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Variations of Tetrahedral Kites


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The tetrahedral, like most box kites, has a huge number of variants, which you can use to make your own tetrahedral different, to any others you may find. This page presents many of the tetrahedral kite variations...
* Structural Arrangement of Cells
* Regular tetrahedron formation
* Long formations
* Wide formations
* Dimensions of a Tetrahedral
* Irregular and Unusual Tetrahedrals
* Cell Construction Variations
* Composite Variations

Of the categories, changing the structural order of the cells is generally easier, while modifying construction requires forethought as the spar lengths change. Combining the two methods can also lead to some very interesting results.

Structural Arrangement of Cells

Rearranging the cells of a tetrahedral kite is the simplest form of kite variation. Even so an infinite number of variations exist. Below I will list the most common variations.

Regular Tetrahedron Formation

The more common variants of the tetrahedral kite, form in themselves giant tetrahedral. The diagram below shows the four simplest regular tetrahedral structures. The colours have been chosen to show the kites layers to make it easier to understand.

[Diagram]

[photo]

I myself had trouble stabilising this regular tetrahedral. However, Spence Wikel's 16 cell Sierpinski Tetrahedral (expand the photo, right to see), shows one recommended solution. The addition of extra side bridles ensures that regular tetra's, can't just suddenly swerve to either side due to wind changes or sail flap. The bridles in that case become unbalanced and forces the tetra back on course real fast.

The later "wide" tetra's below do not have this problem as they have more side-by-side bridle lines due to their width. "Long" tetras also are more stable due to the extra length.


4 Cell Tetrahedral

[photo] This is the most basic tetrahedral construction and one which almost all tetrahedral kite plans build. Unfortunately is it is also the most unstable of all the tetra kites and will often loop and dive, and tumble around the sky before crashing back to earth.

The reason for this instability is two-fold. First the kite is small in size relative to amount of frame work needed in the kite. Tetras with more cells (NOT larger cells) provide more lift for their weight, and thus fly better, especially in lighter winds. Still the weight tends to make the kite swerve from side to side in large figure 8's. Having said this an ultra light straw and plastic tetras of this type, seems to have no trouble flying well, and rock steady.

The second reason for its failure to fly well is that the kites centre of gravity is very high with regard to the kite sail structure. Larger tetras has more sail above the centre of gravity which ensures that kite know which way is up. The high dihedral angle of the wings then makes other larger tetras rock steady when flying.

16 Cell Sierpinski Tetrahedral

[photo] This is the simplest way of using a basic four cell tetrahedral plan to build a large much more stable tetrahedral kite.

Make four of the above 4 cell kites, and then tie or clip them together (corner to corner) using fishing clips, split rings, curtain rings, normal string, ribbon, wherever, to create a larger 16 cell tetrahedral kite.

The variation is called a "Sierpinski Tetrahedral Structure" after a 'fractal' geometric pattern of the same name for 2 dimensional triangles. For more information of that fractal see Fractals, and Fractal Dimension, for a more mathematical overview, of the Sierpinski Triangle from which the Sierpinski Tetrahedron was an 3D extension. You may be also interested in The Sierpinski Tetrahedron, and from the same author, Building paper Sierpinski Tetrahedral.

This is an interesting structure as while it is solid looking it also has a sort of 'swiss cheese' holey effect, which makes it fascinating to look at. Especially when flying in the air. Even graham Alexander Bell experimented with this tetrahedral variation, (see below).

It is also the easiest compound regular tetrahedral structure to build, as the connectors only have to deal with either 3 spars at the corners or 6 spars elsewhere in the kite (same as for a 4 cell tetrahedral above). All the other variations have joint involving 9 or ever 12 spars all jointing together at the same point, which can get difficult to build.

Other examples are...
[photo] One commercial model flown by Al Hargus III, from an article in Kite Life EZine (May98) -- now offline.
[photo] Spence Wikel also has built one. His web site contains lots of photos of this and another tetra he has built.
[photo] Here is a lovely tie-died straw tetra, by Ernie

64 Cell Sierpinski Tetrahedral

[old photo] Being a 'fractal' the Sierpinski Tetrahedral structure can be increased even further by building 4 of the 16 cell Sierpinski structures above, (16 four cell tetras) to create a 64 cell variation, or a 3rd level Sierpinski tetrahedral. A four cell tetra is a level 1 Sierpinski Tetrahedral.

