Lecture 11: Spreadsheets
for Engineering
Applications – part 1
BJ Furman
16APR2012
The Plan for Today
Spreadsheets for engineering applications
- part 1
Charting and data presentation
Example: LVDT calibration
Adding a trend line to data
Numerical integration
Numerical differentiation
Learning Objectives
Create effective charts and graphs
Explain the difference between a line chart
and a scatter plot
Add and format secondary axes
Annotate and format a chart for presentation
in a written report
Find the area under a curve using
trapezoidal integration
Graphical Presentation in Engineering
Presenting data in graphical form is
extremely important!
A picture really is worth a thousand words!
Especially for engineering!
Excel (or other spreadsheet program)
offers very powerful, easy to use graphical
presentation tools.
Get good at using it!
LVDT Sensor
Linear Variable
Differential Transformer
non-contact, friction-free
position sensor
infinite resolution
absolute position
measurement
robust
Need to calibrate
Measure output voltage
as the core is moved
known amounts
Plot voltage vs.
displacement
http://www.rdpe.com/us/hiw-lvdt.htm
http://www.macrosensors.com/images/tutorial_page_images/images/fig1.jpg
http://www.transtekinc.com/assets/images/240ACTION.gif
LVDT application – Road Simulator
http://www.swenox.com/gtc/images/4-axis-durability-rig.jpg
Calibration of LVDT Sensor
Method used by LeroyCrandall Geotechnical
Laboratory
LVDT body
http://gees.usc.edu/soilab/Calibration.htm
LVDT core
core motion
Micrometer head
http://gees.usc.edu/soilab/Photos/Calibration%20Pictures/mvc-159f.jpg
XY Scatter vs. Line Chart
What is the difference?
Different treatment of the x-axis data
XY Scatter Chart: for x data that varies continuously
Interpolating between points makes sense
Ex. temperature vs. time over 24 hrs
Line Chart: for x data that is categorical or equally spaced
Interpolating between points may not make sense
Ex. average lab report score for Tues, Wed, Thurs sections
XY Scatter Chart
o
o
o
o
Line Chart
x-axis data varies continuously
o x-axis data will be equally spaced on
Actual x-axis data that is unequally
the chart (beware!). If the actual x
spaced will be plotted properly
data is not equally spaced, the plot will
good for analyzing trend in data
be misleading.
most often used for engineering
analysis
See: XY Scatter vs. Line Chart.xls
XY Scatter vs. Line Chart, cont.
Smoothed line or not?
Generally, not
Smoothed line can be misleading unless
generating function is a good representation of
actual behavior of the data
Better to leave as points or fit a regression
line/curve that is a likely candidate to describe the
underlying behavior
right-click | Format Data Series | smoothed line check-box
Analyze LVDT Calibration Data
curve fit.xls
Plot data
Add trend line with the
wizard
Get the trend line
using SLOPE(),
INTERCEPT(), OR
LINEST( )
returns an array
formula must be
entered as an array
cntrl+shift+enter
output array is 5 x
nindep_var +1 data sets
Displ. (mm) A/D signal (V)
5.08
8.0188
4.572
7.5003
4.064
6.756
3.556
5.9277
3.048
5.1086
2.54
4.2706
2.032
3.4
1.524
2.5562
1.016
1.6895
0.508
0.8319
0
-0.0256
-0.508
-0.9036
-1.016
-1.752
-1.524
-2.6273
-2.032
-3.4366
-2.54
-4.3106
-3.048
-5.1587
-3.556
-5.976
-4.064
-6.7865
-4.572
-7.4911
-5.08
-8.0548
LINEST() statistics
Adding Data Series
Cases where you might have additional data to
add to a chart
Calculations on a data set
Multiple data sets
Right-click in the plot region
‘Select Data’ (2007) or ‘Source data’ (2003)
Add a data series
Name
X values
Y values
If x values are the same as previous, can just cut-and-paste
Example: LVDT_dataset_for_lecture.txt
Adding a Secondary Y-axis
Sometimes it is useful to plot multiple data
sets on the same graph that have the
same x-values, but vastly different yvalues.
Example: voltage divider.xls
Adding Names to Ranges
Highlight names and values
Result
2003: Insert / Name / Create / Left column
2007: Formulas / Defined Names tab / Create
from Selection / Left column
Formatting Your Chart
Default is probably not the best!
Publication or presentation?
Publication
No fill of chart background
No fill of data point markers
B&W markers, lines, annotation
Use line types that can be differentiated in a B&W photocopy
Maximize chart area
For landscape orientation, title goes closest to the spine
Annotate well
Descriptive title
Labeled axes with units!!
Error bars with measured data
Creating a Figure
Maximize the information transfer
What will the busy (or lazy) reader actually
read of your report?
Structure of figure annotation:
Figure number
Figure title
Figure caption
Really important and often overlooked!
Figure Example
Figure number
Figure title
must be
referred to in
the report
Descriptive
Figure caption
The key
information you
want the
reader to
understand
from the figure
Note inset figure
and additional
annotation for
clarity
(Furman, 1991)
Numerical Integration
Trapezoidal
integration
Ex. area under a
curve
Area Under ( 3+2cos(px/10) )
5
4.5
4
3.5
3
2.5
2
p
y 3 2 cos( x)
10
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Numerical Integration, cont.
Divide into trapezoids
Calculate the area of the
trapezoids
y yi 1
Ai i
( xi 1 xi )
2
Sum areas
Voila!
Results
Exact
21.3661977
Numerical
21.3137515
Numerical Integration (recap)
Can think of
integration as
finding the
area under a
curve
Break area
up into
trapezoids
http://people.oregonstate.edu/~haggertr/487/integrate.htm
Numerical Integration Example
http://www.onid.orst.edu/~hag
gertr/487/integrate.xls
Numerical Differentiation
First derivatives
(Larsen, 2009)
Numerical Differentiation, cont.
Second derivatives
(Larsen, 2009)
Prose vs. a Figure
Which would you rather look at?
Tube wall and reflector pin temperatures
vs. time during the radiative heating
feasibility test.
The focus of the concentrator was brought
into axial alignment with the tube bore at
about t=1.4 s and re-adjusted at about t=5 s.
The radiant flux impinging on the bore of the
tube was estimated to be about 1.65
MW/m^2 from measurements made after the
test. The tube wall temperature rises rapidly
to about 275 ºC in comparison to the reflector
pin, confirming predictions that non-contact
heating using a radiant source and an
internal conical reflector is indeed feasible.
Or
References
Furman, B. (June, 1991). A new, thermally
controlled, non-contact rotor balancing method
(Doctoral dissertation). Available from University
Microfilms International (UMI No. 9205634).
p. 227
Larsen, R. W. (2009). Engineering with Excel,
Pearson Prentice Hall, New Jersey. ISBN 0-13601775-4
Engineering with Excel companion website:
http://www.chbe.montana.edu/excel/EngExcel3.
htm. Visited 25OCT2009.
