Why did early US fighter planes like P-40 and P-39 have the poor performance single-stage, single speed turbo-superchargers compared to what the European fighters had and the differences in performance? The P-40 was still a tough fighter with descent performance that was kept in service and produced through the whole war, so you'd think with an upgraded turbo-supercharger it could have been even better.
This might help answer your question: http://www.enginehistory.org/Convention/2009/Presentations/SuperchargingAllison.pdf