Does my 2006 BMW 325 really need to run premium gas?

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Interesting. I looked up the compression ratio for my 20+ year old Corolla w/4AFE engine. It is spec’d at 9.5 Like I say my 40+ year old truck is 8.2 . Those were the famous smog years. Since it was carb equipped, they probably had to lower the compression ratio to meet the EPA guidelines. The 2016 Corolla engine seems to be in the 10 to 10.5 range. The Prius engine compression is 13.5? And that works fine on 87 octane? hmmm … I wonder, is that specific to the hybrid design? Or are there a lot of non-hybrid engines these days sporting 13.5 compression and running on 87 octane?

I love it ,the pat answer on the Ecoboost and supercharged trucks around here is "it does just fine on regular’'Really ? Why waste the money on a premium engine if you are too tight to fuel it correctly.Always makes me shrug ,when I notice how smug some people are ,when they act like they know more then the people that built the things

RTFM READ THE FRICKIN MANUAL please, and let us know

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There are several other factors besides compression ratio that affect the tendency of spark knock.
This paper on the Toyota 1zzfe (1998-2007 Corolla/Matrix) mentions combustion chamber design and its affect on spark knock.
They really boil down to a combination of heat, pressure and time.
Spark knock is the spontaneous combustion of unburned fuel/air in the combustion chamber.
It occurs after the spark plug has started the normal combustion process.
It’s a much faster version of the spontaneous combustion that can result from leaving oily rags piled up.
Because spark knock is affected by intake air temp it’s possible that lower than recommended octane might be OK in the winter and higher than recommended octane might be advantageous in very hot summer weather.
The Owners Manual has to make a recommendation/requirement that is a safe compromise for all conditions.