When Pure Maths is not Enough

Wednesday, June 10, 2009

(Will falling wind speed curb turbine plans?)

http://www.thestar.com/sciencetech/article/648631

You gotta admire the mathematicians at the Toronto Star; at least, you can once they get back from lunch.

Here’s a dozy little quote at the foot of an article: “Pryor said a 10 per cent change in peak winds would translate into a 30 per cent change in how much energy is reaped.”

I read that, and thought “I bet they don’t take into account the fixed overhead of wastage through friction, resistance and so on”.

To check my theory I did a Real Simple Spreadsheet; you can do it, too, if you don’t trust me:

Remembering, as Mr. Puzey my physics teacher taught us, that the energy of a fluid is proportional to the CUBE of its velocity, here’s a little table of velocity Vs. energy. You’ll notice straight away that I’m not saying whether the velocity is kilometers per hour, which is how fast the wind blows in Canada, or miles per hour, which is how fast it blows in the U.S.A.

It just BLOWS, OK?

The cube of 60 is 216,000.

The cube of a speed just 10% shy of 60 is 157,464.

And so on.

The left column starts at 60 KM/h, or 60 mph, or 60 fps, or whatever units you play with.

Each item in the column is 10% less than the item above it.

The item to the right is the cube of the speed, in whatever energy units correspond to your units of velocity.

Now let us track the percentage reduction in energy for each of the 10% reductions in velocity:

Huh? The percentage reduction is a consistent 27%, which we think must correspond to the reported 30%.

Why is this?

Well, if the energy is proportional to the CUBE of the velocity, then the reduction in energy must be proportional to the CUBE of the reduction in velocity.

Calculate 90% multiplied by 90% multiplied by 90%.

Or if you prefer, 0.9 multiplied by 0.9 multiplied by 0.9.

You’ll get 72.9% or 0.729.

Subtract that from One, and you’ll get that magic 27%.

(This starts to sound like “Take away the number you first thought of and ….”)

Of course.

My guess is that the study's lead author, Sara Pryor, knows her arithmetic, knows her physics, and merely quotes (1-0.10^3), a mathematical truism unrelated to wind turbines. There’s no meat on THIS bone!.

Can you say “I need more grant money to make a proper examination of these factors”?

Try it, go on!

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