- Welcome to engineering with Rosie.
This video will be the first in a series
that answers the question,
how does a wind turbine work?
In this video I'm going to talk about the energy in the wind
and how efficiently wind turbines can transform
that to electricity.
I'll be following up with videos
on the aerodynamic theory that you need
to know how to analyze and design a wind turbine later.
(upbeat music)
Wind turbines convert the kinetic energy
of moving air particles to electrical energy.
Modern wind turbines generate torque
when air flowing over the blades creates a lift force.
The wind turbine blade is oriented
so there is a component of the lift
that acts in the right direction to turn the blades.
The blades are connected to a hub,
which is connected to us shaft,
which may be connected to a gearbox,
which is connected to a generator.
Air is made up of a lot moving particles
which have mass, M and velocity, V
and therefore kinetic energy, E.
So, this equation tells us that faster moving air
has more energy than slow moving air and likewise,
air with more mass has more energy.
The mass of air is measured
by its density rho times the volume.
The main factors that affect air density
are temperature and altitude.
So, turbines in cold locations
at low altitudes can generate more power
than in warm locations at high altitude,
if the wind speeds are the same.
The wind turbine blades sweep out the disc
and over time it captures some of the energy
of the air flowing through that disc.
If we call the area of the disc, A,
then a one meter thick cylinder of air
would have A times rho kilograms of air in it.
And if the wind speed is one meter per second,
then the mass flow
is one times A times rho kilograms per second.
If the wind speed is V meters per second,
then the mass flow
is V times A times rho kilograms per second.
The amount of kinetic energy of that air
that passes through the disc is the power,
the amount of energy per unit time.
So the total power, P of air with
the wind speed, V flowing through a disc with area A
is given by this equation.
The wind that flows through the disc swept out
by the turbine rotor comes from way up wind of the turbine
and extends way downwind.
You can visualize this as a stream tube.
And of course,
some of the energy is taken out of the air by the turbine.
That's the whole point of the wind turbine.
We already saw that the amount of energy in the air depends
on the mass and the speed of the air.
And since the turbine doesn't consume any of the air,
every air particle that enters the rotor disc
also leaves it.
So the mass of the air at any location in the stream tube
is the same.
So if the air particles kinetic energy is reduced,
but the mass of the air stays the same,
then we know it's speed must decrease
when the wind turbine extracts energy.
Since the masses are same all along the stream tube,
but the speed changes, the width of the stream tube changes.
It's wider downwind of the turbine,
when the wind speed is low and narrower upwind
when the wind speed is relatively higher.
It's not physically possible
to extract all the energy from the wind
as that would mean that the wind velocity
was reduced to zero downstream of the turbine.
Without any velocity, the air particles
would just kind of pile up there behind the turbine.
That's obviously not possible.
So there is a maximum amount of the energy
that can be extracted.
And this maximum amount was calculated by a guy called Betz.
The maths is a bit more complicated than I wanna get into
in this video, but I will link in the description
to where you can see the derivation
in case you're interested.
The Betz limit shows that the maximum amount of energy
that can be extracted from the stream tube
is about 59%.
So that is the maximum efficiency
that any wind turbine can have.
You can add shrouds or diffusers to turbines
to increase the amount of energy capture.
Some experts say that that allows you
to exceed the Betz limit.
But it's because these additions are increasing
the diameter of the stream tube that hits the rotor.
The maximum efficiency is still 59%
of the energy in the stream tube.
Modern wind turbines are already close
to 50% efficiency.
So they are not actually that far away
from maximum efficiency.
So this is something handy to remember
if you see a new wind turbine technology reporter
that claims to be drastically more efficient
than the current state of the art.
If it's only extracting kinetic energy from the wind,
then it can maximum reach 59%.
So that is a basic principle
of how wind turbines convert energy
from moving air particles
to mechanical energy of the rotor,
where it is then converted to electrical energy
by the generator.
In the next video in this series,
I will explain the aerodynamic theory
that you'll need to understand and analyze
how the air hitting the verta blades, causes them to turn.
So make sure you keep an eye out for that video.
If there were any topics in today's video
that you found confusing,
or you feel like need a deeper explanation,
then please let me know in the comments.
And if it's a short answer, I will reply to your comment.
But if it's a big topic,
then perhaps it could be a future video.
I really like to get my ideas for videos in that way.
If you found this video interesting or helpful,
I would like to see more videos like this, then please like,
and subscribe and share with your friends.
I'll see you next time.
(upbeat music)