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Yes it will alter the strength and charecteristics. It will weaken slightly more than the percentage you reduce the cross section. Under terminal load it will break at the narrowest point. It will flex a little and then fracture with little warning due to the eneven load charecteristics of a bobbin tapered shaft. C/F rod behaves much the same as hardened steel in this respect. If you do decide to taper it down be careful how you do it. Sanding it down will cause piles of potentially harmful dust. Tapering unevenly i.e. off centre will weaken it still more. Machining in a lathe is possible if you use VERY sharp tools, and a travelling steady post, similar to those used for aluminium. Wear a mask, vacuum up the dust, carbon dust is thought to cause similar lung tissue damage as coal dust, and there is no point taking a risk. Epoxy coat the finished part. I have done this successfully for a guide roller to control the spinnaker retrieval on my sailboat. Hope this helps.
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