[photo] The photo to the right shows Mr Bell himself flying such a third generation Sierpinski Tetrahedral, and was taken in 1903 at Bell's home on the island of Cape Breton, Nova Scotia, Canada. An amazing sight indeed.
[photo]

Shown left is a colourful 64 cell Sierpinski tetra made by Volere Volare of Italy.
[photo]

And again to the left is a 64 cell drinking straw tetra made for a UK Children's Science TV Series Big Bang. The view is from directly below the kite, looking upward.
[photo]

And 64 cell tetra, made with a ring and rod construction method, made by Rob Rob Thomlinson and Tony Broad in England. You can see more of it on their site.
[photo] [photo]

And here is a tetra-lite design (Bamboo BBQ skewers and thin plastic tubing), from K÷vessi Zsolt in Budapest. This design allows it to fold up flat for transport.


10 Cell Solid Tetrahedral

[photo] The 10 cell is the next 'solid' structure after the 4 cell tetrahedral. Each side of the kite is formed from 3 regular tetrahedrons with no gaps or holes as the Sierpinski structures above. This is also much more difficult to build as some of the joints in the tetrahedral kite involve 9 spars coming together at the same point. That is a lot of spars!

Ross Leighton <leighton@ozemail.com.au> has built the pictured 10 cell tetrahedral from 6mm dowel. You can find his email in the responses to my own tetrahedral kite plan page. He has also provided me with photo showing how he created the '9 spar joint', required for this kite.

20 Cell Solid Tetrahedral

The next solid tetra is 20 cells. However not only do you have a number of '9 spar joints', the 20 cell tetra also has a '12 spar joint' in the very middle of the kite. This is the largest joint in any tetrahedral kite, so if you can figure how to build it, you can build tetras to any size you like.

This is also equivalent to the 16 cell structure where the 'hole' in the middle of the kite has been filled in with 4 more cells. This of course makes the kite less 'holey' and much more solid looking, than the 16 cell Sierpinski structure.

This structure is very large, and very very strong. However I would not continue this process further to 5 cells per edge. Why? Because, while the tetra gets larger, and stronger, the wind would start having problems penetrating to the cells at the rear of the kite. This in turn reduces the gain in lift and increases the drag of the kite making it less efficient.

100 Cell Tetrahedral!

[Diagram] Using the same 'Sierpinski' like structure as for the 16 cell tetra above, the 10 cell 'solid' tetrahedral can be expanded into monstrous proportions. A 100 cell Tetrahedral Kite!

This is done by making 10, 10 cell solid tetrahedrals, and joining them in the same way as a 10 cell tetra (fractal like). [photo]

A a class of fourth grade students in Bakersfield, California, made such a tetrahedral using straws and brightly coloured tissue paper. You can see more photos of their effort on the page 100 Cell Straw Tetra, final construction and results. Congratulations a job well done.

160 Cell Variation

[photo] Instead of using 10, 10 cell tetra's you can instead use 10, 16 cell Sierpinski tetrahedrals, to form a 160 cell tetrahedral. Its is sort of an a mixture of the regular tetrahedral structures above, and is probably a little easier to build than the 100 cell version, as it is more open.

The photo to the left shows Diane Hislop, a school teacher with one such kite made by his primary school class after the success of their 100 cell tetrahedral.


Long Tetrahedral Structures

The above 'regular' tetrahedral structures are fine, and look really great in the sky. However, instead of adding cells in all directions you can instead increase the length of the tetrahedral kite.

Mr Bell's early experiments with tetrahedral kites did just that, and one of the more famous tetrahedral kites is his boat tetra.

Bell's Tetra 'Boat' is created using 20 cells in total. A standard 4 four cell tetrahedral is continually added to, to extend the front and rear faces, until it is 7 cells long (1 wide, 7 long, 2 height), forming the boats 'hull'. On to the top of this two regular 4 cell tetras were then added, forming the boats 'sail' or 'bow', depending on exactly where they were placed.

