Ok Time to put a shoe in this one.
Octane ratings come from a test rig that measures the point in a set test bed engine at which a particular fuel pre-ignites, in comparison to a standard mix of Iso-Octane and Heptane.
91 RON Fuel pre-ignites at the same point as a mix of 91% Iso-Octane and 9% heptane.
All engines from the factory are tuned initially to run on the lowest standard octane fuel available in the country of origin, be it 91 octane, 95, 98 or 2.2 . From their, specif models can be tune with different base fuels in mind, but all will have the ability to be run on the base fuel mixes, somehow. More often by reducing the amount of spark advance to limit pre-ignition.
This very often means that each cars ECU has 2 spark maps. 1 for High octane fuels, and 1 for Standard.
NO-WHERE has flame speed, or anything else been mentioned.
It is interesting to note that Ethanol and methanol share a RON rating when pure of 129, and are frequently added to fuels as an octane booster.
Changing from a 91 Octane fuel to a 98 Octane fuel can have no effect on the engine if the engine does not have a spark map to take advantage of this change.
Other additives in the fuel may affect performance. However a 91 Octane fuel with the performance additives from the very best premium fuels will perform identically to a 98 Octane fuel with the same additives - unless the ECU has the Spark Map to take advantage of it.
This spark map is commonly referred to as the Tune.
Now listen up. this is where you people go wrong.
The ENERGY VALUE of Heptane, per Kg is 44.592 Mj / Kg
The ENERGY VALUE of Iso-Octane, per Kg is 44.374 Mj / Kg
Click Here for Data
The Total maximum energy liberation in burning 1kg of 91 Octane Reference fuel is 44.57238 MJ
The Total maximum energy liberation in burning 1kg of 98 Octane Refernce fuel is 44.58764 MJ
Since the average efficiency of the combustion engine is less than 20%, the difference between the 2 is
0.003052 Mega Joules per Kg . 1 Kg = 1.34228 litres (745g / litre but varies brand and type to type).
So for every Litre you burn, you have an additional .00227374 Mega Joules of energy to play with. This is cut big time by the efficiency of the internal cimbustion engine which is less than 20%.
87 Octane Fuel has 44.4 Mj/Kg, Aviation Petrol (Not kerosene based jet fuel) has 46.8 Mj/Kg.
Picking something like 45.2 as the 91 Octane energy value, by switching to 98 from 91 octane you have about .0002515% more liberated energy to play with (.00227374 / 9.04 - which is the 20% effeciency value of my guesstimated 45.2 MJ figure).
So for all of those that travel additional miles or get better performance from 98 Ron without tuning for it ? I call scientific bullshit.
Word of warning - Theres plenty of chance there are other factors involved than just octane rating. But since this discussion was all about octane ratings to start with....