Power Output vs. Turbine Blade Pitch Angle
Nick Fillion, Brian MacDonald, Alex Magill
April 27, 2011
Group 3
Abstract
We investigated the relationship between the power output of a wind turbine relative to
the pitch of its blades and the speed at which the turbine was rotating. By modifying the tail rotor
of a remote control helicopter, we were able to construct a horizontal axis wind turbine (HAWT)
that could be dynamically controlled while in the wind tunnel. The results of our testing in the
wind tunnel show that the range of optimal pitch angles increases as wind speed increases. The
knowledge gained from this experiment is easily applicable to future turbine designs. Given the
nature of our experimental rig, it would be very easy for future groups to expand upon our project
and collect a more comprehensive set of data.
1 Introduction
Wind is arguably the most easily accessible source of power on earth. Given the fact that
there is a global trend towards using alternative energy sources, it seems likely that wind power
will be a prominent alternative energy source. However, there are some issues with harnessing
wind power. There is an ideal range of wind speeds for producing power, and the wind speed
often fluctuates in and out of this range, making it hard to have a consistent power output from a
turbine. If a turbine could adjust the pitch of its blades based on the speed of the incoming wind, it
is possible for the turbine to produce close to ideal amounts of power across a large range of wind
speeds. It is for this reason that we sought to investigate the relationship between wind speed,
rotation rate of the turbine, and the power output of the turbine.
Our project is an expansion of the 2007 experiment by M. Burgstrom et al.[1] In the 2007
experiments the group attempted to find an optimized angle of attack for a turbine regardless of
speed using a fixed angle turbine. Our group will be following the ‘07 suggestion of testing
attack angles over a wide range of angles. The ’07 report is useful as it gives some guidelines
that our group can follow including testing at less than 40% of the maximum power in the wind
tunnel. The ’07 group began to see issues with their structures at this velocity and reported that
oscillations started to affect the “rotor shaft as well as the L-bracket of the mount”. Furthermore
the ’07 group had a helpful equation for calculating the available power in the wind, which we
will be employing:
!
Pmax=!ρairAdiskVair3
(1)
Testing Apparatus
Our testing apparatus was a combination of several electronic and physical systems. A short
description of each system used is below.
Light Sensing Diode: We attached a clear tube to the mounting post for our turbine with a light
sensing diode (LSD) inside of the tube. Additionally, a laser was set up outside of the tunnel and
aimed directly at the diode. The LSD emits a voltage when the laser excites it. Whenever a
turbine blade interrupts the laser, the LSD does not produce a voltage. By recording the voltage
2 output by the LSD, we were able to determine the rate at which the turbine was rotating, which
was very helpful when determining the efficiency of the turbine.
Turbine: Our turbine was constructed from the tail rotor assembly of the Thunder Tiger Raptor
0.60 Helicopter. This rotor system was then mounted on a PVC pipe, which was subsequently
mounted on a wooden block that was modified to be able to attach to the load cell. We linked the
turbine to a rear-mounted motor with a piece of rubber fuel tubing. This tubing acted as our
driveshaft and gave us some leeway when trying to align the motor with the driveshaft of the
turbine. We also attached a servo (essentially a linear actuator) to the mounting block and linked
the servo to the pitch control mechanism on the rotor. From there, the servo was linked to the
pitch control mechanism on the servo. This allowed us to change the pitch of the blades while in
the wind tunnel. Figures 1 and 2 in Appendix B show the turbine setup.
R/C System: We used the R/C system from an old remote control plane that belongs to the
primary author. This system included a servo, a battery, transmitter, and receiver. One of the
joysticks on the transmitter would “lock” so we could leave it at a specific setting for a long
period of time. This made it very easy to test a wide range of blade pitches in a very time efficient
manner, as we did not have to remove the turbine from the wind tunnel to change the orientation
of the blades. Figure 4 in Appendix B demonstrates the characteristics of the R/C transmitter
Inclinometer: We created an inclinometer to help determine the pitch of the blades at each
setting. We attached a plumb line to a protractor and laid that perpendicular to the tip of one of
our blades. We then measured the angle of the blade at each setting on the control (10 in all, plus
the “zero” setting). From this, we learned that each increment on the transmitter equates to a 2.5o
change in pitch. This gives our blades a range of 25o, with 0o equating to the blades being
perpendicular to the airflow.
Testing Procedure
Before we could begin testing, we needed to calibrate the wind tunnel and our load cell to ensure
accurate data collection and analysis.
Wind Tunnel Calibration: The wind tunnel is run on %power, not wind speed. Before we could
run any tests involving our turbine, we needed to find a relationship between the power at which
the wind tunnel was running and the wind speed inside the tunnel. To calibrate the wind tunnel,
3 we put a pitot tube into the center of the wind tunnel and had it attached to a u-tube manometer.
We then ran the wind tunnel at 5% power intervals from 15% power up to 100% power. We then
calculated the velocity in the wind tunnel by using the equation
V= 2
!"#$%&
!"#$
𝑔∆ℎ
(2)
From this, we were able to find a linear relation between the wind speed and power setting of the
wind tunnel. This relationship is shown as
𝑦 = 0.6079𝑥 − 2.5341.
