Transcript Final-Presentation-RET

The Power of Math
by Lauren Sanderson
mk
Final Presentation
DATE
Knoxville, Tennessee
This FNET Map Gradient Display tries to keep the frequency right at 60
Hz and the amplitude at 120 Volts.
Video:
https://www.youtube.com/watch?v=FaxsaQkdrkk
Figure 1: Image taken from http://fnetpublic.utk.edu/gradientmap.html
Have you ever heard of a power outage? Do you know what causes a power
outage? Look at the graph below.
Figure 2: Image taken from https://www.youtube.com/watch?v=awvS4TtN77E
Project 1: Keep it Frequent!
• Students will understand that there has to be exactly enough power on the grid
for what is being used by consumers after watching the assigned videos and
reading the assigned articles.
• Students will use their knowledge of how to recognize and construct sine
functions to determine how frequency, amplitude, and DC offset will change
what a light bulb does.
• They will conduct an experiment that will show the effects on two different light
bulbs.
• The class will use their discoveries to discuss how this experiment relates to the
sine function and real-life situations. They should address how our world would
be affected if we had a power outage.
• Then, using the oscilloscope, they will see the exact sine curve that the voltage
makes.
4
Project 1 Summary (continued)
• After the experiment, students will research how electrical engineers use
trigonometry every day. They will also use a simulator for trig functions on
a graph and the unit circle.
• Students will analyze what contributions relate to changing the efficiency of
the light bulb and how it could affect the power grid. They should make the
connection that if our sine waves do not stay constant on the FNET, we
could have a power outage.
• Students will then write a discussion board post detailing what they have
learned about electricity, the power grid, light bulbs, and the relevancy to
trigonometry.
Materials Needed
• NI myDAQ equipment (one per group)
• computer (one per group)
• download NI ELVISmx Instrument Launcher (should be done by the
teacher prior to the experiment)
• breadboard (one per group)
• two LED lights (per group)
• pencil (one per student)
• paper (two or three sheets per group)
• calculator (one per group)
NI myDAQ Instrument
•
Figure 3: myDAQ image taken from https://www.google.com/search?q=myDAQ&espv=2&biw=1002&bih=605&source=lnms&
tbm=isch&sa=X&ved=0ahUKEwi52KzIiZvNAhUHYyYKHXeQD8cQ_AUIBygC&safe=active& ssui=on#imgrc=ipa5ddFPidxqcM%3A
Function Generator
Figure 4: Function Generator image taken from https://www.google.com/search?q=myDAQ&espv=2&biw=1002&bih=605&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi52KzIiZvNAhUHY
yYKHXeQD8cQ_ AUIBygC&safe=active&ssui=on#safe=active&tbm=isch&q=ni+elvismx+instrument+ launcher&imgrc=QhZ8-lPEXZMxuM%3A
Student Procedure
Videos to watch before the experiment:
Get Started Using NI myDAQ with LabVIEW for Education
https://www.youtube.com/watch?v=RsD2tHbuAF4
AC vs DC Explained and How to Use an Oscilloscope
https://www.youtube.com/watch?v=8VEg6L2QG5o
Online Articles (read before the experiment):
Oscilloscope
https://learn.sparkfun.com/tutorials/how-to-use-an-oscilloscope
How to Use a Function Generator
https://www.youtube.com/watch?v=jWDJeiH6veQ
Breadboards
http://education.curent.utk.edu/wp-content/uploads/Breadboard-.pdf
Student Procedure (continued)
• On the breadboard, plug in the red cord to the second hole from the top
left.
• Plug in the black cord to the first hole on the top left.
• Take an LED light and put it in the fifth hole down from the left side,
• to the first and second hole.
• Once you have all of those securely fastened, on your computer, change
the DC offset to 2.1 Volts, have the AC Voltage Amplitude at 0 Vpp, and the
frequency at 100 Hz.
• Adjust the DC Offset to different positive and negative voltages. Record in
the chart what you notice.
Student Procedures (continued)
• Select “Stop” and change the DC offset to 0 V (Volts). Keep the frequency
at 100 Hz (Hertz). Change the amplitude to no more than 5 Vpp (peak-topeak Voltage). Record in the chart what you see.
• Change the frequency between 1 - 10 Hz, the amplitude between 3.2 – 10
Vpp, and leave the DC offset at 0 V. What do you notice? Write it down.
• Adjust the frequency between 11 - 34 Hz. What do you notice? Write it
down.
• Take the second LED light and put it 10 holes down on the left hand side.
