A Roots blower is a simple device that moves air from one side to the other. The volume of the air chambers within the blower do not change as they move from one side to the other so the air is not compressed at all inside the blower. This style of pump can, therefore, be used for pumping liquids.
A screw compressor is very similar but the air chambers reduce in volume during the stroke so the air comes out compressed.
The pressure increase from a roots blower is because it is stuffing air into a volume faster than the air is being removed. So, an Eaton M45 with 0.69 litres of displacement per revolution is stuffing that amount of air into the intake plenum. If the plenum is very small, say 1.5 l, then the pressure fluctuation at each pulse of the supercharger will be high but also the rise of pressure at fast throttle openings will be fast. If the intake plenum is large, say 4 l then adding another 0.69 l of air doesn't raise the pressure as much. The larger volume plenum results in a much more steady plenum pressure with the actions of a pulsing blower and discrete intake valve opening events. Larger plenum = more "lag" but easier to tune.
If a compressed air line is connected to a large expansion chamber, held at low pressure (ie not sealed), there will be a sudden pressure drop into the chamber and yes, there will be a temperature decrease. This is certainly the case if you have a turbo or screw compressor connected to a narrow pipe, then an expansion chamber. It is not the case with a roots blower because there is no pressure at the outlet of the blower unless there is a restriction to cause that pressure. If you were to connect a roots blower to a restrictive pipe or a pipe with a restriction at the end, then discharge that into an expansion chamber, you would get a decrease in temp. That would be counter productive though because you only got the high temp/pressure due to an unnecessary restriction in the first place.
Roots blowers have moving parts in contact with air. To ensure un-lubricated parts don't wear, they don't actually touch. There is a gap between the lobes and between the lobes and the housing. This gap must be maintained under all loads and temperature (expansion) effects so it can be a reasonable clearance. These gaps allow back leakage, reducing the blower's efficiency at low revs. Performance curves are not available for AMR300 AMR500 SC12 or SC14 blowers but are available for the Eaton range. If you look at the M45 curves, you will see that there is a sweet spot on the blower curve where maximum boost for minimum heat generation occurs. At low revs the efficiency is bad (but hard to determine because of limits to published data) and at high revs efficiency is bad too but acceptable up to the max revs of the unit.
See below for 5th generation curve. This is a much more efficient charger than the ones you'd get off a MINI. The older performance curve is around but I haven't searched for it for a long time.
http://www.eaton.com/EatonCom/ProductsS ... /index.htm
Some older data here: (also see the MP45 page)
All of the above curves bottom out at 4,000 rpm charger speed, which says to me that this is the lower end of where they are designed to operate. I don't think the theory of using a big charger so it is lazily producing boost is a good one. (Could be very wrong and very happy to receive test data for actual installations)
Now an M45 has slightly twisted rotors which reduces outlet pulsing but it doesn't have any coating on the lobes. The Eaton blower range has end inlet and side dischanrge. The AMR and SC blowers do have a teflon coating and have side entry and discharge. In the absence of curves for all, it is not possible to say whether the AMR and SC range are more or less efficient than Eaton. It could well be that the teflon coated lobes allow much better low speed efficiency?
Back to the sizing. If you use an M45 with 0.69 l per rev on a 1.3l motor with peak revs of 6,500, then the charger is bigger than optimum. If you set it up to spin to max revs when the engine is at max revs, then it will be above it's allowable boost level. If you set it up to reasonable boost levels, then it speds much of it's time at below 4,000 revs where it may be very inefficient. BUT, it may well be operating at peak efficiency when the engine is at peak revs so it could be a fantastic match for a peak-power engine.
Factory installations and common kits for M45s are on 1.6 or 1.8 motors and all produce around 135-150 kW (180-200 Hp). If you are aiming for that power from a mini then it is the right choice. If you simply want a cheapish charger and accept is isn't a perfect match it is also a right choice.
I have used an M45 on a 1.8 l motor and the boost level at just off idle was great but measurably lower than at peak power. I think that on a 1.3 l motor, aiming for about 8lb of max boost, then the boost off idle may be quite poor (but I can't comfirm and would really like someone to publish results).
So if an AMR500 has similar performce to an M45 but is 0.5 l per rev instead of 0.69 l and can also be spun to 15,000 rpm then it appears to be an entirely appropriate size for a 1.3 l motor intended for about 8lb of boost and with torque not peak power as the aim so redlined at 6,500.
As stated above, an SC12 is from a 1.6l (4AGZE) making about 130kw (173 Hp). If your aim is to have a mini engine with 110Hp but lots of torque then really you only need a charger 2/3 the size of an SC12. You certainly don't need an SC14.
Personally, I'd prefer a (semi)screw compressor ( http://www.sprintex.com.au/sprintex/wp- ... eSpecs.pdf
) with substantially higher efficiency than any roots type but who has $2050 for the base charger?