[Diagram]

Wide Tetrahedral Structures

More commonly today, and in Bell's latter experiments, tetrahedral kites were extend by adding cells along the left and right faces of the kite. This allows the kite to catch more direct wind thus producing greater lift, and less drag than a similar long tetrahedral.

[Diagram]

The above diagrams show some 2 cell long ''wide'' tetrahedrals of increasing width. while the next diagram if of 3 cell long ''wide'' tetrahedrals.

[Diagram]

I have found from personal experience that wide tetra's are so much more stable than the regular tetrahedrals. I think that may be because the bridle is forked to two or more points side by side, which has a huge stabilising effect on the whole kite, preventing spins and spirals, due to wind turbulence.

Tetrahedral Dimensions

Note the number of cells a tetrahedral has does not specify exactly the size and shape of the tetrahedrals. For example we have now seen 3 different 16 cell tetra's. As such, to uniquely specify a tetrahedral you really need to specify the width and length of the kite (in cells) on the bottom most layer, and the kites height in the number of cell layers.

For example a regular 4 cell tetra would be 1 cell wide, 2 cells long and 2 high or 1×2×2 tetrahedral. As another example, the 13 cell, 'wide' tetra (above), can be classed as a 4 wide, 2 long and 2 high, or 4×2×2 tetra.

Note that multiplying these dimensions does NOT give you the number of cells. These kites are not rectangular or cubic in nature, and as such a straight multiplication will fail. Any one out their like to figure a formula?.

Also you will note that the height (or number of layers) of a tetra is usually equal to its length. As such the height may be left off the kites size, when the tetra is completely filled out with cells. This is not always the case as the designer may have decided not to fully fill it out, height wise, especially for 'long' tetrahedral kites. The hull of Bell's Boat (above) is an example of a 1×7×2 tetrahedral. [photo]

Here is a photo of a 5×3 'wide' tetrahedral (34 cell) built by TetraLite Kites.

Other photos of 'wide' tetra's include...
A 6×5 (110 Cell) TetraLite (more info from 'Big Tetra' Page)
A 'flattened' 7×2 (24 cell) tetrahedral by Carl Crowell
A 3×4 (40 cell) Holger's Tetra from Fan° 1999

[photo] To the left is a photo of a great looking 2x3 (16 cell) tetra by Bob Hogan (who's web site has disappeared) .

[photo] Shown right is a photo of Paul Chapman's 5×4 (60 Cell) wide tetra. This was found in High as a Kite, Gallery 4

The record for a multi-cellular tetrahedral is 3,393 cells known as the "Cygnet" and was itself a 'wide' variant. This was set by the inventor of this type of kite, Graham Alexandra Bell (See What is a Tetrahedral Kite?). This kite only had one flight, being towed into the air by a steam boat, and carried a passenger.

[old photo] Maybe you would like to beat this record! Good luck.

Here is a photo of one of Mister Bell's earlier wide tetras. This one is a 13×12 cell tetra. Anyone like to calculate the number of cells?

Irregular Tetrahedral Structures

The modular nature of tetrahedral structures is very versatile for kite building. below are a few very unusual and irregular tetra's. The names, like 'exotic' and 'keystone', are only a descriptive reference to the kites shape.
[Diagram]

The 'exotic' kite use 5 normal tetra cells but the 6'th is split in half and used on either side of the kite. Another description of it is to take a 7 cell wide tetra (2 wide, 2 long, and 2 high) and remove half the uppermost corner cells on each side. From head or tail on, the kite looks vaguely hexagonal in shape.

[photo] [photo] The 10 cell 'keystone', is basically 3, 4 cell tetra's, which all share a single cell in the middle of the kite. When flying it has three 'points' facing forward into the wind. It is called a 'keystone' as its shape when seen front on, looks vaguely like the keystone used in a stone arch.

[photo] To the left is a photo of a solid but incomplete (thus irregular) tetra flown at Long Beach in 1998. Also note that the edges of the cells are curved slightly to prevent edge flap. That is because this tetra used a corner bracing method of construction. [photo]


Shown right is a distant photo of a 55 cell tetrahedral, in a airplane-like structure. It consists of a 34 cell wide tetra, joined to a 10 cell wide, by a set of 11 extra cells. The kite known as 'Cometa' was created by Erik Delgado.


