Member since 1/26/12
Date: 1/26/12 2:55 AM
Dear pattern cutting experts,
I have a specific question, that I have been wrestling with for quite some time now, so I just posed it on my facebook wall, and someone reacted to it by telling me about PatternReview.com, and I do think I have now finally struck gold!
I have invented a new geometric structure that I call "Power Flower", that needs less material to make a bigger shelter because it distributes (flow) the energy (power) more harmonically around,
It can be woven from any kind of material. Here are some pictures of it on my blog where I made it from woven willow, and also from long plastic tubes and various other materials: www.p0werfl0wer.blogspot.com
I have recently emigrated from Holland to Kenya, and now I would like to utilize this structure, by building a "Power Flower Greenhouse", to make the cheapest greenhouse in the world, by covering the woven structure with an umbrella shaped material made from 10 patches sown together.
Greenhouses give more and bigger yields on a smaller space, and need less water because the evaporation is contained, so if I can make a cheaper one, then that would make this option available for more people here in Africa, where a lack of water, food and money are the biggest problems in the world.
If each of the 10 patches would have straight edges, then they would form a pointy pyramid shape, with 10 flat sides, instead of a rounded umbrella shape, so my question to you is:
HOW CAN I CALCULATE THE CURVE AND SIZE OF EACH OF THE 10 PATCHES?
I know there MUST be a formula that answers this question, that relates the diameter of the total sphere to the amount of patches that make up this sphere that would look like a beachball.
It would be easiest if I could draw this curve on the material by tying a marker to a rope, to draw each of the two curves that together make one of these patches, but how long should that rope be, and how far apart should I attach the two centerpoints at the other end of these ropes, to make something similar to the shape of a "Vesica Pisces"(http://en.wikipedia.org/wiki/Vesica_piscis).
The shape of the Vesica Pisces is made by two circles that overlap in the middle, where the outer diameter of each circle is crossing the center of the other, while for making the shape of the patches I need, to make the umbrella/beachball shape, the circles should be further apart.
How far apart, and how big are these circles in relation to the total sphere that the 10 patches would make when sown together?
The cover must be 1/3rd of a sphere, and will then look like an umbrella with 10 patches, with a outer diameter of 13 meters, so the total sphere, that would look like a beachball with 10 patches, would have a diameter of around 15 meters.
People that know in what shape to cut the patches that make hot air balloons might also know more about this.
PLEASE HELP ME OUT!
Paul Bruno.Vesica Pisces expanation by WikipediaMy Webpage
Member since 7/30/02
Date: 1/26/12 4:13 AM
OK, this is more of a maths question than a sewing one & I know there's some here who are much more mathematically inclined than me, but here's some starting thoughts:
Do you particularly need the shape to end up being 1/3 of a sphere? I would suggest calculating on a hemisphere & then chopping the bottom off your pattern piece if you want it to be shallower.
For a hemisphere:
The base measurement for each piece will be (Pi * diameter) / 10.
The height of each piece will be (Pi * diameter) / 4.
I can't offer any suggestions as to how to get the exact curve shape, to be honest I would try it with paper and see what results you get.
But, again, for your purpose is exactness necessary? Or is 'close enough' going to be ok?
Interesting project - once you get it sorted out I'd love to see the finished product.
Mel (Melbourne, Australia)
New York USA
Member since 3/16/07
In reply to Paul Bruno
Date: 1/26/12 10:28 AM
The gist of it is like what's shown in the photo.
Or to see photo click here. It's not showing right in the preview.
What's shown makes a cone with a 30deg angle at the top, that rounds off at the tip. If you want to make a true sphere, then the sides of the "wedge" should be circular, with a radius equal to (# wedges)/2 * (radius of sphere).
You would need to add a seam allowance to either side of the wedge shown. I wouldn't go any less than 2cm (about 3/4 in.) for something for exterior use like this. It's fairly easy to add the SA with a see through ruler.
You can probably refine the shape a little more, but I think you'd need to make a scale model (about 6in. across), then make a prototype. Your frame isn't going to be smooth unless you use an infinite number of circles, and I'm not even sure it converges to a sphere all the time. Certainly not a sphere of the same size, if you allow the circles to slide relative to each other.
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