Make sure the frequency is between 1 – 10 Hz. What happens?
• Adjust the frequency between 11 – 34 Hz. What happens?
How does this relate to trigonometry?
• Students will help me come up with a graph to represent when the light
bulb was shining and when it was not.
• There should be a relationship between their graph and a sine curve.
• We will discuss how changing the a value and b value in our sine function:
y = a sin bx will affect the graph and the lightbulb.
• They will use the oscilloscope to see the sine waves.
• Students will research how electrical engineers determine what frequency
and amplitude is needed to make use of the Power grid most efficiently.
• Students will write a discussion board post detailing what they observed
during the experiment and how it relates to math.
Voltage
4
3
2
1
0
0
5
10
15
20
-1
-2
-3
-4
Voltage
Light not visible
Light not visible
25
30
35
Oscilloscope
Figure 5: image take from:
https://www.google.com/search?q=oscilloscope&espv=2&biw=1002&bih=568&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjSlOrT2rbNAhVJ2T4KHehDB9AQ_AUIBygC&safe=active&ssui=on#safe=active&
tbm=isch&q=oscilloscope+from+computer+screen&imgrc=1hg5pK7IsxLzZM%3A
Extension: Simulator for Trig Functions
•
Figure 6: Image taken from: https://phet.colorado.edu/sims/html/trig-tour/latest/trig-tour_en.html
Project 2: Light Bulbs Are Curvy!
Figure 7: Trigonometry Clip Art image was taken from
https://www.google.com/search?q=trigonometry+clip+art&espv=2&biw=1002&bih=612&source=lnms&tbm=isch&sa=X&ved=0ahUKEwioyM6P9bbNAhVG6SYKHX8KAjUQ_AUIBigB&safe=active&ssui=on#im
grc=CFAaKehp5PYf5M%3A
Project 2: Summary
• Students will have to watch the video on how light bulbs work and read the
assigned online articles to get an idea of what a power factor, watt, and the
power grid is.
• Video:
How Modern Light Bulbs Work
https://www.youtube.com/watch?v=oCEKMEeZXug
• Assigned Articles:
http://energy.gov/science-innovation/electric-power
http://energy.gov/science-innovation/energy-sources
http://energy.gov/energysaver/lighting-choices-save-you-money
• Next, they will conduct an experiment of three different light bulbs to
determine what their power factor is, the temperature, and the amount of
watts used.
• They will have to determine which lightbulb is the most efficient for the
power grid and which one is the cheapest for consumers.
Summary of Project 2 (continued)
• Once the students have learned about the power factor, they should use
their prior knowledge to graph a cosine function.
• There will be a discussion on how the graph will change. The relationship
between the power factor and cosine graph should be discovered.
• The formula for the basic cosine graph and transformed cosine graphs
should be discussed.
• The class will use their discoveries to discuss how this experiment would
change in a real-world situation. Students will write a letter to their parents
explaining which light bulb they should be using throughout their house.
Summary of Project 2 (continued)
• After the experiment, discussion, and letter, students will use a simulator
for sine or cosine curves and see if the skateboarder has enough speed to
get over the curve.
• Next, students will research how electrical engineers determine what
voltage they need to put on the power grid and what could affect the power
factor from not being close to one.
• Students will then write a discussion board post detailing what they have
learned about the power grid, the power factor, cosine equations, cosine
graphs, and applications within real-world situations.
Materials Needed
•
•
•
•
•
•
•
•
•
•
Computer (one per group) to read the articles and watch the video
Experiment data collection sheet (one per group)
Infrared Thermometer (one per group)
Kill-a-watt meter (one per group)
LED light bulb (one per group)
Incandescent light bulb (one per group)
Compact fluorescent light bulb (one per group)
Three Lamps (per group)
Pencil (one per group)
Paper (two or three sheets per group)
Infrared Thermometer - used to determine the temperature of the light
bulbs
Figure 8: Infrared Thermometer image taken from
http://usa-shop.online/good/32374063240?gclid=CLyKm4zFvs0CFUw6gQod0y4MwQ
•
Kill A Watt – used for the power factor and the amount of watts used
Figrure 9: Kill-a-Watt image taken from https://www.google.com/search?q=kill-awatt&espv=2&biw=1002&bih=605&source=lnms&tbm=isch&sa=X&ved=0ahUKE
wjuxd37zJvNAhXQdSYKHV9XBlIQ_AUICCgD&safe=active&ssui=on#imgrc=sdaT1bxKlq4J5M%3A
Incandescent Light bulb
Figure 10: Incandescent light bulb image taken from
https://www.google.com/search?q=incandescent+light+bulb&espv=2&biw=1002&bih=605&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiF2N2S0JvNAhV
EcRQKHWXIDvQQ_AUIBigB&safe=active&ssui=on#imgrc=113abVDqvtriAM%3A
LED Light Bulbs
Figure 11: LED light bulbs taken from
https://www.google.com/search?q=led+lights&espv=2&biw=1002&bih=605&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjH0um7uJ3NAhWEZiYKHTwIC
YIQ_AUIBygC&safe=active&ssui=on#imgrc=gvZ72QLBYeubBM%3A
Compact Fluorescent Light Bulb
Figure 12: Compact fluorescent light bulb image taken from
https://www.google.com/search?q=led+lights&espv=2&biw=1002&bih=605&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjH0um7uJ3NAhWEZiYKHTwIC
YIQ_AUIBygC&safe=active&ssui=on#safe=active&tbm=isch&q=compact+flourescent+lightbulbs&imgrc=tk6l-eIPba-dFM%3A
Student Procedure
• Read the online articles and watch the video that was assigned.