(3)
Where x is the power setting of the wind tunnel and y is the wind speed in m/s. From this, we
were capable of calculating the wind speed inside the tunnel at any power setting.
Load Cell Calibration: In order to determine the drag forces acting on our turbine, we attached it
to a load cell while it was in the wind tunnel. We attached a bar to the load cell and systematically
hung weights from the load cell in 0.5 kg increments, 15cm from the load cell. The load cell was
attached to an NI-6009 DAQ. The load cell produces a voltage when a force is applied, and the
DAQ reads this voltage and reports it to LabView, which records the voltage. With the data
recorded by LabView, we were able to find a relationship between the voltage emitted by the load
cell and the force applied to the load cell. This relationship is defined by the equation
𝑦 = −27060.67𝑥 − 2.62 (4)
Where x is the voltage emitted by the load cell y is the force in N. By using this relationship, we
were able to calculate the drag forces on the turbine.
We tested our turbine from 15% power to 40% power at increments of 5%. At anything above the
40% power setting, we became concerned that the turbine would suffer a catastrophic failure. As
mentioned earlier, the rotor assembly was being used in a different capacity than originally
designed. We had the motor differentially wired to a nominal1 ohm resistor and a NI-6009 DAQ.
With this setup, we were able to record the voltage and current passing across the resistor. We
also had the load cell DAQ running in the same VI, which allowed us to see the drag forces and
turbine voltages side by side. In the VI, we converted the voltage output to power via 𝑝 =
plotted it.
4 !!
!
and
In our first run of tests, we ran our VI for 10 seconds at each pitch setting. After several
cycles through, we realized that our data had far too much electric “noise” to be useful. This was
attributed to the DAQ being located so closely to the motor of the wind tunnel. We combatted this
by braiding the wires leading from the motor to the DAQ and setting up a butterworth filter on
our voltage readings. This gave us much cleaner data, but it took roughly six seconds for the filter
to initialize. Given that we were out of time, we realized that we would have to come back and
test again.
In our next round of tests, we realized that our VI was only reading half of the voltage
being emitted by the motor (as measured via a multimeter set up before the DAQ). Given our time
constraints, we decided to run the VI only for drag forces and rpms while recording the voltages
by hand. We would wait for the reading on the multimeter to center around a value before
recording the data. We believe that this method was accurate to within ±0.05V. Our VI for the
laser break would take 500 samples at a rate of 5000Hz. All of this data was written to .lvm files
and then opened in Microsoft Excel for further analysis.
Data Analysis
Once we had our data in Excel, we could start to look for trends within the data. The first
step that we took was to use equation (3) to find the free stream velocity in the wind tunnel. From
there, we used equation (1) and the physical properties of the turbine to determine the amount of
power available in the wind tunnel. This information allowed us to calculate the Coefficient of
Performance, CP, which is the ratio of power generated by the turbine to available power in the
wind.
We then took our data from the LSD system and calculated the tip speed of the blades.
𝑇! =
!"#×!!
!"
×𝐿
(5)
Knowing the tip speed of the blades allowed us to find the tip speed ratio, 𝜆, which is the ratio of
Ts to the free stream velocity. [2]
𝜆=
5 !!
!
(6)
We then plotted the 𝜆 vs. Pitch data that we had as well as Power vs. Pitch to try and find
correlations between these values.
Meaning of Data
While researching the idea of unity and tip speed ratio, we noticed that the 2008 report
“Optimization of Wind Turbine Blade Shapes” mentioned that there was an optimal 𝜆 for a blade
design, where the Cp, and therefore power output of the turbine was highest [2], but not delve any
further into the subject. After performing further research, we found that there was an equation to
find this optimal 𝜆 [4]
𝜆!"# =
!!
!
(7)
n is the number of blades on the turbine. By substituting 𝑛 = 2 into (7), we get a 𝜆!"# of 6.28. If a
blade is operating at 𝜆 = 1, it is said to have achieved unity. The blade’s tips are traveling at the
same speed as the wind. If the turbine is operating at 𝜆 > 1, its blades are generating lift, causing
them to rotate even faster. [2]
Results of Testing
At 15% power (7.23 m/s), we achieved a maximum power of 0.802 W. This power output
occurred when the blades had a pitch of 7.5o (In our testing, 0o pitch equated to the blades being
completely perpendicular to the wind. Under these settings, 𝜆 = 5.76, which is very close to the
ideal value calculated. The power output was predictably low, and as the pitch increased past 7.5o,
the power output decreased. We were expecting this behavior from the turbine and were happy to
see that it followed our expectations.
At 20% power (9.92 m/s), the maximum power produced was 1.538 W, nearly twice the
power produced at 15%. This power output also came at a 7.5o pitch and 𝜆 = 5.74, which is
essentially identical to the previous 𝜆 value. However, as the pitch of the blades increased, the
power output did not drop off as sharply as it had when the tunnel was operating at 15% power.
The increase in power produced was proportional to the increase in wind speed.
