OK, two more.
Higher octane fuel won't increase your gas mileage unless what you normally use causes knocking or pinging. The octane rating of gasoline is NOT a reference to the power it contains, but how well it can resist "detonation."
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To provide smooth power to the vehicle, the gasoline needs to expand in an exponential manner during the entire down stroke of the piston during it's power stroke.
That means the gasoline needs to burn in a controlled manner rather than exploding and delivering all of it's power in a flash.
If the engine is under a high load and the cylinder pressure increases to the point that the fuel explodes instead of burning, you have ping. That "ping" sound is that explosion of the fuel causing the piston to descend rapidly enough that the connecting rod bearing penetrates the oil barrier and makes metal-to-metal contact. "Ping!"
However, if the gasoline explodes because of the residual heat in the cylinder while being compressed, that is knock.
Both ping and knock indicate the fuel's octane rating is too low for operating conditions. The higher the compression ratio the more likely that detonation (knock or ping) is to happen.
Higher performance engines traditionally have higher compression ratios so they can get more power from the same displacement.
To prevent the gasoline from detonating (exploding) instead of burning, the octane of the blend needed is increased.
Since higher compression engines produce more power for the same displacement than low compression engines, and since higher compression ratios make detonation more likely to happen, the high output, high compression engines use high octane fuel.
Since the high output engines use high octane fuel, it has become associated in people's minds that the higher octane fuel provides more power.
This is not true. Higher octane just makes it harder for the fuel to explode instead of burn, and has NOTHING to do with how much energy there is in the fuel.
(Some modern engines that control their engine's advance with input from a "knock sensor" CAN pull slightly more power from a high octane fuel while under full load, since the controller doesn't retard the timing quite as much at maximum load. For normal driving this usually isn't noticeable, and will not increase gas mileage.)
OK, Second item.
The purpose of keeping the tank more full in winter is to reduce the amount of damp, cold air in the tank, which reduces the amount of water that condenses out of the air in the tank overnight. This reduces the water contamination of the fuel.
(A secondary reason does not apply to our cars since they are front drive. In typical rear-drive cars with gas tanks mounted in the rear, the additional weight of a nearly full tank can often increase traction in snow.)
Now I'm tired of typing, and will shut up for a while.
Tomas