• Make a prediction for which light will be the most efficient for the power grid
and which light bulb will be the cheapest for the consumer.
• Turn on the lamps.
• Turn on the infrared thermometer and point it at the light bulb. Record the
temperature from each light.
• Plug the cord from each lamp into the Kill A Watt meter and record the
power factor and how many watts are being used.
• If time permits, explore what happens when you plug in your laptop and
change the brightness. Try your cell phone.
The power factor will stay constant when there is a good resistor. This
would be represented by a cosine graph. The graph of the current will
stay in alignment with the voltage when we have a resistor .
When there is not a resistor acting with a current, you might have an
inductor. The inductor would cause the graph to be shifted to the left
due to magnetic field. This causes a misalignment of the two waves
which causes our power factor to be less than one. This could look
something like the graph below. The blue line represents our voltage
and the red line represents the current that has an inductor
When there is a capacitor reacting with a current, the current will shift to the
right. It will look similar to the graph below. The blue line represents the
voltage. The red line represents the current with the capacitor
The Math Behind it All
• We are starting off with the standard formula for a cosine curve, which is
y = a cos b(x). The a value will represent our amplitude, which is how high
or low the graph will go from zero.
• Another way to calculate amplitude is to subtract the minimum from the
maximum, and then divide by two.
• The b variable will help us find the period. The period is the length of one
cycle. To calculate the period for a cosine function, we will have to set the
period equal to two times pi divided by b. You will have to cross multiply to
determine what b is equal to.
MATH! (continued)
• When we have an inductor or capacitor, the graph will be shifted to the right
or to the left.
• The standard formula for a transformed cosine function would be
y = a cos b(x – h) + k.
• If the h value is positive, the graph will be shifted to the right. If the h value
is negative, the graph will be shifted to the left.
• If the k value is positive, the graph will be shifted up. If the k value is
negative, the graph will be shifted down.
Experiment
• Start with three different kinds of light bulbs. We will use an incandescent,
compact florescent, and LED light bulb. Determine the power factor, the
temperature, and the amount of watts being used for each light bulb. What
can you conclude about this? Which light is the most efficient for the power
grid? Which light will be the cheapest for the consumer?
Extension: Simulator for curves
•
Figure 13: Image taken from: https://phet.colorado.edu/sims/html/energy-skate-park-basics/latest/energy-skate-park-basics_en.html
Project 3: Wind Turbine Power Calculations
Figure 14: image take from:
https://www.google.com/search?q=oscilloscope&espv=2&biw=1002&bih=568&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjSlOrT2rbNAhVJ2T4KHehDB9A
Q_AUIBygC&safe=active&ssui=on#safe=active&tbm=isch&q=wind+turbine&imgrc=PuR0bIpfw8ECFM%3A
How a Wind Turbine Works
Figure 15: Image taken from:
https://www.google.com/search?q=oscilloscope&espv=2&biw=1002&bih=568&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjSlOrT2rbNAhVJ2T4KHehD
B9AQ_AUIBygC&safe=active&ssui=on#safe=active&tbm=isch&q=wind+turbine+diagram&imgrc=4nbr4ASlGfQVxM%3A
Figure 16: Image taken from:
https://www.google.com/search?q=oscilloscope&espv=2&biw=1002&bih=568&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjSlOrT2rbNAhVJ2T4KHehD
B9AQ_AUIBygC&safe=active&ssui=on#safe=active&tbm=isch&q=wind+turbine+diagram&imgrc=35Rglzrx1SpR2M%3A
Project 3: Summary
• Students will have to watch the video on how a wind turbine works and
read the online articles to get an idea of what kinetic energy, Betz Limit,
power coefficient, wind speed, mass flow rate, energy flow rate, tip speed,
and rotational speed is.
