 00’). A single point is known on this
line. It is X = 455.25, Y = 570.75. See the sketch.
Not to scale:
Line 1
Line 2
The designer will be connecting these lines with a curve and needs to know the point that these
lines would intersect. Develop the solution paying attention to organization, and significant
digits. Appendix A of your text reviews the general solution to this type of problem.
B) Review Example Problem A-4 in Appendix A. The solution to this problem brings out three
key issues that are helpful in general problem solutions:
1) The solution to surveying problems can be eased by temporarily establishing a new
coordinate system.
2) Multiple solutions may be present, the engineer/surveyor must be cautious to select the
appropriate solution..
3) Standard equations using trigonometric relationships, when placed in a general computer or
calculator program, may lead the analyst to an incorrect solution. What can be done to adjust the
equations?
The first two points will be evident as you study the problem. For Item (3), study the
author’s solution to problem A-4 and carefully compare Equations (1.) and (1.A). The author
switched some values. Identify the difference that you see. Could we have a general set-up in
Equation 1 that would avoid the need to change the equation? Do not spend a great deal of time
looking for a “magic solution” at this time. The problem will be addressed in class.
Write one or two sentences on each of the three issues above to show that you
understand how problem A-4 demonstrates the concept mentioned.
Section 2 Variability of Measurements
Several opportunities for error exist in any measured value. In surveying, examples of
sources of random errors are our inability to
 exactly read a value with our measuring device,
 place an instrument exactly over a point, or to
 sight on the exact same point for every measurement.
Throughout the semester we will study these errors further, but the objective of this portion of
Lab 1 is to examine the variations in lab measurements from previous classes to see the pattern
of errors that are typically found due to these random errors. The data set contains estimates of
distances along sides of a survey boundary. The distances were determined by “pacing” , i.e.
estimating the length of a line by counting the number of steps taken along the line. If the
surveyor has calibrated the length of his or her step (pace), the distance can be calculated.
Distance = pace length * Number of paces.
A histogram of the errors and the statistical variations will be developed and examined.
An Excel data file entitled “Pacing_errors” can be downloaded from the CE 111web
page. Save that file to your personal media disk or to the My Documents file on the hard drive if
you are using the CE computer labs. (While working in the computer labs, it is always
preferable to work from the system drive and then save your results back to your drive when the
work is completed).
The file shows results from students’ pacing efforts to estimate line lengths by “stepping - off”
the distance with a calibrated pace. The “Error per 100 feet” variable is of primary concern. A
portion of a similar file is shown here..
Table 1 Example of pacing error data
Reported Reported
Paced dist taped dist
(feet)
(feet)
Measured True
Error
163 164.714
-1.714
160.925 164.714
-3.789
149.95
148
1.95
Error per100
feet
-1.04
-2.30
1.32
The “true distances” were obtained and reported by the students using taping techniques and are
considered to be more reliable than paced distances. Then:
Error = “Paced dist.” - “Taped dist”.
As a general statement, we will always express error as
Error = Measured value – True value
so we have a consistent mathematical sign.
At this stage the instructor has not questioned the reported values of the students. The final
column in the table is the pacing error per 100 foot of line length.
2 .a) Develop Histogram and Chart
Use the Excel histogram function to develop a histogram of the “error per 100 feet” .
Identify your own “bin” sizes so you have at least 6 equal sized bins (except the range of a bin at
each end of your groupings goes to - or + infinity). Select your bin sizes so the expected
average of one of the bins is 0.0 ( Note: A bin with a range from -0.1 to +0.4 would contain 0.0,
but we wouldn’t normally expect the average of that bin to be 0.0). . As a reminder, Excel’s
Histogram algorithms are found under TOOLS /DATA ANALYSIS / HISTOGRAM . The
HELP menu can assist you with the Histogram tool in Excel..
Use the Chart capability to plot the histogram data. Be sure to include descriptive titles
2.b) Based on your previous knowledge of random error distribution, does the histogram have
the shape you expected? Explain.
2 c) Use the spreadsheet to determine each of the following for a sample of size n.:
Mean
= ____________
Standard Deviation of a sample (Sx) = ____________
Variance (Sx2)
= ____________
Standard error of the mean (Sxbar) = ____________ (Sxbar) = (Sx)/√n )
Recall that the standard deviation relates to the range of individual values observed in a sample.
The standard error of the mean is indicative of the range in the mean values, if the means of
several samples of size n were to be evaluated. We would expect less variation among the means
of several samples than we do among the n individual observations of a sample. As seen in the
equation, the deviation in the sample means equals the standard deviation of the individual
observations divided by the square root of the sample size n.
For large samples with normal distributions we expect, with 95% confidence, that the true
mean to be within plus or minus two “standard errors of the mean” of the observed mean in our
sample. In general, the individual measurements would be within plus or minus 2 standard
deviations of the observed mean 95% of the time.
2 c) Because the measuring tools in this survey were not equivalent (different sets of legs in
each case), we can’t justify doing a rigid statistical analysis on these data in the traditional sense.
However, we will need variances and standard deviations throughout the semester. Let’s use
this opportunity to demonstrate that you know how to use your calculator functions to compute
the mean, standard deviation and variance. Using only the three values in column 4 above,
calculate the following:
Mean
= ____________
Standard Deviation of a sample
= ____________
Variance
= ____________
Standard error of the mean
= ____________
If you don’t know how to do these, check with a fellow student, and get out your manual.
Now is the time to learn.
2 d) Experienced surveyors can typically estimate distances by pacing with a relative precision
of +/-1 foot of error per 100 feet. If our novice surveyors would be given an OK only if they
have errors of +/- 1 foot per 50 feet, how of the students in the sample should recalibrate the size
of their pace before doing the pacing exercise again? ( Remember, A single number is not an
acceptable answer; you must explain to the reviewer the basis for your answer)
2 e) Review the reported data from the 30 students.. What consistencies or inconsistencies do
you think exist. I am looking for your thoughts regarding expected precision and reported
precision (significant digits concern).
Section 3 Field Work
In the field - OK, OK this one could be iffy but today the weather is wonderful with no snow
in sight. Each student can begin to assess the variation in his or her own pace and be prepared to
estimate a field distance later. A test course has been set out along the sidewalk running from
the Town Engineering Building towards Howe Hall. The starting and ending points are marked
at sidewalk joints near the fire hydrant southeast of Town Engineering and at a joint almost
directly east of the Design Center Building sign. Prior to Friday of Week One, walk this “course
with a consistent size step that is comfortable to you and record the paces to the nearest 1/2 pace.
Repeat this a minimum of 4 times. To be effective you must keep focused and be careful on this
task
a) The “true” length is 201.9 feet. For each trial, determine your average pace length.
b) From the four+ trials calculate mean and the standard deviation of your pace length.
A measure of your consistency can be obtained by calculating X in the following ratio:
1 / X = (Standard Deviation of Pace Length)./ Mean Pace length
Are you attaining a 1/100 consistency here? (i.e. X = 100 or above when you solve for X? )
How about a 1/50?
If not at least 1/50, you should recalibrate your pace. We will use this skill when we go outside
in the near future.
LABORATORY REPORT
Prepare a laboratory report that addresses all the questions above. Remember that an
organized presentation of your results is key to a good report. A basic title page for the report
must be prepared. The report should begin with your statement of the laboratory objectives and
conclude with a summary of the principal points you learned. The problem statement you are
reading now should be attached to your word-processed report.(Appendix A?).