me have long head tube
Join Date: Oct 2005
Location: Chapel Hill, NC
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The derailler will probably have enough capacity to take up the slack - the range is only 27t. However, the issue is whether the derailler will move at an angle that can handle a 30t large cog. Shimano "road" rear deraillers are rated to 27t max cog, although in practice 28t always works, and often 30t will work too. However, a 30t large cog isn't always a sure bet with this setup.
I run a 13-28 7-speed freewheel on my commuting bike, with a single chainring. So, similar setup. But I've got an old Shimano Exage rear derailler, designed for mountain bikes (so, long-cage), with an official max-tooth capability of 32t, functional to 34t.
If you're using friction-shifting, this is probably irrelevant; your derailler will handle it. But if you're using indexed shifting, 30t large cog with a road rear mech is a "maybe."