how do we know which size pulleys and belt we require when setting up our supercharged system?

so my questions is how do we measure what boost we will achieve relative to the displacement of the engine / pulley size on the supercharger twin screw roots type and crank pulley, also is there a way we can monitor and have like a fail safe measure in our tune if we over boost

While the expected boost can be calculated to some degree based on the displacement of a supercharger (assuming positive displacement) and the displacement of the engine, aspects such as the volumetric efficiency of the engine and cam profile will ultimately affect the final boost so there's some amount of trial and error involved. If you're dealing with a manufacturer or supplier of a supercharger kit for a particular engine, they will have done the development work and will be able to give you a pretty accurate idea of the boost you can expect to see.

Once you've got a particular setup operating and you know what boost you have, it's pretty easy to calculate a new pulley size to get to your desired boost pressure. For example if you have a 100mm pulley on the supercharger and you have 12 psi currently but want 16 psi, you can divide the pulley size by your target boost and then multiply by your current boost - (100/16) * 12 = 75mm. If you were to change the crank pulley size then you need to swap the calculation since we need a bigger pulley at the crank to spin the SC faster - (Crank Pulley Diameter/12) * 16 = New Crank Pulley Diameter.

I hope that helps.

that does Andre thanks but also how do know which dampener i would need use as if i have a low boost application to start to have a safe engine stock, but intend on later on fitting the engine with the necessary components to ei forged pistons /rods/ bearings and upgrade the fueling system with much larger injectors.My engines capacity at stock is only 4.5 -5 lbs of boost capable others have tried and failed by putting on the kit and they are running 6 lbs of boost and bye bye motor as the top ring groove is too high for top compression ring and it fails miserably as a result.

When you are stepping pulley sizes on positive displacement chargers you need to do the ratio of target absolute pressures (not just boost) to diameters. So you would add atmosphere to both the current and desired boost before doing the ratio to get the correct new pulley size.

@Michael, interesting point. I've used the gauge pressure calc above in 2-3 instances and have generally come out bang on my target. My thought process here is that the supercharger is working at a pressure ratio with ambient pressure at the inlet. Have you got any references to calculating pulley size based off absolute pressure ratios? I'm just interested to read more as running the calc I did above based off absolute pressure yields a massively different pulley result.

@Wilfred, give this simulator a try as it's about the best I can offer. Note that it is specific to the Eaton range of superchargers but if you know the supercharger's displacement then you should be able to match it up with some reasonable accuracy. http://autoapps.eaton.com/Simulator/Landing.aspx

Obviously depends somewhat on air temp and changes in blower VE with both speed and PR to some extent, which may make that look right for small changes but consider this case: working just on boost pressure if you nominated 0.01bar boost as a new target (or even 0.1 bar boost) from say 1 bar, you would have an enormous pulley (if starting with something in the usual 60-100mm range), your assumption would suggest it will still be a slight pressure rise above atmosphere post blower, in reality the engine will be pulling vac on the blower; the engine cycle displacement is much greater than the blower cycle displacement driven by the pulley ratio in that case.

When you initially size a blower you are using absolute displacement/VE of blower and motor. To approximate ideal generated pressures, due to blower VE and charge heating having counter effects in terms of outlet pressure/volume it gets pretty close to ideal volume/pressure.

Using current and target absolute pressure ratios for pulley sizing is the same as using the engine and blower displacement which are absolute.