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The Allison that about 4% bigger in displacement need a two stage supercharger to pick up 2,000ft of altitude??
Something was not right with the Allison two-stage supercharger if it can barely beat a single stage supercharger.
Not all superchargers were created equal.
The last sentence is very true. It is also true for Allison-made 2-stage superchargers - the 1st gen of the service-worthy types, as on the P-63A, was not as good as second version, let alone the 3rd version (the one with aux stage turning now faster, and has the carb between the stages). The 1st generation also benefitted less with ram effect (1500 ft gain in rated alt vs. 4000 ft for the engines installed on P-63C and later); ram air intake was certainly not in the best position for either engine it had. Difference in rated altitude was ~6000 ft between the engines (no ram), or 8000-8500 ft with ram.
Granted, lack of intercooler hampered the power of the engine, especially at altitude, the latest 2-stage V-1710 when operating on 3200 rpm was about the equivalent of the Merlin 61 from 1942 with regard to the altitude power. With that said, IMO, the main problem of 2-stage V-1710 was that it was perhaps 6, if not 12 months too late to matter. Add to that these engines were installed on the aircraft irellevant for ww2, to wrap up the story.
The intercooled V-1710-119, for the P-51J, was to be the best of the lot, with 1200 HP at 3200 rpm @ 30000 ft, but again it was too late.