Carbon nano tube sheets

You forget that strength is primarly only in 1 direction I think will find it probably preforms worse then kevlar vest in many respects.
 
Woven super-carbon (generic name for any synthetically structured, strong carbon) may be a better alternative. Theory suggests it may be possible to make threads of the stuff as much as one hundred times the strength of steel. Current best is at around thirty times the strength of steel. These types of threads were to be used in the whole "Space Elevator" concept, due to extreme tensile strength, so you can easily see their benefits in body armor.

Later

Dio
 
The hard part is in getting long fibers of the stuff and threading them together to get strands that can be handled to make stuff with. The current fibers are still microscopically small, and grown at random. And the tensile strength is mostly in the length of the fibers. If they're less than a mm long, the resulting strands won't be very strong and really hard to thread together.

Edit: so it's actually much easier to just put and press them together to form tiny sheets, than making strands. But there aren't very many applications for those tiny sheets.
 
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