Jasen Betts wrote in a message to Roy J. Tellason:

 RJT> That depends.  I've known of some people who did *lots* of fairly
 RJT> short trips, and that ran their battery down because they weren't
 RJT> running long enough to put the charge back into it.  This may
 RJT> have been in colder weather,  may have been with the heavy use of
 RJT> a lot of accessories,  too,  I don't recall

 JB> my altenator's a bit weak it can't run the headlights, engine fan,
 JB> and wipers while the engine is idling, so if I enter traffic-light
 JB> territiory on a rainy night
 JB> I've got to watch out.

Are you sure it's the alternator,  or is it possibly engine RPMs too low? 
Maybe you have a bad diode in there...

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