Prop theory is incredibly complex - ask a helicopter pilot! The aeroplane I flew for many years, the C-130 Hercules, was initially produced with 15.5ft 3-bladed props which worked very well at high cruising speeds (the early Herks cruised at around 340kts TAS), but were crap at slow speed where you really needed to get the power working for you to get into and out of short, unprepared strips. From the C-130E (and retrofitted to earlier C-130s), the aircraft had a 13'8" four-bladed, 'paddle blade' prop that halved the take-off run. It lost 10-15kts at cruise speed, but could lift another 20,000lb (an extra 400shp per engine from the C-130K helped too!). The supersonic tip thing is managed by making the prop constant-speed, which was a technology developed before WW2. The Herk's engine/prop combination was totally constant speed, with the engine always turning at 13,800 rpm and the prop at 1021 rpm.