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What is the difference between high octane and low octane fuel? I'm not asking if one is better than the other for my vehicle, specifically, but rather what occurs differently both scientifically and mechanically when either is used?

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So-called "octane number" is a measure of how much the air-fuel mix is resistant to detonation.

The higher the "octane number" is the more resistant it is and the more is can be compressed without exploding. The higher the pressure is at the point the air-fuel mix ignites the more efficient the engine works.

Modern engines are designed for some rather high air-fuel mix pressure, if the mix ignites before that pressure is reached the engine just won't work right, because ignition will happen at the wrong moment of the engine cycle. That's why only fuel with right "octane number" should be used for any engine - depending on how that engine is designed, otherwise it just won't work right. The vehicle manual usually specifies which "octane number" is right for that vehicle engine.

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Ah, great explanation. Thank you. –  HaL May 13 '11 at 14:16
    
Just to add a tad to what's already a good and thorough answer... higher octane is more detonation resistant because it is not as easily combustible. This is why sometime people actually see drop in horsepower/mileage when they put higher octane into the car than what is recommended by the manufacturer. Sometimes when people buy a new car, they feel like they should only "put the best" in it, but in case of gasoline, spending more on gas than they have to, actually doesn't do anything and reduces performance –  DXM May 29 '11 at 9:41
    
DXM's point is sometimes true, but not for high compression engines. The 'best' fuel is the one specified in the manual. –  Rory Alsop Jul 25 '11 at 22:44
    
Too high octane fuel will waste money and reduce performance. Too low octane fuel will lead to pre-detonation which will melt expensive bits of your engine and make you cry. I've seen horrifying pictures of what happens when people double the turbo boost pressure in their engines and don't think of upping the octane rating of the fuel to compensate for the increased pressure in the cylinders. THe compression RATIO stays the same, but the VOLUME of gases per stroke increases, leading to higher pressures. –  Juann Strauss May 4 at 18:31
    
@JuannStrauss: Why would too high octane fuel reduce performance exactly? –  sharptooth May 5 at 6:31
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