Centrifugal SC Pulleys

Hello, I apologize in advance if this has already been asked before, but I've got some questions regarding pulleys for a centrifugal supercharger. My goal is to choose a combination that will get me as close to max SC RPM near the top of my engines RPM range without exceeding it. For some context, I'm looking at purchasing a Vortech V3-Si to put on my 2013 Camaro LS.

Firstly, how would I determine the correlation between a pulley's size and rpm for a given shaft diameter?

Second, how do you calculate the final drive RPM of the setup from crank to supercharger once I know the previous figures?

Third, does the diameter or placement of an idler pulley have any effect on the stated ratios? (I would not think so but I'd rather ask than be wrong.)

If anybody knows the above equations or can educate me on steps I'm missing it would be a huge help.

Also, the V3-Si's max RPM happens to be 5200. I understand that the amount of boost you end up making is affected by much more than just how fast you spin the turbo or in my case centrifugal pump, ie the amount of impedance by heat exchangers, bends in the pipe, bypass relief etc. But theoretically I'd think it's safe to say that if you want the most linear power curve possible, you'd gauge your pulleys in such a way that the supercharger (5200) reaches it's max output by the same time the engine does (let's call it 6800 RPM). Is this line of thinking correct? Would there be any reason to bring my final ratio closer to 1:1 so that the supercharger reaches max rpm lower in the power curve? I would think for safety it would be a good idea to make sure you never run it right at the absolute max at any point. Let me know what you guys think!

According to their site, https://vortechsuperchargers.com/products/v-3-si-supercharger?variant=7813348993 , the max' impeller rpm is 52 000, with a internal step-up ratio of 1:3.61, so the input shaft max'rpm would be 14 404 rpm.

With a peak rpm of 6 800, there would be a step-up ratio of ~1:2.12. Which may be rounded off to 1:2,. but direct ratios like that would normally be avoided - check out "hunting gear ratios" for the reasons.

In practice, you will probably run a lower over-drive ratio to minimise over-boosting, but that will depend on the specific requirements of your system, for example, larger engines will have a greater air demand and will reach lower boost for the same impeller speed, as will vehicles with more restrictive 'upstream' ducting, and the reverse will also apply.

As you're still to make the purchase, I'd suggest talking to Vortec and buying the kit they recommend - that will have all the mountings, belts, hoses, etc. required and their recommended drive ratio for your application. If when installed you need to fine tune it, or you rebuild the engine to accept more boost, you can just swap to another pulley, as required.