Wind Efficiency
Introduction:
Wind mills work by its blades generating a lift; this is due to their shape and angle. With more
curved air blades, the more curved side generates low air pressures pushing down while the high
air pressure pushes under the opposing side of the blade perpendicular to the ground. The net
result is a lift force perpendicular to the ground, the direction in which the blade must turn. An
opposing force called drag, however, this counteracts the element of perpendicular force (Gurit).
This opposing vector is caused by too much parallel wind push on the blade with relation to the
ground (Gurit). At an optimal angle, where drag is minimized and lift is maximized, the most
effective blade shape could be determined. However, because we cannot optimize the angle of
all blades, we will set the blade at 45 degrees as a control for each blade angle. Due to a likely
hood for great amount of drag, the blades where the wind will make less contact will have less
parallel drag. The amount of energy that the blade captures is based on the lift drag ratio. The
following equation shows the amount of power that the windmill P = Cp½ ρ A v3 (Gurit)
Where Cp represents the efficiency of the blade, a value from 1 to 0.
Whereas the blade with the most perpendicular force will generate greater power because of the
greater rotational speed, which is the result of the air pressure difference in wind blades.
Equivalently, if the blades increase in circularity the greater power generated. In circularity, the
more generated power because of the less drag compared to less circular blades and because of
the great amount of perpendicular air pressure. Thicker blades without circularity will have
more drag and a diminished perpendicular vector quantity.
The following procedures were followed in conducting the experiment
1. Obtain an 3 Adaptable Learning Turbine Kit (includes at least 9 dowels and 9corroplast
sheets), Screw driver, standard roll of scotch painter’s tape, a pencil, a meter stick, one
flat surface, one chair, two text books, multimeter, positive and negative probes, one
protractor, one metal fan with power outlet, circuit, and resistor
2. Assemble the Adaptable Learning Turbine Kit from page 2 to 8.
3. Cut each sets of three blades into each of the three shapes as shown in Figure 1. (nine
blades total), Once a corroplast blade is made the, trace the outline with a pencil on the
two other Corroplast blades for each set. (9 total blades, 3 sets)
Figure 1- (Optimizing, 4)
4. Then tape dowels to the end of each of the blades so that the dowel is secured to the back
of each blade. Leave 5 centimeters of dowel at the end of each blade. Also tape the
dowel to the back of the blade, so that the end of the blade is perpendicular to the hub.
5. Next insert each blade of each set into their hubs with the dowel, respectively for each
blade shape. Insert each 120 degrees apart from each other around the hub. Use the
protractor against the hub to angle each blade 45degrees, each in the same direction.
Secure the hub with the blades attached in each.
6. Then hook the multimeter appropriately to the generator with the positive and negative
probes. Set the multimeter to test voltage first. Note: Important to start at 200V then
gradually down to 20V. With Amperage, set the resistor to 200 ohms then down
acoordingly
7. First set the multimeter to 20V before staring the fan
8. Place the base of the fan on a chair and adjust so that the fan is in balance. The center of
the hub holder on the base of the fan should be level with the center of the fan. The fan
blades on the windmill blades should be facing directly at each other, parallel to
eachother.
9. Put each blade hub in the hub connector to the base so that its parallel to the windmill
blades.
10. Connect a resistor to a circuit board so that volts per ohms can be tested. Make a series
circuit with one resistor connection.
11. First testing volts, then ohms, set the metal fan to lowest setting. Test for each blade type
three times each.
Figure 2- Lab apparatus (showing before Design #2 trial #3 with multimeter hooked up to
windmill that is generating power. The metal fan, when turned on generate the white
blades to move.)
In order test the experiment solely on blade design, the following controls will be set in the
experiment:
The windmill will be the same length away from the fan each time. The wind will be coming in
at a 90 degree angle each time, the intensity of the fan is this is so that different air flows are not
a factor.
Other controls include that the base of the wind mill, the hinges, and the electric generator are all
kept the same throughout the experiment. The only thing that should be changed from each step
is the different blade hubs with the different blade designs.
Each of the angles of the blades is kept the same. The material of the blade is kept the same. The
experiment was done in a closed, wind-free environment. When cutting the blade material, make
sure that length
In the data processing, We cannot accurately predict the power generated from the blade because
of an inability to measure the velocity of the wind and its density. The following equation shows
the amount of power that the windmill P = Cp½ ρ A v3 Where Cp represents the efficiency of
the blade, a value from 1 to 0. We do not have proper instrumentation to calculate outcome, and
moreso % error.
Data Collection:
Figure 3- Observations
Design #1
The blade is spinning
faster than other
Designs, yet
considerably low
power generation.
Resistance
Design #2
Blade spinning at
consistent rate, no
wobble, hub detached
after the last trial.
Noticeably varying
resistance reading.
