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Forum Index : Windmills : Windmill Math

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MacGyver

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Joined: 12/05/2009
Location: United States
Posts: 1329
Posted: 05:54am 04 Jun 2010
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Crew

One of the hardest things building windmills is getting all three blades at exactly 120 degrees apart. Anything else throws it out of balance and it wobbles all over the place.

So, the big question: How do you divide a circle into 3 equal parts without having a PhD in mathematics?

Here's how:

First off, a little information. The length of the sides of a "hexagon" (six-sided shape; all sides equal length) which is super-scribed by a circle (drawn inside a circle, so the corners touch the outside edge) is equal to the radius of the circle it sits in.

Now what?

Here's what you do:

Pick a center for your circle and mark it. Now, using a compass (pointy on one end, pencil on the other end -- a drawing tool and not the thing you use when you're lost in the woods!), set it to the radius of the circle you want and draw a circle. The radius is the distance from the center to the outside edge of the circle. Once you've set the radius leave it alone -- you'll need that setting to make this work!

For a windmill hub, the circle you draw would be the size of the hub on which you wish to mount the blades.

Leaving the compass set to the radius of the circle, grab a straight-edged ruler and draw a line through the center of the circle (you marked it, remember?) and make the line cross the circle you've drawn with the compass.

Still with me?

Now take the compass with that same radius setting and put the pointy end where the straight line crosses the edge of the circle and draw a tiny rounded line across the outside of the circle.

Next, go to where you just drew the line and do it again. Do this all the way around the circle and you'll have six exactly equal pieces of pie. For thirds, just choose every other one.

Easy, huh?



. . . . . Mac
Nothing difficult is ever easy!
Perhaps better stated in the words of Morgan Freeman,
"Where there is no struggle, there is no progress!"
Copeville, Texas
 
GWatPE

Senior Member

Joined: 01/09/2006
Location: Australia
Posts: 2127
Posted: 02:13pm 04 Jun 2010
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Hi Mac,

basic maths like this has been around for a while, now, and without the need for a PhD.

Good you are having some fun.

Gordon.
become more energy aware
 
mbombay
Newbie

Joined: 17/09/2008
Location: India
Posts: 5
Posted: 04:12pm 05 Jun 2010
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-

That was enlightening.

-
 
ChrisOlson

Regular Member

Joined: 19/01/2010
Location: United States
Posts: 60
Posted: 03:00am 06 Jun 2010
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  MacGyver said   Crew

One of the hardest things building windmills is getting all three blades at exactly 120 degrees apart. Anything else throws it out of balance and it wobbles all over the place.


I use a slightly more crude method. Simply lay the hub and blades on the shop floor so it looks good. Measure the distances between the blade tips, add them all up and divide by three. The result is the distance between the blade tips to have a balanced assembly.

Adjust the blades accordingly, holding them in place on the hub with c-clamps, and drill the holes.
--
Chris
off-grid in Northern Wisconsin, USA
 
MacGyver

Guru

Joined: 12/05/2009
Location: United States
Posts: 1329
Posted: 03:23am 06 Jun 2010
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ChrisOlson

That's another good method. Thanks for adding it.

Measuring tip spread is the way I balance; that and actually weighing my blades. I'm just always wanting to place things 120 degrees apart for one reason or another, so I looked it up and posted the 'how-to' here, thinking others might benefit.

I've actually studied geometry, algebra and trigonometry like everyone else, but it was 50 years ago. Heck, I can barely remember where I put my chuck key and glasses half the time!



. . . . . Mac
Nothing difficult is ever easy!
Perhaps better stated in the words of Morgan Freeman,
"Where there is no struggle, there is no progress!"
Copeville, Texas
 
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