The roots blower as a compressor for turbine operation requires several stages. A single stage cannot cause the correct combustor pressure. BUt simple low speed roots systems can function.
SO three roots style angled shafts can cause correct condition. A self power as a roots exhaust shaft pair would suffice. SO turbine blades are NOT demanded for flow engines.
Powering the compressor shafts by roots shaft will function.
Now the cost of manufactuer is the entire issue. How easy can roots appear? Where low air pressure conditions are not the issue, low sea level pressures and weight is not the issue a roots engine appears technologically easier to manufactuer.
Cars may operate. Now to enable easy manufactuer a single set of shafts for all four locations can be made. A single shaft at ten thousand rpm.
All cars could be roots style as an efficient alternative to turbine engine. And the low rpm advantage would be an added bonus.
So a good blower shaft design is availabe to make root engines.
It is an ingeniuos single mold design. A common foundery could make the shafts!
Douglas Eagleson Gaithersburg, MD USA