Design #3
Blades spinning at
consistent rate. blade
is spinning around the
same rate as the other
designs. The
multimeter did not
measurement of
uncertainty was
greater than normal.
Not a great amount of
unsteady flow
Fluctuating around 1
ohm. Great amount
of resistance.
wobble when
measuring resistance
and voltage.
Ohms law states- that electric potential over the amount of resistance is equivalent to electric
current
𝑉𝑜𝑙𝑡𝑎𝑔𝑒
𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
= 𝐶𝑢𝑟𝑟𝑒𝑛𝑡
To evaluate for power, voltage and current must be considered
Voltage and resistance were measured by the multimeter
𝐶𝑢𝑟𝑟𝑒𝑛𝑡⦁𝑉𝑜𝑙𝑡𝑎𝑔𝑒 = 𝑃𝑜𝑤𝑒𝑟
Because the amount of flow through the potential will evidently result in power
Figure 3- the Voltage, Resistance, and power Calculated for Trial 1 through Trial 5, respectively
(with examples of Calculations)
Design #1
Voltage (In
Volts)
1.3±.8
1.28±.1
1.31±.15
1.24±.05
1.4±.05
Resistance
(in Ω)
7.4±.4
7.4±.4
7.1±.5
7.5±.5
7.8±.3
Power (in
Watts)
0.23±.15
0.22±.03
0.24±.04
0.21±.02
0.25±.02
Example of Calculations
Resistance
(in Ω)
15±1
15.8±1
16±.8
16.2±.5
16.4±.5
Power (in
Watts)
0.49±.07
0.55±.05
0.36±.03
0.50±.02
0.51±.04
Example of Calculations
1.3𝑉
= .18𝐴
7.4Ω
. 18𝐴⦁1.3𝑉 = 0.23𝑊
Design #2
Voltage (In
Volts)
2.7±.2
2.95±.1
2.4±.1
2.86±.05
2.89±.15
2.7𝑉
= .18𝐴
15Ω
. 18𝐴⦁2.7𝑉 = 0.49𝑊
Design #3
Voltage (In
Volts)
1.47±.1
1.4±.1
1.46±.1
1.37±.1
1.43±.1
Resistance
(in Ω)
1.5±.1
1.4±.1
1.5±.1
1.4±.1
1.4±.1
Power (in
Watts)
1.44±.19
1.40±.20
1.42±.14
1.34±.19
1.46±.21
Example of Calculations:
1.47𝑉
= .98𝐴
1.5Ω
. 98𝐴⦁1.47𝑉 = 1.44𝑊
Example of Uncertainty Calculation:
.1
.1
(1.47 + 1.5) (1.44) = ±.19
Figure 3-
Power Generated in Watts
Average generated power of each
blade
2
1.412
1.5
1
0.5
0.482
0.23
0
Design 1 Power
Design 2 Power
Design 3 Power
Note: the percent error could not be calculated. To calculate expected power produced, velocity
of the fan could not be measured. More so, efficiency variable could not be predicted either.
These go into account predicting the power of the blades.
Conclusion:
Because of the great amount of power generated by design #3, despite uncertainties, it is valid to
accept that it did generate the most power. Design 2 generated the second most power while
Design 1 generated the least power. Our hypothesis was that the more circular the blade was, the
greater the power generated, because circular blades allow for greater perpendicular force due to
greater air pressure. Design 1 was the least circular and produced the least amount of power, as
predicted. Design 3 was the most circular design, and it produced the greatest amount of energy.
This shows that there was a general trend: as the circularity of the blades increased, so did the
power generated, just as predicted. Thus our hypothesis is valid. Also, the information from the
source was also supported. This information said that the more circular blade will create more
perpendicular force and less drag, while the rectangular blade creates more drag while spinning
(Gurit).
Some errors in experimentation include not measuring the velocity of the wind. Because we did
not measure the velocity of the wind, we could not evaluate the percent error in the data to
determine its validity. To improve upon this, we can use an anemometer to measure wind speed
of the fan. Other failed methods include not measuring the area of the blades or calculating the
circularity. If many different sets of wind blade sets were increased in circularity gradually, then
a relationship of circularity on wind blades will be determined.
To further investigate into wind blade efficiency, the optimal angle of the blade will be tested.
Because we were unable to find sources regarding optimal blade angle for a wind mill, the tests
may have had a different outcome (the perpendicular air pressure to drag ratio can be varied with
different blade angles). Once we find optimal power generating blade angles, this experiment
can be repeated with a different control of the optimal blade angle of each blade.
Works Cited
“Optimizing Windmill Blade Efficiency”. UC Riverside.
Gurit.“Wind Turbine Blade Aerodynamics”. retrieved from:
http://www.gurit.com/files/documents/2_aerodynamics.pdf