At 25% power (12.34 m/s), the turbine had a peak output of 2.56 W at a pitch of 7.50. This
significant jump in power output could not be solely explained by the increase in wind velocity.
6 The turbine was operating at 𝜆 = 5.97, which is even closer to the optimal value of 6.28. As we
increased the pitch of the blades, the power output stayed relatively level for two more settings
and tapered off very slowly. In fact, the 𝜆 values rose, reaching a peak of 6.07 before falling in
conjunction with the power output.
Unfortunately, we were not able to record the turbine’s rate of rotation at higher power
settings in the wind tunnel. This was due to heavy vibrations in our system, making it impossible
for us to get consistent readings from our diode because it was moving in and out of the laser’s
path so frequently. However, the power vs. pitch curves for tunnel settings of 30%, 35%, and 40%
appear to follow the trend that we noticed in our first three tests. All of the corresponding graphs
are located in Appendix A.
Discussion
While it appears that we have found a correlation between pitch, 𝜆, and wind speed, our
testing has also left us with many questions. From research in literature and past projects, we
know that wind turbines can operate at a maximum efficiency of 0.59 according to Bentz’ limit.
Additionally, many modern, commercial, HAWT systems run at efficiencies in the range of 0.40.5. Our turbine was running in the range of .003-.016, which is significantly lower than the
operating ranges of commercial wind turbines. We singled out two likely causes: blade design and
internal inefficiencies. The blades on commercial turbines have a very noticeable “sweep” to
them. While our blades were clearly airfoils capable of producing lift, they were “flat,” i.e. they
did not have any sweep to them. For the purpose of converting energy from free wind into
mechanical power, a swept blade is much more efficient as it is capable of capturing more of the
wind flow and converting it to torque acting upon the more. As for internal inefficiencies, our rig
was not designed to be used as a power-generating turbine. It is the tail-rotor of a helicopter: the
blades are generally rotating parallel to the wind rather than perpendicular to it. There was likely
significant power loss within the bearings of the system and the motor itself. Fortunately, these
inefficiencies did not prevent us from gathering meaningful data.
Conclusion
From our results, it is clear that as wind speed increases, a turbine will operate near
peak efficiency over a higher range of pitch settings. We had set out to try and find a relationship
7 between power output and blade angle. This data quantitatively shows that different pitch settings
produce different power outputs, and that this relationship changes along with wind speed. Future
groups could easily expand upon this project. Suggestions include experimenting with different
blade geometries (in a slightly different manner than the ’08 group) and devising a system that
will record turbine rotation data at higher wind speeds than we did. From our knowledge, no
group has had great success in getting a model turbine to run safely at more than 40% or 45% in
the wind tunnel. Groups could also try and design a system with fewer internal inefficiencies,
which would lead to a higher power output from their turbine.
References
[1] Burgstrom, M., Fishback, J., Ivancic, S. “Wind Turbines: Power Control Through Pitch
Regulation” (2007)
[2] Ahl, B., Chebot, D., Sikes, N. “Optimization of Wind Turbine Blade Shapes” (2008)
[3] Huebsch, W., Munson, B., Okiishi, T., Young, D. 2007 A Brief Introduction to Fluid
Mechanics chapter 7 Wiley: Hoboken, NJ
[4] Ragheb, M. “Optimal Rotor Tip Speed Ratio” (2011)
8 Appendix A: 𝜆 vs. Pitch and Power vs. Pitch Graphs
Tip Speed Ra*o Tip Speed Ra*o vs. Pitch 8 6 15% Power 20% Power 4 2 0 0 5 10 15 20 25 30 Angler of A2ack (ͦDegres)
Figure 1: Graph of Tip Speed Ratio vs. Pitch
15% Power (≈7.232m/s) Power (W) 1 0.5 0 0 5 10 15 20 25 30 25 30 Blade Angle (Degrees) Figure 2: Graph of Power vs. pitch at 15%
20% Power (≈9.922m/s) Power (W) 1.5 1 0.5 0 0 5 10 15 20 Blade Angle (Degrees) Figure 3: Graph of Power vs. pitch at 20%
9 25% Power (≈12.341m/s) 3 Power (W) 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 25 30 Blade Angle (Degrees) Figure 4: Graph of Power vs. pitch at 25%
30% Power (≈15.392m/s) Power (W) 5 4 3 2 1 0 0 5 10 15 20 Blade Angle (Degrees) Figure 5: Graph of Power vs. pitch at 30%
10 35% Power (≈18.480m/s) Power (W) 8 6 4 2 0 0 5 10 15 20 25 30 25 30 Blade Angle (Degrees) Figure 6: Graph of Power vs. pitch at 35%
40% Power (≈21.518m/s) Power (W) 10 8 6 4 2 0 0 5 10 15 20 Blade Angle (Degrees) Figure 7: Graph of Power vs. pitch at 40%
11 Appendix B: Images and Models of Turbine System and Components
Figure 1: The Turbine During a Testing Run
12 Figure 2: Test rig assembly
13 Figure 3: Rotor assembly
14 Figure 4: Remote Control
15 Figure 5: Rotor assembly and PVC mount
16