Video (watch before the activity):
How do Wind Turbines Work?
https://www.youtube.com/watch?v=qSWm_nprfqE
Online Articles (read the day before the activity):
Wind Turbine Calculations
http://www.raeng.org.uk/publications/other/23-wind-turbine
How much Energy is Converted from the Wind by a Wind Turbine?
http://www.weset.org/worksheets/ws-07.pdf
Wind Energy
http://www.umanitoba.ca/outreach/crystal/Wind%20Energy.pdf
Project 3 summary (continued)
• Next, they will have to make some calculations to fill out a chart for the tip
speed, the power coefficient, the amount of power, and the amount of energy for
each given time and wind speed.
• They will have to interpret a chart in order to determine the power coefficient.
There will be a discussion on how a wind turbine converts kinetic energy into
rotational kinetic energy into electrical energy that can be used on the power
grid.
• The class will use their discoveries to discuss how this experiment would
change depending on certain variables.
• After the experiment and discussion, students will use a wind turbine simulation
to change different variables such as blade length, tip shape, blade pitch, airfoil
shape, blade twist, and turbine height to see how we can generate the most
power.
• Next, students will research how electrical engineers predict how much energy
will be produced by a wind turbine for the energy market and why that is
important.
• Students will then write a discussion board post detailing what they have learned
about the wind speeds, power, energy, wind turbines, and applications within
real-world situations.
Materials
• Computer (one per student) to read articles and watch video
• Activity Sheet (one per group)
• Calculator (one per group)
• Pencil (one per student)
• Paper (one per student)
Student Procedure
•
•
•
•
•
•
Read the online articles assigned and watch the video.
Make a prediction as to how the tip speed will affect the power coefficient.
Read over the activity sheet.
Make your calculations.
Fill in the chart.
Analyze the chart that you created. Do you think it is accurate? How do
you know?
• Go to the simulator online and see who can produce the most power for the
most houses.
• If time permits, start researching how wind turbines work and create
energy. Can the energy be transported?
Calculations
The calculation for the tip speed
ratio is as follows:
 = blade tip speed
wind speed
The blade tip speed can be derived
from the length of the blades used
in the turbine and the rotational
speed of the turbine. We will use D
to represent diameter. This can be
done by using the following
equation:
Blade tip speed = rotational speed (rpm) * pi * D
60
Figure 17: Image taken from: http://www.raeng.org.uk/publications/other/23-wind-turbine
Power coefficient (Cp ) versus tip speed curve for wind turbine.
The extractable power from the wind can be calculated from the formula:
Pavailable = (1/2) 𝜌Av3Cp where 𝜌 represents the air density, A represents the
area of the swept area of the turbine, v represents wind speed, and Cp
represents Power Coefficient.
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
12
14
16
Chart to Complete
Wind
Speed
(M/S)
1
3
5
7
9
11
13
15
17
19
21
23
25
27
Total
Time
(Hours)
 Tip
Speed
Cp Value
Power
(kW)
Energy
(kWh)
531
1407
1831
1769
1386
913
524
249
105
39
12
3
1
0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Chart Completed
Wind
Speed
(M/S)
1
3
5
7
Time
(Hours)
Tip Speed
Cp Value
Power (kW)
Energy (kWh)
531
1407
1831
1769
X
X
X
11.67
X
X
X
0.27
X
X
X
483,833.9993
X
X
X
3,386,837.995
9
1386
9.08
0.4
1,523,442.33
13,710,980.97
11
913
7.43
0.42
2,920,558.064
32,126,138.7
13
524
6.28
0.37
4,246,882.838
55,209,476.89
15
17
249
105
5.45
4.80
0.32
0.24
5,642,379
6,160,224.006
84,635,685
104,723,808.1
19
39
4.30
0.18
6,450,179.594
122,553,412.3
21
12
3.89
0.12
5,806,007.991
121,926,167.8
23
3
3.55
0.08
5,085,246.318
116,960,665.3
25
27
Total
1
0
8,770
X
X
X
X
X
X
X
X
23,726,954.06
X
X
655,233,173.1
Extension: Wind Turbine Simulation
•
Figure 18: Image take from http://scienceofeverydaylife.discoveryeducation.com/innovation/labs/wind-energy/wind.swf