AAA rechargeable cells would require more frequent replacement/charging unless you used a low self discharge cell such as Sanyo Eneloops. Also the computer body would be way too big for most folks. Current draw is in the same range as a watch so button cells are the most compact and logical solution.
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Gear Hubs Owned: Rohloff disc brake, SRAM iM9 disc brake, SRAM P5 freewheel, Sachs Torpedo 3 speed freewheel, NuVinci CVT, Shimano Alfine SG S-501, Sturmey Archer S5-2 Alloy. Other: 83 Colnago Super Record, Univega Via De Oro
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http://groups.yahoo.com/group/Geared_hub_bikes/