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Turbos at altitude: The Final Answer
The reason you can get a turbo to produce the same pressure regardless of
altitude (within reason, of course) is because a turbo is basically a
turbine, so turbine theory applies. It turns out that a turbine's flow
rate is roughly proportional to the *SQUARE* of its RPM. Because of this
fact, there will always be an RPM under which it flows too little, and an
RPM over which it flows too much. This is why you need a wastegate: you
want it to kick in when the turbine RPM reaches that "Too Much" regime so
that you have a constant intake pressure from then on. If you go to a
higher altitude, the "Too Much" regime is simply shifted to a higher RPM,
but since you have the Square law on your side, you can achieve the same
boost level you had at sea level.
Since a supercharger's output is simply proportional to it's RPM (not the
square of the RPM as in the case of the turbo) you don't need a wastegate.
Since you don't have the Square law on your side anymore, it's boost
pressure will always be relative to whatever the ambient pressure is.