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Am I correct that TT helmets do nothing for safety, and are only for speed?
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To an extent, you are correct. The old TT helmets (2003 and earlier I believe) are basically fairings. I have the giro one the USPS team used and trust me, you do not want to take a spill wearing that. It literally is like one of those red dixie plastic cups. No protection whatsoever.
The newer helmets used in the tour have more protection.