Research on Kite Lines
Research 1:
Dyneema is a synthetic fiber based on ultra high molecular weight polyethylene, 15 times stronger than steel and up to 40% stronger than Kevlar.
It is usually used in bulletproof vests, bow strings, climbing equipment and high performance sails in yachting
[Source from http://plastics.inwiki.org/Dyneema]
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Research 2:
Dyneema vs Kevlar:
Dyneema is stronger (higher breaking load)
Dyneema lasts longer
Dyneema weights less
Dyneema resists much better to UV light
Dyneema has lower dielectric constant (about 2.2 vs 3.8 for Kevlar)
Dyneema has excellent abrasion resistance, low moisture absorption, very low
elongation, excellent flex fatigue resistance
[Source from http://lists.contesting.com/_towertalk/2002-02/msg00548.html]
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Research 3:
Paragliders lines were formerly made from aramid fibers (Kevlar).
The problem with aramid is that the strength decrease quickly while the lines are getting old.
Kite lines in counterpart are made from high density polyethylene (dyneema, spectra) which keeps its strenght better, but the drawback is that it is prone to elongation; which is not really a problem on kites.
Then paraglider manufacturers began to use a mix of dyneema / kevlar lines to get the best of both, for low and high suspension cones (i dont remember which was made of what btw)
So you'll probably find dyneema lines under "kite lines" and aramid lines under "paraglider lines", whatever you will be using these rope for. Some dyneema lines were also made specially for paragliders, with an outer sheath to protect the lines, while kite lines are usually naked (dyneema doesnt really needs any protection because it is really abrasion and uv resistant).
[Source from http://www.paraglidingforum.com/viewtopic.php?t=20994]
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Conclusion: