Renewable Sources of Energy
Simple Explanation
Renewable sources — solar, wind, hydroelectric, geothermal, and biomass — are naturally replenished on a human timescale, offering an ongoing supply of energy that does not run out the way fossil fuels do.
Why Do We Need It?
As non-renewable supplies dwindle and their environmental costs grow clearer, renewable sources are the primary long-term answer to sustaining the world's growing energy demand.
Formula
Power Available from Wind
P = ½ρAv³
The power carried by moving air through a given area depends on the air density, the swept area of the turbine blades, and — most steeply — the cube of the wind speed.
- P
- — power available in the wind, in watts (W)
- ρ
- — density of air, in kilograms per cubic metre (kg/m³) — about 1.2 kg/m³ at sea level
- A
- — cross-sectional area swept by the turbine's blades, in square metres (m²)
- v
- — wind speed, in metres per second (m/s)
When to use it: Whenever estimating how much power a wind turbine of a given blade size could generate from a given wind speed.
Worked Example
Find the power available from a wind turbine
A wind turbine has blades of radius 20 m, sweeping through air of density 1.2 kg/m³, in a wind of speed 10 m/s. Find the power available in the wind.
Why Does This Work?
The kinetic energy in a mass of moving air is ½mv², and the mass of air passing through the turbine's swept area every second is ρAv (density × area × speed) — combining these, the power (energy per second) works out to ½ρAv³, which is why wind power grows so steeply with wind speed.
Real-Life Example
Why wind farms are built in especially windy locations
Wind farm developers carefully choose sites with consistently high average wind speeds, even if it means building far from cities.
Because power depends on the CUBE of wind speed, even a modest increase in average wind speed dramatically increases the power a turbine can generate — making site selection critical.
Practice
A wind turbine has blades of radius 10 m, air density 1.2 kg/m³, and wind speed 8 m/s. Find the power available, in kilowatts.
HardCommon mistake
Forgetting that wind power depends on the CUBE of wind speed, not the speed itself — doubling the wind speed multiplies the available power by a factor of 8, not 2.
Quick Review
- P = ½ρAv³ — wind power grows with the cube of wind speed.
- Solar, wind, hydro, geothermal, and biomass are the main renewable sources.
- Naturally replenished, offering an ongoing (not finite) supply.