Great information here, most of the input in regards to the compromises brought about in evaluating the various ways to achieve certain performance levels is spot on.

Just my $.02, In regards to the original post about blowers, that has been covered here very well. In short, if specific RPM range with given displacement doesn’t yield the desired power level for the application, such as small displacement for size/weight/packaging reasons and spinning it faster and utilizing a PSRU to keep prop speed in check is not an option, forced induction will deliver, (forced induction can always be had with all those other enhancements for even greater gains

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For most applications/missions including aircraft service where the power plant runs under high loads for extended periods vs sprint applications, turbo charger checks most of the boxes with only a little compromise, mostly for its superior efficiency in the energy consumed to produce the added HP it delivers. Super Chargers do have the advantage of usually being easier to package. Of the 2 major types, Positive Displacement and centrifugal, the Roots or Positive displacement is great at filling the cylinders at all RPM’s but at the compromise of elevated charge temperatures for given boost level, (high charge temps are undesirable for many reasons), and required HP to deliver desired HP gain at the prop, (net power). Centrifugal has comparable air charge heating as Turbo though at the expense of requiring more input power from the crank for given level of power output at the prop vs turbo, (takes out more tax in terms of power required if same impeller/housing used. The turbo will generate more available “net” power for given boost level on same power plant). Also the centrifugal boost curve isn’t linear and that nonlinear curve is “rpm” dependent for the S/C, Turbo is exhaust flow dependent which is a byproduct of load.
As an aside, as been mentioned a few times, there is no replacement for displacement, that adage still holds true today as it did in the 60’s, especially if max RPM is limited. Power levels for a given RPM and displacement, (torque output at a given RPM when built and tuned for max output), have increased a little since the old days but not substantially. Where it has increased is due to refinement in control and delivery means of air and fuel to the chamber, chamber design, and some reductions in induced internal frictions. The big gains were seeing in today’s automotive, ATV/snowmobile, etc, power plants at the production level is enhancements in the engines ability to breathe more efficiently at higher RPM’s, the finer control over the tune, fuel delivery etc, couple that with some of the advancements in materials used for critical components and the reliability/longevity is increased.
Regardless, for all my projects the first design criteria for the power plant is always choose as much displacement as can be had for a given weight/package for the application, then power adders after that such as boost or higher RPM with regearing for the desired output, (PSRU). If boost is required I would first try to incorporate a turbo. If a Turbo can’t be made to work/fit then would I look at centrifugal S/C or possibly higher engine RPM with a PSRU.
Thank you for letting me share my $.02, really enjoy following along these types of threads, lots of good valuable insight and experience being shared in this group.