I didn't notice any thermodynamic rebuttal in any previous posts. I did see an arguement that a stopped engine puts off more heat than a running engine, and pretty much tuned out after that statement.
The factory battery only lasted 5.5 years in my bike, I don't see much of a problem there. I'll concede the starter sees more use and may well retire early. I can deal with that.
As for charging, you don't have to guess how long it takes to recharge. Lead acid batteries should be charged no faster than c/3 for maximum life, where c is the amp-hour rating. The FJR has a 14 amp-hour batter, so c/3=4.67. I'm gonna call it 5 because I like to keep things simple. The starter on the FJR typically draws 80 amps (look around the forum for confirmation). We'll assume 1 second of cranking for a hot start - frankly it's less. So we've drawn 80 amps for 1 second. The discharge rate is 16 times higher than the charge rate, so we need to charge 16 times longer. Lead-acid batteries are roughly 85% efficient on charge, so you need to put in more energy than you took out, so the charge time is longer still. Nonetheless, the battery is fully charged from the hot start within 30 seconds of riding. Your guess is off by 2 orders of magnitude.
The problem with your post is that although you claim the charging "guess" is off by two orders of magnitude, it is you who has no idea what he is talking about.
The little equation you posted up is very fancy, and could be entirely correct, but for a CAR. I donno of you have realized this, but the FJR is not a car. It's charging system is powered by a stator, not an alternator, and it does not reach full charging capacity until about 5 thousand RPM.
Your equation's theory has been trumped by nearly 10 years of practical use. If a person commutes on their bike, and it is shorter than about 15 minutes, after about a week of start ups, and short rides, the FJR will start to show signs of a weak battery. After about 2 weeks, it may not start at all. A good long ride at higher steady RPMs will bring things back to normal.
So, instead of pulling the newb trick of spouting off how smart you are or how much you know about engines, understand that the people on this board have been riding, maintaining, working on, and discussing this bike for years. Some people here, who have proven themselves smart, instead of just claiming it, have probably forgotten more about this bike than you'll ever know.
So, sit back, drop the "I'm smarter than you" attitude and learn something. Lest your FJR disproves your mathematical theories and leaves you stranded somewhere.