Turbine Performance Calculator
These performance calculators will help you determine how well your small wind turbine is performing. You do not need to use KidWind gear to use the Performance Calculators, but you can if you want! You can calculate the performance of any small turbine using these calculators.
There are four performance calculators: Power Output, Energy Output, Turbine Efficiency, and Tip Speed Ratio.
You will need some basic tools to collect the required data so we can evaluate your performance.View these tools
- Multimeter and Resistors - To collect power and energy data you will need a measure your voltage across a known resistor. Learn more about how to do this on the turbine tips page. Remember if you are using an AC generator you should rectify the output then measure the voltage across the resistor.
- Wind Speed Meter - To calculate turbine efficiency and tip speed ratio you need to know the wind speed hitting your turbine. There are a number of ways to measure this.
- Tachometer - To calculate your tip speed ratio you will need to know the RPM of your turbine. Here are a few tools to help you do that.
YOUR TURBINE'S POWER:
This calculates the power output of your small turbine in watts and milliwatts. All you need to do is measure your voltage across a known resistor.
- Watts (W) = v² (voltage) / ohms (resistance)
- Milliwatts (mW) = W (watts) * 1000
If you know how much power you are generating, the wind speed, and how long your blades are, you can calculate the efficiency of your turbine. Based on the Betz Limit, the highest this can be is 59%. Please note: this efficiency calculator is only useful for horizontal axis machines. We're working on a vertical axis calculator.
- Available power = 0.5 * πr² (swept area) * 1.23 kg/m³ (air density) * v³ (velocity cubed)
- Turbine efficiency = W (watts generated by turbine) / Available power * 100 (to get percentage)
Turbine tip speed ratio
DIST BLADE TIP TRAVELS IN 1 REVOLUTION:
REVOLUTIONS PER SECOND:
VELOCITY OF THE BLADE TIP:
TIP SPEED RATIO:
If you know the diameter of your wind turbine rotor, the velocity of the wind, and your RPM, you can calculate TSR. Generally the higher your TSR, the more electricity you are going to be able to generate on a three bladed turbine.
This calculator uses your blade diameter to determine the distance your blades travel in one revolution. Using RPM it then determines how many revolutions your blades make in one second. With these numbers it can then calculate the velocity of the blades in m/s and compares that to the velocity of the oncoming wind.
What is Tip Speed Ratio (TSR)
Tip Speed Ratio (TSR) is a ratio of how fast the tips of your turbine blades are moving relative to the wind hitting the turbine.
Example: If the wind hitting your turbine was traveling at 5 m/s and your blade tips were moving at 5 m/s you would have a TSR of 1.
What is an optimal Tip Speed Ratio?
Well, that depends on a number of factors such as rotor diameter, blade width, blade pitch, RPM needed by the generator, and the wind speed. Typically higher TSRs are better for generators that require high RPMs - but the wind speed characteristics at your particular site will make a big difference.
What is happening?
If the rotor of the wind turbine turns too slowly, most of the wind will pass undistributed through the gap between the rotor blades. If the rotor turns too quickly, the blurring blades will appear like a solid wall to the wind.
When a turbine blade passes through the air it leaves turbulence in its wake. If the next blade on the spinning rotor arrives at this point while the air is still turbulent, it will not be able to extract power efficiently from the wind. However if the rotor spun a little more slowly, the air hitting each turbine blade would no longer be turbulent.
- Distance blade tip travels in one revolution (m) = 2π²
- Revolutions per second = rpm / 60
- Blade tip velocity (m/s) = distance blade tip travels in revolution / revolutions per second
- Tip speed ratio = Blade tip velocity / Wind speed (m/s)
This calculator can be used to help quantify the amount of energy your turbine transferred from the wind to lifting the weights. You can also use this data to calculate the average power output of your turbine.
- Work (Energy Transferred) (J) = Force (N*m) x Distance (m)
- Average Power (w) = Energy Transferred (J) /Time (s)
As your wind turbine operates, measure the voltage at 5 second intervals, for 60 seconds. You will be measuring the voltage across a known resistor and enter that into the spreadsheet. The total energy produced is equal to the voltage at each measurement squared, divided by 10. The total energy for each 5 second segment is the power times 5 seconds.
|Time period (s)||Voltage||Voltage²||Voltage²/Resistance||Energy produced (mJ)|
|Total Energy (mJ)||0|
The primary unit of energy is the joule (J). It is defined as the work required to move an object 1 meter against a force of 1 Newton. This is about the energy required to lift a 12 oz soda can 1 foot straight up.
Power is the rate at which energy is used and is measured in watts (W), which is 1 joule transferred every second, or J/s. Power and energy are similar to speed and distance. Velocity multiplied by time gives the total distance traveled. Power multiplied by time gives the total energy used or produced.
To measure the work done by our turbine, we will attach it to a load, and measure the power transferred to the load. Our load for this experiment should be a resistor. A resistor resists the flow of current, and in doing so converts the kinetic energy of the electrons motion into heat, basically acting like a small toaster!
To measure the power, we would have to measure simultaneously the voltage and the current - at a KidWind Challenge we have fancy software to do this. In your home or classroom you can do it more simply with this app and a multimeter.