noted..regarding the ethanol..as far as leaving the tank empty i would never do that..look at how many people selling older bikes have rusty old fuel tanks (inside) and have to coat them...my 81 CB 750 F tank(32 yrs old) on the inside looks like it just came from the dealer.....no room for condensation means NO rust... if your not shure how good the fuel will be in the spring drain it and use it in the lawn mower...just my opinion.
Rust is a good point and it's worth noting that all the calculations were done on jet skis which have plastic tanks, however, I believe most new vehicles including the R6 use a new anti-rusting material on the inside of tanks. But I concede, fill your tank.
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The question is not if I should use stabilizer or not. It is should I use it if I will ride it around the block at least once a week during the winter...
then you are asking whether or not you should use it... lol
put it simply, fuel stabilizer is used whenever gasoline is going to be stored for a while.
with that being said you have a ~4 gallon tank... so riding your bike 1 mile a week during the winter isnt going to consume fuel to the point that the need for stabilization isnt needed.
the next time you begin to ask yourself whether or not you have to stabilize the fuel, just ask yourself how long is it going to be stored...
just because you ride it a mile a week doesnt make all the gasoline in the tank consumed (depending on how much you had in there to begin with but you get my point). you're still storing whatever you had minus 1 mile worth of gas.
Startron shooters. $3, does your whole tank, AND treats fuel for ethanol. It's a no brainer. Fill it to the top, and let this disipate the small amount of moisture/sweat that builds up. It will also keep the ethanol fuel in our area from breaking down, or corroding shit.
It's what we use in the boats, they use and sell tons of it at the marina for the lake I live on. It's well proven, and especially awesome for us guys with carbs. Other bikes, and many carbs have rubber like tips on the float needles and the ethanol fuel just dissolves it over time. Between that, stabilizing the fuel for up to a year and treating for ethanol, it's the best $3 (each shooter $6 as shown) you can spend.