Cell Construction Variations

[photo]

Flattened Tetrahedral

Replace the trailing edge spar of each cell, or four cell unit, with one about 25% longer in length. This will greatly reduce the dihedral angle of the tetrahedral (which is no longer a regular polyhedra), and thus presents more surface area to the wind. The covers of the tetrahedrons will now form about 90 degree angle instead of the steeply sloping one slightly greater than 60 degrees. [photo]

The tetrahedral thus created will still look like a normal tetrahedral kite but will pull just a little more. The kite however would be a little bit more unstable, and may need to have more cells, to make it larger and more stable, or a tail added to the trailing cell(s).

By increasing the trailing edge to 50% longer, the kite will become closer to a normal dihedral angled kite, but will require a tail to stabilise the kite. Also the way a tetrahedral kite is framed so that it does not allow the leading edge to stretch slightly up and backward would also cause the kite to be unstable. Very tight cell 'skins' are also recommended.

A good example of a highly flattened 24 cell tetrahedral was created by Carl Crowell

High Aspect Tetrahedral

Instead of just making the trailing edge longer, you can also make the side edges longer (or shorten the cells spine :-) so that the tetrahedrals are very wide.

A photo of a ultra high aspect ratio tetrahedral by Carl Crowell, is a extreme case of this type of tetra.

Distorted Tetrahedral

You can also distort the tetrahedral by making the rear side edges longer than the forward side edges by the square root of 2 (about 1.41). By doing this the angle between the leading edge and the forward side edges is a 90 degree angle and the kite cell surfaces become half squares or 90-45-45 triangles!.

[photo] The "Chicago Fire" tetrahedral kite, with its distinctive white and black striped panels on the left side and solid colour panels on the right is one of the more famous, distorted tetrahedral kites. None of the two sides, or the leading or trailing edges are the exact same length! though it seems to contain an angle fairly close to (but not quite) a 90 degree angle.

David Petre <dpetre@driveninc.net> wrote to add the following about this commercial tetra...
The spine is 62cm total length and the spreader is 79cm total length. Those two spars are long, and extend beyond the kite itself , with one end a ferrule and the other an extension to push into the ferrule to connect the cells. The cell itself has a spine of 55cm, a spreader of 72cm with a leading edge of 45cm and a trailing edge of 61cm.

I bought the first 4 cell unit and it didn't fly very well, so I had to buy 12 more for a total of 16 to get a good stable kite. The cells are held together with bunji cords.

 

Composite Tetrahedrals

If you really want to be different you can produce a composite structure using both a structural arrangement of cells, AND changes to the individual tetrahedral cells.

Making a different change to each individual cell in a tetra can lead to some very interesting a weird designs. Tetras can become very un-tetrahedral in style, though still being based on that cellular design.

[photo] For example the photo left is a tetralite 10 cell 'keystone' design in which the side cells have a 50% longer bracing spar.

In fact by some small changes you can also help reduce much of the heavy sparing normally required for a tetrahedral...

[photo] [photo] [photo]
For example, by using a variation on the mast-braced cell construction method, I was able to create a variant based on a "Tri-D" (or Peter Lynn) box kite, I call a Tetra-Tri-D (See photos above).

The resulting "tetra" is a 'long' 1×4×2 variant, but with one side of each of the 6 top level cells folded down horizontally. In fact it is braced the same way as a Tri-D Box, which greatly reduces overall weight of the kite from a typical tetra of that size. The kite was built from the ripstop cells from my 16 cell tetra (See photo in the regular area above), which due to its weight, was never fully stable. This kite on the other hand was rock steady, flying all day on a light sea breeze in the morning, until the rear two cross spar dowels broke when the wind became near gale force in the late afternoon.

[photo] To the left is a photo of Robert Harvey's composite tetra of similar design to my tetra-tri-d. This kite was the winner of the Cellular Kite Category at the Festival of Winds, Bondi, Sydney, Australia, in September 2001.

Skys the limit, build your own unique variation.



Created: 16 June 1996
Updated: 4 June 2002
Author: Anthony Thyssen, <anthony@cit.gu.edu.au>
Special Thanks to: TetraLite Kites for the use of their photos.
A large sheet of various tetra styles
WWW URL: http://www.ict.griffith.edu.au/anthony/kites/tetra/variations/