Taking a gamble I emailed the owner of the page to find out more, only to discover these tubes were Mark's own design, and he was willing to let me publish those plans on my web site. Thanks for sharing your plan with us, Mark. - Anthony.
The tail essentially consists of a single bulge spiralling around a tube. The outside bugle catches the wind very slightly causing the whole tube to slowly rotate. A spiral of color will thus move down the length of the tube. As the far end is fully enclosed, their is no wind movement inside the tube itself.
Below are Mark Neuhaus's original instructions, plus my explanation and working notes. Enjoy, and mail me your results.
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.
The diagram of the pieces for the twist tube is as provided by Mark. The only change is that the diagram has been enlarged to fill the page better, and add Mark's suggested dimensions (in inches).
Essentially the tube is a normal cylinder with a bulge which spirals around the cylinder. You can stretch or shrink the lengths of the pieces to tighten or spread out the spiral, or increase the height of the curve slightly to make it even more pronounced.
Making thick cardboard, or thin plywood templates is highly recommended, especially for piece #9 which you need lots of. You may like to make 4 or more of these so you can better lay out the template on the fabric (see photos). The dimensions are not critical and can be directly scaled to metric units, or to whatever size you like.All pieces also have a 1/4th inch (5mm) hem, notched at the corners for sewing. I used a small plastic pulley wheel which I ran around the edge of the template with a pencil in the middle to draw out those seams very very quickly.
If you study the measurements closely you will find that the slanted edge is calculated to cover 1/8th of the cord (straight) length of the curve (16 inches) on the main #9 piece. Thus 8 pieces are required to go around the tube once. If you change the number of start pieces this length will also need to be modified to suit.
The height of the curve is not critical and reduces in size as you progress from piece 8 down to piece 1. That way the 'bulge' of the twist also reduces in size as you approach the ends. To make the curve I suggest placing three pins in a pinboard (two ends and the middle) and bending a piece of 2mm fibreglass rod (or whatever) around those pins to make a smooth curve. It's actual shape is not critical.
What is important is that the curve (in this case the curves height and length) of one piece, matches the curve of the next piece. This way the length and shape of the curve is the same for both pieces allowing you to place the pieces exactly on top of each other. You can then sew the curve with the pieces lying flat. Folding the last sewn curve under and out of the way then lets you easily sew the next piece to the 'chain', in the same way.
The final main seam of the tube (all those slant edges) is more tricky and I suggest you the first pin a few edges together before you start sewing along them, going round and round the cylinder (inside out).
Cutting the pieces using cardboard templates
Sewing the pieces into a long strip, 7 white then 2 red!
and final inflation test, and slowly spinning result!