# How Small Windmills work

## Overview: How Small Wind Turbines work

The Small Wind Turbines are upwind, horizontal-axis wind machines where the rotor spins in front of the tower about a line parallel with the horizon. It comprises of following main components:

- A propeller (also termed as windmill) made out of aerodynamically shaped rotating blades mounted on a shaft.

- An Alternator or Generator for producing the electricity when the shaft is rotated.

- A Tail or Vane at the back of the wind turbine is used to steer it into or out of the wind automatically.

- A well anchored, robust and tall Tower for mounting the Propeller Blades along with Alternator or Generator and Tail.

Principle

The Windmill extracts energy from moving air by slowing down the wind, and transferring this harvested energy into a spinning shaft, which usually turns an alternator or generator to produce electricity. The power available in the wind that can be harvested depends on two factors i.e. wind speed and the area swept by the propeller blades.

Power available in wind (in Watts) is as follows:

P = ½ x J x A x V3

Where J=air density=1.23 kgm3 at sea level

A = swept area in square meters = pi x r2 where r is the length of the propeller blade.

V=wind velocity in meters per second (m/s)

If we work out the calculations for a 5-feet diameter windmill in a 10 mph wind:

5 feet = 1.524 m. Therefore Swept Area A = pi x r2 = 3.141 x (1.524 / 2) 2 = 1.8241 m2

Wind Speed V=10 miles per hr (mph)=4.47 m/s. So Power available (Watts)

= ½ x 1.23 x 1.8241 x 4.47043 = 100.22 Watts

As evident from the above calculation, there is very little power available in low winds. Firstly, as seen from the above formula, when the wind speed doubles, the power available increases 8 times. Suppose the Wind Speed is increased (doubled) for this 5-foot rotor from 10 mph to 20 mph (4.47 to 8.94 m/s),

The Power available (Watts) = ½ x 1.23 x 1.8241 x 8.94083 = 802 Watts

Thus, the only way to increase the available power in low winds is by sweeping a larger area with the blades. The Power available increases by a factor of 4 when the diameter of the blades is doubled. Hence if we use a 10-foot (3.048 m) diameter rotor for a 7.30 m2 swept area in a 10 mph wind,

Power available P = ½ x 1.23 x 7.30 x 4.47043
= 401 Watts

But, in a 20 mph wind condition, P = ½ x 1.23 x 7.30 x 8.94083 = 3209 Watts

However, there’s no way to harvest ALL of this available energy and turn it into electricity. As per Betz Law, 59.26% is the absolute maximum limit that can be extracted from the available power.