I've read a number of people say they dont bother with premium fuel because their car runs better on low octane... I'm just wondering if anyone can back this up with some reasoning.

Cheers

 

If that was true we wouldn't make any power overhere: the lowest we get is 95ron, the next being 98 and 99+.
The thruth is not lower is better for the engine, but just that higher isn't needed. In other words: why bother buying expensive (hell, what's expensive, you guys pay way less then us) fuel if cheaper will do just as good.
One execption though: high powered (high boost) turbo engines will benefit from better fuel as it will help avoiding early detonation which, esp. under boost, can be fatal for the apexseals. If you're running NA, you don't need the better fuel. But it won't harm either.

 

Ah so basically its because the compression is relatively low, theres no need.

Are there any figures/formulas that relate compression to the octane fuel used?

 

it's not the compression only: one of the main problem area's in piston engines are the valves. After a while they get covered in carbon, and they become of course very hot. The combination of these two facts makes them rather troublesome. Fuel (or better: mixture of fuel and air) tends to burn around these hot valves, esp once they aren't perfectly smooth anymore (due to carbon build up etc). The incoming mixture always has to pass these hot valves, so some will tend to ingite there. Higher compression makes this worse.
In a rotary engine, even a higher compression one, this problem does not occur. First of all, they don't have valves. Second, the hot spot of the engine (combustion chamber) is perfectly sealed from the cold (intake area) one. Whereas in a piston engine, the intake is of course right in the hot area. Therefor valves etc never really cool down.
The incoming mixture in a rotary engine will stay relatively cool (at least not hot enough for self-ignition) up to the moment where it is ready to be burned.

 

That is a rather nice feature Thanks for the info!

 

Lower octane = higher heat content = good. The rotary isn't thermally efficient, so it wants higher heat content. Back in the day, before the 7 (I think) the Mazda pits at LeMans and other endurance races smelled like Kerosene.