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Sturmey hubs are not completely impractical for time trialling.
Here's my attempt to use one. I didn't really set out to prove the value of hub gears, but I had a frame I wanted to use which wasn't really suitable for fixed. I found I was getting results as good or better than I'd been getting on my conventional semi - modern geared bike, so I had this wheel built with a Fiamme sprint rim and bladed spokes. The hub is an AM, that is, a 3 speed medium ratio.
With the 15 sprocket as shown and a 51 tooth ring this gave gears of 79,90 and 104" - the equivalent of a block with 13,15 and 17 tooth sprockets. I found this suited me for flattish courses like the F1 (The A1 road based on Tempsford near Sandy, Beds.)
Other (much more illustrious) Sturmey users have been Sid Ferris, Ray Booty (his straight out RRA 100 record) and Cliff Smith (24 Hour Champ. 1964), among many others.
It’s true. My grandpa time trialed in the 1920s and early 30s and for the rest of his life thought derailleur gears were the work of the devil. Sturmey all the way! Their close ratio hubs were still being used by time trialists into the 50s and 60s in the uk.