It all adds up for Chris, but you may need a calculator


When I visited Denmark a similar wind farm looked like this. The beach scene below is at an Emglish resort area, and the race scene is from last year's ocean race around Great Britain.

Two if by Sea
By Chris Stimpson


The second-most frequent response I get when I explain the value of Horseshoe Shoal for the Commonwealth's first utility-scale wind farm is along the lines of: "what's wrong with Otis, or along Route 6;  there's plenty of wind there."  (The most frequent response, of course, is: "I'm all for renewable energy, but can't they put it off someone else's shore?"  Well of course, people on the shores of Buzzards Bay, Rhode Island Sound, Bigelow Bight and Massachusetts Bay think totally differently from you, so why not?)

As a non-mathematician it pains me to resort to mathematical answers, but they do have the advantage of being based on something other than conjecture, opinion, misinformation or personal taste.  If you don't agree that two and two make four, you probably don't make a good spokesperson for any cause, no matter how noble.  Besides, whenever I explain this particular mathematical truth, I find the beneficiary of the explanation either fully understands the Cape Wind project for the first time, or-after a suitable pause-reverts to the abovementioned most frequent response.  Sometimes both.

So here comes the math.  Ready?

P = ½ rV3A

Where     P = the power, in Watts, of wind passing through a circular area
    r = air density, in kg/m3
    V = wind speed, in m/s
    A = the area, in sq. m, swept by the circular rotor

 Still with me?  If so, you're ahead of where I was during my only calculus course, when I kept expecting Mr. Page to turn from the blackboard and explain between fits of laughter that the whole thing was a joke that math. teachers liked to play on students before getting on with trigonometry.  But even a mathophobe like me can understand the formula I just inflicted on you.  In fact, it's a breeze (sorry).

I should also explain that the formula is theoretical, by which I mean it doesn't take into account such variables as power coefficients and mechanical and electrical efficiencies of specific turbine models.  But why should it?  For this example, we're assuming we have two identical turbines, one plonked in the water on Horseshoe Shoal, the other rising from the ground in the Mass. Military Reservation, whether the Military want it there or not.

The other arguments that apply equally to our two hypothetical turbines are A and r, if we assume the turbines to have the same rotor dimensions and the air density to be identical in both locations.  So what's left?  Looks like V-the wind speed-which is, according to the person seeking wisdom from me, the same at the MMS/Route 6 as over the Sound.

english_beachkid334 The fact is, V is the only true variable in this example.  And we know (from observation, not opinion) that the average wind speed over the Shoal is 19mph, compared with 15mph over those land-based sites.  Not a huge difference, is it?  Not enough to ruin the pristine Sound that should be a sanctuary with an industrial development that will kill birds and spill oil and be a danger to navigation and wreck tourism and homev alues...  Sorry again;  funny how all those ideas tend to run together.

But back to the math.  Did you notice that the wind speed is cubed in the formula?  Right, out with the pocket calculator (they actually work better when out of the pocket).  

Horseshoe Shoal: 19 x 19 x 19 = 6859 Watts
MMR/Route 6:     15 x 15 x 15 = 3375 Watts

Shocker, isn't it?  For a mere 4mph more in wind speed, you get twice the power output!  Or to put it another way, if you take the wind farm you were planning to build on the Shoal and relocate it on land, you cut your saleable product in half.  

ocean_racing If you're a private company, it's hard to finance a project when your potential output is reduced by 50%, particularly when Cape Wind Associates must, like any other producer, sell their power into the grid at a competitive wholesale rate or no supplier will buy it.  (Oh yes-and if you're not a private company, but some public entity, you'd be using taxpayers' money to achieve that non-result.  That wouldn't just be a bad business plan, that would be an irresponsible waste of your tax dollars).  In short, if Cape Wind were to be relocated to a much less productive land site, it would not be economically viable.  

Well now, that was a new, and quite unlooked-for role for me-math. teacher to the masses.  But here's a thought to take away with you:  as you log in to compose a rejoinder to the above, see if you can couch your response in the same terms as the original, i.e., factual rebuttals of my slender grasp of the mathematical arts.  

chris_stimpson_150 Because I've heard all the rest.

Chris Stimpson is a Secretary of Clean Power Now, a grassroots group providing information and education on renewable energy. Chris has worked in local media since moving here.  Chris Stimpson, a 25+ year resident of the Cape and former RAF aviator, has worked in the media and communications field since 1982.  As secretary of Clean Power Now, he has been in the forefront of renewable energy issues for nearly four years.

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