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Cut out 2 sets of pieces 1 through 8, these make the ends of the tube shrinking the twists into a more normal tube openings. Then cut out lots of #9 pieces. I use 180 pieces for a 30 ft tube.
Grain makes no difference here at all. Nor should anyone waste time hot cutting, as no air passes by the edges. I use an exacto knife and run it over a sharpener stone every once in a while.
To one of these sets of 8, cutout and sew 8 of of those pieces that look like a teacup with a hat, to the flat, un-slanted ends. Double hem the teacup hat to reinforce what will become a flower-head like opening for the tube.
For the other set cut and sew the 8 triangular pieces to form a tapering pointy tail.
Sew all the pieces together, side by side, starting with piece 1 through to 8 (with their tea cup pieces), then all the 9 pieces, and ending with the second set of pieces 8 down to 1 (with the pointy tail triangles). Before too long you'll have this nice slanted, real long mess.
Then you sew slanted sides together, the point of #1 to the first piece 9 in the 'chain' of pieces, in one LONG seam all the way from one end to the other, to form a inside out tube. Pins may help with this step.
When finished you can turn the tube inside out and take a look at the basic result. 8 bridle lines are attached to loops you can now sew to the tips of the 8 triangular points of the tubes opening. The lines are then collected together to a swivel to allow the tube to slowly spin.
I also always sew some ribbon in the final tapering point, so I can attach another tube or tails. I've gone back and sewn in a small sleeve at the "V" notches of the flower-head opening and inserted a thin flexible rod. It isn't needed but holds the mouth open and helps keep it inflated when winds are light.