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Education and Careers

How much energy is in the wind?

See also:
Extracting energy from the wind
Calculations for wind energy statistics

Any object which moves has kinetic energy. The formula for kinetic energy is Equation 1:

Kinetic energy = ¹/₂ mu²

where
m = mass (kg)
u = speed (meters per second)

For example, if a car of mass 1000kg is travelling at a speed of 10 meters per second, then it has a kinetic energy of:

¹/₂ x 1000 kg x 10 ²m²s^-2= 50,000 kgm²s^-2 = 50,000 Joules = 50 kiloJoules (kJ)

The wind has movement and therefore kinetic energy. We use the same formula for working out the kinetic energy of moving air, but we have to be more precise in defining what is meant by the 'mass' of air. We have to talk about the kinetic energy of a particular volume of air.

Imagine you are standing in a field, facing into the wind and holding a hoop above your head. We can work out how much air goes through the hoop each second with Equation 2:

V = A u

where
V = Volume of air per second
A = area of the hoop
u = the speed of the air (wind)

Using the density of air, approximately 1.2kgm^-3, we can calculate the mass of this volume of air:

Mass of air per second = Vd

Combining these equations gives:

Mass of air per second = Aud

where
A = area of the hoop
u = speed of the wind/second
d = density of the air

Examples

(The answers are given at the end of this factsheet)

1) Calculate the mass of air per second passing through a hoop with an area of 0.75m² if the wind was blowing at a speed of 8.1 m^-1.
2) Now work out the kinetic energy of this mass of air

To do this we have to use Equation 3:

kinetic energy through hoop per second = ¹/₂ Aud u² = ¹/₂ Adu³

We now know how the kinetic energy of the wind is calculated. It is the kinetic energy of the mass of air which passes through each square metre of space (in line with the wind) in each second. It is measured in units Jm^-2s ^-1 (i.e. joules per square metre per second.)

Power is energy per unit time (Js^-1), so what we've worked out as the kinetic energy of the wind is really the power of the wind.

The units of power are Watts: 1 Watt = 1 Joule per second, i.e. 1W = 1Js^-1.

3) Assuming that the density of air is 1.2 kgm^-3, use Equation 3 fill in the following table.
In the final column divide the power per square meter by 60 W to find the number of 60 Watt light bulbs which could be fully lit by the power of the wind

Estimating wind speed

A quick and easy way to estimate the speed to the wind is as follows:

Take a ping-pong ball and a small stone and hold them exactly 1 metre above the ground (a grassy area is best). Make sure that the wind is not obstructed by anything or anyone then drop the ball and stone at the same time. The ball will be blown downwind and the stone will drop vertically. Measure the distance between the points at which the stone and the ball first hit the ground and use the table to find out what the wind speed was.

Answers

1) mass of air per second = 7.29 Kgs^-1

2) kinetic energy through hoop each second = 239.1 Ws ^-1

3)