V-1710 supercharger development potential

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I think it is too bad that Allison never developed an integral 2-stage, multi-speed supercharger. But, we can't change what happened and they didn't ever develop it. They did make the Auxulliary-stage unit but it was heavy in comparions to an integral unit and too long for other than specialized uses.

They are quite interesting to see in person though, and are not difficult to overhaul, being VERY similar to a nosecase overhaul.
 
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The early example of V-1710 - the F11R, with a 2-speed S/C was the prototype featuring a 'mixed-flow' supercharger designed by TEC company, of Mr. Birmann. The S/C measured 10.25 in in diameter and was geared 8.80:1 in high speed, and made same power at 16000 ft as the other engines with same gearing at 12000 ft. It was also slightly better at altitude than V-1710s with 9.60:1 S/C gearing, but those went into production, not the F11R, that made more sense for bomber aircraft due to higher TO power.
Too bad the F11R's S/C was not geared 6.93:1 and 9.60:1, the power would've been at least on par with Merlin 20s, and much better more flexible than other 1-stage V-1710s.
With the tip speeds of the 9.6:1 9.5" impeller already pushing supersonic speeds (depending on temperature), the 10.25" impeller at 8.8:1 would be getting pretty close as well. 9.6:1 would be too high, but perhaps very slightly higher (say 8.9:1) would be possible without major losses in efficiency, but 8.8:1 really is already pretty close to the limits.

That said, assuming the figures are accurate, that engine would at least have been better than the single speed single stage models, and apparently without an increase in length (so closer to adapt to existing airframes, unlike the aux stage models). The low gear would certainly help with take-off performance and WEP at low level
 
The Merlin 20 series was turning a 10.25 in impeller at 9.49 times of crankshaft rotation speed. Max tip speed was 1273 fpm. The V-1710 with 10.25 in impeller and 9.60:1 ratio will mean tip speed by a bit over 1%, so were at under 1290 fpm. Not much of a problem, in light of what Merlin 20s accomplished at it's tip speeds?
With a rated height (in 2nd gear) being at 18500-19000 ft (for 1120 HP?), installing a water-injection system should be worth an effort?
In F, E and G series V-1710, the 8.8:1 gearing means that drive wheel has 56 teeth, and driven wheel has 15 teeth; the 9.60:1 means 56 vs. 14 teeth. In case yet another redesign of S/C drive-train is not undertaken, an 'in-between' gear ratio cannot be installed.

added: the Merlin 46 and 47 featured the impeller of 10.85 in diameter. Gearing was 9.06:1. That will mean tip speed of some 1287 fpm. Rated height was at 22000 ft, where the engine produced 1100 HP, boost +9 psig was there. Provisional chart.
Being a single speed engine tailored for high altitudes (being a 1-stage engine), the power was not that great at medium and, especially, at low heights.
 
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The engine with a 2-speed S/C having a 10.25 in impeller and 9.60:1 gearing (in 2nd gear) was intended to power cargo aircraft. 3200 rpm was allowed for take off, compression ratio was 6.50:1.
The serially produced G6 have had CR of 6:1, along with bigger engine-stage S/C impeller.

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