Monday, March 5, 2012

TI-Nspire STEM Project Challenge final report

Wind Turbine Blade Quantity Optimization


  • Guiding Question: What is the optimal quantity of blades on a wind turbine?
  • Designers must balance turbine blade numbers between too much weight for wind to offset the inertia of the blades, and too few blades to maximize the amount of wind power gathered.
  • Many other turbine-like systems use three blades, such as outboard motors, aircraft propellors, squirrel-cage fans, and windmills.
  • The need for alternative energy is growing.
  • Energy can be harvested from the wind using turbines.
  • Optimizing the number of blades maximizes the amount of energy collected.
  • Production costs often delay the monetary returns of efficiency.
  • When more turbines are added to a turbine system, the system gains more inertia.
  • Often, turbines with two blades are used for higher wind speeds.
  • Three blades are more efficient than two, due to lesser rotor loading, and fewer aerodynamic losses. They are also quieter.
  • Parts of a Turbine:
  • Tower: wind speeds are faster at greater altitudes.
  • Blade : much like an airplane propellor, turbines use numbers like 1, 2, 3, 4, & 6.
  • Generator : converts kinetic energy to electrical energy.
  • Controller : shuts turbine down at high speeds.
  • Nacelle : cover of generator/controller
  • Anemometer : measures wind speed
  • “Many modern wind turbines use three blades because they give greater dynamic stability than either two blades or one.” (Gipe 104)

Hypothesis -If three blades are used on a turbine, then the turbine will have an optimal rotational velocity.

Experiment - Materials:

  • TI-Nspire CX CAS
  • TI-Nspire Lab Cradle
  • Vernier Rotary Motion Sensor
  • Vernier Hand-held Anemometer
  • PC with TI-Nspire student software
  • Connector USB Cable for TI calculator
  • LEGO set 9688 (Renewable Resources)
  • Crusader floor fan
  • Honeywell squirrel-cage fan
  • Duracraft squirrel-cage fan
  • Fan speeds (measured with anemometer)
  • Low: 1.0 m/s
  • Medium: 5.2 m/s
  • High: 15.3 m/s
  • Procedure
  • Place Duracraft fan a meter away from the makeshift LEGO/rotary motion sensor turbine; connect the turbine to the TI-Nspire lab cradle.
  • Measure the fan output at the turbine using the anemometer and the TI-Nspire.
  • Collect the data for 10 seconds per trial using the Rotary Motion Sensor for six, three, and two blades on the turbine.
  • Repeat the previous two steps with the Honeywell fan, and again with the Crusader fan. All fans should be set to their respective “high” settings.
Variables: Independent - wind speed, blade number, Dependent - rotational velocity of the turbine.

Data & Results

Blade # High (rad/s) Medium (rad/s) Low (rad/s)

3 98.5 86.3 23.8

6 94. 1 67.0 28.0

2 103.2 74.4 27.4

All values are arithmetic averages of the respective data collected.

Error & Uncertainty

  • Used rotary motion sensor backwards, collecting negative data.
  • No wind-speed proportionality to real-life situations.
  • “Spikes” in the data, from sensor errors offset the mean value of the data.


Refutation of Hypothesis

If three blades are used on a turbine, the turbine will have a maximum energy output under medium wind speeds. However, under higher or lower wind speeds, fewer or more blades optimize the amount of energy gathered, respectively.

A Better Experiment

  • Reverse fan blades to switch negative data to positive.
  • Use a LEGO energy sensor to measure the energy output of the turbine.
  • Perform larger more realistic scale tests.
  • Use more realistic wind speeds.

What We Learned

  • Physics behind turbines
  • Using the Vernier DataQuest and TI-Nspire student software more efficiently.
  • Data collection and organization skills.


  • Paul Gipe, Wind Power, page 103, 3, & 4

J-Term Wind Turbine Experience

During a two week internship opportunity in January, I interned at company called Performance Services. They focus on guaranteed energy savings. In order to accomplish these savings, they generally redesign the heating ventilation and air conditioning systems of k-12, healthcare, and higher education buildings. However, another aspect they look at is the viable sources of alternative energy that can complement the energy savings of their current project. During my experience with them, I was able to actually visit a site where they were installing wind turbine for a high school. I learned many interesting things such as: the higher up a turbine is placed the faster the winds will be that it will experience, many people find wind turbines unsightly and the blades of the turbine can cast a very irritating flickering shadow there are differing regulations, depending on state laws, that determine how close a turbine may be to any building or how tall it may be; when a building is not using all of the output of a privately owned turbine, the extra power generated can often be sold back to an electrical company; most turbines are made outside the United States.

From this I learned that a Turbine near Covenant Christian High School is not possible with the current property that Covenant owns. (Covenant would have to purchase property at a more isolated location). However if this were not a problem, then Covenant could very likely own and make a profit and save money with a wind turbine.

Joe Igleski,

Covenant Christian, Junior

Saturday, March 3, 2012

Graphing Conics and x=

At the Teachers Teaching with Technology International Conference we got a glimpse of what will be coming in the next OS release of the TI-Nspire. This OS 3.2 will provide some unique features that will continue to set the TI-Nspire apart as the tool of choice for mathematical exploration.

I am especially exciting about what some may consider to be a little thing: Having the first option under right-click (ctrl menu) from the entry line be to change the type of graph that can be entered in the entry line. (Note: Even from the Menu it is no longer referred to as “Graph Type.” It is now called “Graph Entry/Edit”) This short cut is a much appreciated efficiency.

image of right-click (ctrl menu) from entry line image of menu, Graph Entry/Edit, Equation

Other features that provide reasons to get excited include:
- Graphing vertical lines from the entry line!
- Graphing inequalities like x<-2. To do this type text on the screen. Then drag it to an axis.
- Similarly, graphing inverse equations, like x=sin(y)
- Conics on a Geometry page.

Others are impressed with these features. See their video on YouTube.