Is octane rating "linear?"

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Probably close but there is a non-linear effect. If you look at the effect lead had on octane, it was very non-linear. The first two grams/gallon had a big effect, the next gram less and so forth. But when tolune, alcohol and othere organics are used. it is much closer to linear.
 
The first amount of octane additive has the most effect. Subsequent additions of the same amount have less effect, and so forth.
The returns diminish.
 
The actual distillate in the base gasoline is a big determining factor of what an octane booster will do. Gasoline is a hodgepodge of distillates that a refinery throws together to make max product for the least money. As long as it meets requirements (octane, vapor pressure etc) then it is good to go.

Going back to lead, some distillates are really sensitive to lead (triptane) and show a big octane boost when lead is added. Some distillates, not so much. There was a lot of research on this during WWII by the Army Air Force to find fuels that would power their new high compression/turbo/supercharged aircraft engines.

I believe some stations now only buy regular and super, and mix them at the dispenser for mid grade product. It is close to linear, as far as octane ratings go on pump gas. When you start mixing leaded racing gas into your regular no lead fuel, then the math goes out the window. It is a huge variable there.
 
It's non-linear, but down around 90 or so, it's fairly close to being linear. But as you go higher and higher, the difference becomes more apparent.

It only takes a couple of cans of octane booster to raise 91 to 93 (for a 15-gal tank), but it'd take 15+ cans to go from 91 to 100.
 
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