# Turbine Performance Calculator

If you're new and need guidance, this document will be your friend

### electrical output ### weightlifting output ### tip speed ratio # What would you like to calculate?

### energy output over 1 minute ### turbine power and efficiency # Energy output over 1 minute

As your wind turbine operates, measure the voltage at 5 second intervals, for 60 seconds. Record the average voltage you see on your meter. This can be challenging (that's the reason why we love data collecting tools from Vernier). For this calculation to work, you will need to measure the voltage across a known resistor and enter that into data into the spreadsheet.

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.

ohms ( ? )

Time period (s) Voltage ( ? ) Voltage2 Voltage2 / Resistance Energy produced
0-4
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5-9
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10-14
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15-19
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20-24
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25-29
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30-34
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35-39
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40-44
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45-49
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50-54
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55-60
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Millijoules over 1 minute = mJ

# Turbine power and efficiency

The turbine power calculator outputs the power output of your small turbine in watts and milliwatts. All you need to do is measure your voltage across a known resistor.

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: the efficiency calculator is only useful for horizontal axis machines. We're working on a vertical axis calculator.

## Calculate power

Equations used

1. Watts (W) = v2 (voltage) / ohms (resistance)
2. Milliwatts (mW) = W (watts) * 1000

volts ( ? )

ohms ( ? )

### Turbine power results

Watts = _____ W

Milliwatts = _____ mW

## Calculate efficiency

Equations used

1. Available power = 0.5 * πr(m)2 (blade swept area) * 1.23 kg/m3 (air density) * v3 (velocity cubed)
2. Turbine efficiency = W (watts generated by turbine) / Available power * 100 (to get percentage)

cm2 ( ? )

m/s ( ? )

### Available power

Watts = _____ W

Milliwatts = _____ mW

### Turbine efficiency

Efficiency = _____%

# Weightlifiting power

This calculator can be used to help quantify the amount of energy your turbine transferred from the wind to lifting weights. You can also use this data to calculate the average power output of your turbine.

Equations used

1. Work (Energy Transferred) (J) = Force (N) x Distance (m)
2. Average Power (w) = Energy Transferred (J) / Time (s)

washers (REcharge kit washers are 13g each)

cm

s

### Weightlifting power results

Millijoules = _____ mJ

Milliwatts = _____ mW

# Tip speed ratio

If you know the diameter of your wind turbine rotor, the velocity of the wind, and your RPM, you can calculate tip speed ratio (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 rotor 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.

Show equations used

1. Distance blade tip travels in one revolution (m) = 2πr
2. Revolutions per second = rpm / 60
3. Blade tip velocity (m/s) = distance blade trip travels in 1 revolution * revolutions per second
4. Tip speed ratio = Blade tip velocity / Wind speed (m/s)

cm (rotor diameter)

rpm

m/s

### Tip speed ratio results

Distance blade tip travels in 1 revolution = _____ m

Revolutions per second = _____

Velocity of the blade tip = _____ m/s

Tip speed ratio = _____