O/k, now imagine you have a roots blower, and you completely removed the outer casing, so the two rotors are just spinning around completely open in the air.
Almost no power is required to turn those rotors. Opening up an direct air path between blower discharge, and blower intake effectively does the same thing. The blower runs with almost zero back pressure, the air freely circulates, and the supercharger takes almost no power to drive.
A screw blower crushes the air between the rotors while the exhaust port is still covered. As the rotors turn further around, the exhaust port becomes uncovered, and blasts already compressed air into the outlet port. Even when running with zero back pressure at the outlet, the compressed air that explodes out of the supercharger outlet port has already been compressed internally, and that consumes some drive torque to do.
While a screw supercharger is extremely efficient when fighting against serious back pressure, it is less efficient than a roots blower when just
coasting along under zero boost conditions.
A roots blower will run almost stone cold when not doing any actual work. But it hates back pressure.
A screw blower always runs hot, even when not producing boost, and that is trying to tell you something. Compressing that air internally generates heat and it consumes power to do so.
But under boost, and working very hard, the screw blower will have a lower discharge temperature, and consume significantly less drive power than a roots blower. The higher the boost, the greater the advantage the screw blower has.
I am just saying that for very low boost applications where light throttle fuel economy is an important factor, the roots blower may still be well worth considering.
For serious high performance applications that must run fairly high boost pressure, the screw supercharger is going to be far superior to anything else.
If I was planning a supercharged street engine I would use a screw supercharger.
If I was planning to build a twincharged street car, I would most likely use a roots blower. The difference in light throttle fuel economy might be as high as 10%, and when petrol eventually hits $2.00 per litre, that may be something worth thinking about if you cover a lot of miles.
Roots lowers are quite efficient in the 5psi to 8psi range, but that is not serious performances territory. Above maybe 12Psi a roots blower is just beating the crap out of the air and adding heat. But 7psi across the supercharger may be all you need for a pretty potent 14psi twincharge.