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I believe the Shimano Alfine is €65 at Rose, it comes with a BB so that should leave plenty for a cog and chain.
http://www.rosebikes.com/article/shimano-alfine-fc-s501-crankset/
I'd just see what kind of ratio you normally run and go up a couple teeth in the back to compensate for off-road use.
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I quickly modeled it in Solidworks and ran some simulations:
Displacement is virtually identical between the stem with and without hole, which seems to indicate it doesn't make too much of a difference. Keep in mind this is a rough model and more importantly I'm a designer who happens to know Solidworks and not an engineer. Someone with actual knowledge about this should probably chime in. @mdcc_tester perhaps?
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Because you're the kind of rider who never compromises on performance.