Mr. Keser – 7/8 Science – Optimal Blade DesignLab
OPTIMAL BLADE DESIGN
CONGRATULATIONS! By reaching this point, you have successfully completed a series of tests to determine optimal variables in turbine blade design. By now you have investigated the optimal pitch, number of blades, surface area and mass. Now it is time to use this data to construct a new set of blades that will produce the most power.
Reporting Your Data
Over the next few class periods you will collect a set of data and calculations based on your turbine blade performance. You will record your data daily and post it on a large chart in front of the class. You will be required to record the following:
Related to Power / Related to Wind & Blade SpeedsVoltage(V) / Wind speed (mph ->mps)
Current(mA) / Tip Speed (rpm -> rps)
Power(W) = V x A / Tip Speed Ratio (rps/mps)
Test Load (ohms) = 30 ohm / Optimal Tip Speed (n)
n=number of blades
Power
When you measure the amperage of your motor you are basically measuring how much torque force you blades are making. Depending on how much resistance you place on the motor it can get very difficult for the motor to spin unless your blades generate a great deal of torque. Short blades will not generate lots of torque, but longer blades can. What this means is that a set of blades that generates the highest voltage...usually cannot generate any current because they generate little torque force.
While challenging to understand the full power characteristics of your wind turbine you must measure voltage and amperage and then do a simple power calculation.
Power = Volts x Amps
Make sure you do the measurements in the same units. Don't multiply volts times milliamps it makes for messy math and incorrect readings. Multiply volts times amps or millivolts x milliamps it makes your life easy!
Wind Speed
Use the Kestral 100 or the Wind Gauge to determine the wind speed in mph.
You need to make sure that your units are all the same. For example: You can’t
use a wind speed in Miles/Hour and a tip speed in Meters/Second. This formula
will help if you need to convert units of velocity:
1 meter per second equals 2.237 miles per hour.
Tip Speed
1. Measure the rotor radius (lengthof one blade)
2. Speed = distance divided by time.The distance travelled is the circumference(2r).
3. Speed:V =The blades travel one circumference(2r) in a rotation time of T(seconds).
You need to know how many seconds it takes the rotor to spin around one time. If
you found RPM, you will need to convert this number. There are 60 seconds in one
minute, so just divide 60 by your RPM value. That will tell you how many seconds it
takes to make one revolution.
Tip Speed= 1 minute x 60 seconds = 60 = sec/rev.
No. of revolutions(N) 1 minute N
Speed: Velocity = 2r
T
Tip Speed Ratio
Now that you’ve made all your measurements, you should be able to figure out
your tip speed ratio (TSR). You already calculated the tip speed in the equation
described above (distance travelled divided by time taken for one revolution).
Now take that number and divide it by your wind speed!
If your TSR is above 1, that means there is lift involved to make your blades spin
faster than the wind speed. If your TSR is below 1, there is a lot of drag going on!
Old windmills used to lift weights, grind grain, or pump water probably had TSRs
around 1. Modern wind turbines have higher TSR values like 5.
Optimal Tip Speed
If you want the optimum Tip Speed Ratio for maximum power output, this formula
has been empirically proven:
4
λ (max power) = n (n = number of blades)
UNITS AND CONVERSIONS
Power (The rate at which work is performed or energy is transmitted)
Watt (W): 1 W = 1 J/s = 1 kg x m2/s31 watt = 1 Ampere x 1 Volt
Ampere (A): Also called “Amp” - The unit of electrical current—The
amount of electric charge per second. One ampere is approximately equivalent
to 6.2415°—1018 elementary charges, such as electrons, moving past a
boundary in one second.
Volt (V): The unit of electric potential difference. One volt is equal to one
Joule of energy per coulomb of charge (1V = J/C)
Remember: Watts = Amps x Volts
A good analogy compares electric circuits to water-filled pipes (like a hose).
In this analogy, Current (amperes) is a measure of the volume of water
that flows past a given point (how WIDE is the pipe?). Voltage would be the
water pressure—how fast the water is moving through the pipe.
So current measures how many electrons are moving through a circuit,
while voltage measures how fast they travel.
milliamp (mA) = .001 Amps
Kilowatt (kW) = 1,000 Watts
Megawatt (MW) = 1,000 Kilowatts = 1,000,000 Watts
Energy (The work done to produce power over a period of time)
Joule (J): 1 m2/s3J = 1 kg x
A Joule is the work done to produce one Watt continuously for one second.
Kilowatt-Hour (kWh): This is the amount of work done to produce one
Kilowatt continuously for one hour. This is the unit that electricity is usually
measured by. Americans typically pay 8—20 cents per kWh.
1 kWh = 1,000 Watt-Hours = 3,600,000 J = 3.6 megajoules
1 meter = 3.28 feet
1 meter/second = 2.237 miles per hour