Finding speed of a wind turbine

Background story

Our college is presently situated in a big sparsely populated campus with a lot of greenery spotted by a few wind turbines (3-bladed, horizontal axis).

All of us are curious about these wind turbines towering over the campus, but most of us don't know a lot about them. For instance, I always wondered if we could climb on to the top of the wind mill and how one would do the repair work if it gets faulty.

Still don't have answers to those, but today I found out something else thanks to a friend, a Physics student who loves his domain enough to actually apply it to things around him (haven't come across many like that).

It was a time of the day when it was quite windy. One of those 'peak wind' times.

We were just standing enjoying the wind flying past us. That was when my friend thought of finding the speed of the wind turbine closest to us which we could see quite clearly.

Method

My friend realized that to find the speed of the blade, we needed:

Length of a blade
Time taken by a blade to finish one complete rotation (360°)

He was observant enough to notice that the length of a blade was almost same as half the height of the tower. This meant that we just needed to have estimate of the height of the tower to estimate the blade length.

My friend figured that the tower was as tall as the combined height of 50 men of 6 feet each. ie, 50 * 6 = 300 feet. (A very rough estimate, but we could always improve it once we got familiar with the way to calculate the blade speed.)

This meant that the blade length was 300/2 = 150 feet = 150 * 0.3 = 45m

As for the time taken by a blade to finish a rotation, my friend used a stopwatch. Came to about 4 seconds.

Calculations

These were the equations that were needed:

Angular velocity = ω = dθ/dt (unit: s⁻¹)
Linear velocity = v = rω

We already had the input values:

dθ = 2π rad (one full rotation)
dt = 4s
r = 45m

and just substituted them in the equations.

Angular velocity of the blade:

ω = dθ/dt
  = (2π rad)/(4 s)
  = π/2 s⁻¹

Linear velocity of the tip of the blade:

v = rω
  = (45 m) / (π/2 s⁻¹)
  = (45π/2) m.s⁻¹
  = 45 * 3.14 / 2
  = 70.65 m.s⁻¹ (approx)
  = 70.65 * (18/5)
  = 254.34 km.h⁻¹

More than 250 km.h⁻¹! That's a lot.. (either that or we messed up in one of our estimations 😅).

Note that this is the speed of the tip of the blade.

About radian

Radian (rad) is the SI unit for measuring angles.

One thing that I had forgotten (from whatever I learned during my school days) was that a value in radian is dimensionless.

Let's see why.

1 radian is defined as:

1 rad = l/r

where:

l is the length of the arc subtending the angle in a circle
r is the radius of the circle

Since both l and r are of the same unit (lengths), radian is a dimension-less value (ie, does not have a unit).

Relation with degree (another unit for measuring angles) :: 2π rad = 1 deg

More about wind turbines

Our brief fixation with wind turbines today piqued my interest and I did some searching online to learn and recall some stuff about them.

Here's some of it.

Parts of a wind turbine

Foundation: Base on which the wind turbine sits on. Being a slender structure exposed to the elements, needs to be quite sturdy.
Tower: Sort of 'hoists' up blades so that it can be at a higher altitude where it will be more windy.
Blades: 'Catches' the wind. Can vary between different types of wind mills.
Nacelle: The part bulging out of the part where all blades meet (the 'eye' of the turbine). Houses gears and breaking mechanisms among other things.

   |
   | ------------> blade
   |
   ▪ ------------> nacelle
  /┃\
 / ┃ \
/  ┃  \    
   ┃    
   ┃ ------------> tower
   ┃    
 ▩▩▩▩▩  ---------> foundation

Types of wind turbines

Wind turbines may broadly be classified into:

Horizontal axis wind turbines
Vertical axis wind turbines

The kind of wind turbines most people must have come across is horizontal axis.

Horizontal axis	Vertical axis
Needs to realign to face the wind	No need of realignment
All blades mounted on same side of tower	All blades needn't be on same side of tower

Wind mills vs wind turbines

I used to think that both were same. But it appears that it isn't so.

Wind mills are more.. well, one could say 'ancient' (still used though). In the sense that they simply convert the kinetic energy of the wind to some mechanical work. They can work only when there is sufficient wind.

Wind turbines are something that evolved out of the wind mills of old. They use the kinetic energy of the wind to produce electricity which may then be stored and used as required.

Here's a table comparing the two:

Wind mill	Wind turbine
Kinetic energy → mechanical work	Kinetic energy → Stored electricity
Energy only when wind is available	Energy even when wind is unavailable
Older technology	More modern
Simpler	More complex

Can a wind turbine be stopped?

Had that question for quite a while. Found out recently that the answer is yes.

A 'braking mechanism' (housed in the nacelle) is part of wind turbines so that they can be stopped when needed. For example, to prevent damage when the wind speed is too high or for maintenance work.

References

(Thanks to Harikrishnan, the friend that I mention in this post.)

(From this blog post onwards, I've started using org files to write the content instead of markdown. 🙂)