Earth and Environmental Science 11–12 · Year 12
Wind turbine output and wind speed: the cube law and the Betz limit
Module 8: Resource Management
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
The power carried by wind rises with the cube of its speed and with the area the blades sweep, and no turbine can capture more than 16/27 of it, which sets where wind farms are worth building.
What you need
- a model wind turbine with a small generator and a 30 cm rotor (15 cm blades), mounted on a stand
- a large electric fan with speed settings, a handheld anemometer, metre rule
- a load resistor (for example 10 Ω), voltmeter and ammeter or a joulemeter
How to do it
- Measure the wind speed at the turbine position with the anemometer for each fan setting (three readings each, averaged).
- Connect the load and record voltage and current at each wind speed; calculate electrical power P = VI.
- Calculate the power carried by the wind through the rotor area, ½ρAv³, and the Betz maximum, 16/27 of that.
- Plot electrical power against v³ and calculate the turbine’s efficiency at each speed.
- Repeat with shorter blades or two blades removed if the kit allows, and compare.
- Use the Earthlearningidea discussion of real turbines to evaluate a wind farm proposal for the local area.
What you should see
For air of density 1.20 kg/m³ through a 30 cm rotor (0.0707 m²), the wind carries 1.15 W at 3 m/s, 5.30 W at 5 m/s and 42.4 W at 10 m/s, and the Betz limit allows at most 0.68, 3.14 and 25.1 W. Doubling wind speed multiplies the available power by 8; the model’s electrical output rises steeply with speed but stays well below the Betz limit because of blade shape, friction and generator losses, and the learner reports the efficiency at each speed. Earthlearningidea notes that full-size turbines start generating at about 4 m/s and are shut down above about 25 m/s.
What changes
- What you change
- wind speed (and blade length)
- What you measure
- electrical power output
- What you keep the same
- same turbine and load
- same distance from the fan
- turbine facing the airflow
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Twice the wind gives twice the power.
- A turbine can capture all of the wind’s energy.
- Bigger turbines produce more only because they are taller.
Safety card
Hazards
- spinning blades and fan
- mains-powered fan cable
Controls
- keep fingers clear and stop the rotor before adjusting
- fan guard fitted; keep the cable away from walkways
Note
The fan is a mains appliance: use a school fan that is tested and tagged, keep its guard fitted and its cable clear of water and walkways; the turbine circuit itself is low voltage. Record a RiskAssess risk assessment following the NSW Department of Education Science safety and compliance page.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Earth and Environmental Science Stage 6 Syllabus (2017), NESA; current, replaced by the 11–12 Syllabus (2025) from 2028EES12-15EES11/12-5EES11/12-6EES11/12-7
- Earth and Environmental Science 11–12 Syllabus (2025), NESA; to be implemented from 2028, not yet taughtEES-11-02
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.
- www.nsw.gov.au/education-and-training/nesa/curriculum/science/earth-and-environmental-science-stage-6-2017
- www.earthlearningidea.com/PDF/393_Net_zero_Wind_turbines.pdf
- education.nsw.gov.au/teaching-and-learning/curriculum/science/science-curriculum-resources-k-12/science-11-12-curriculum-resources/earth-and-environmental-science-year-11-and-12